(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 242572, 6909]*) (*NotebookOutlinePosition[ 243530, 6941]*) (* CellTagsIndexPosition[ 243486, 6937]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Local Mate Competition (LMC). Here we are interested in the \ question: how does the number of mates affect the proportion of resources \ that should be allocated by a hermaphrodite to male and females function in \ order to maximize individual fitness? prepared by Curt Lively, Indiana University. \ \>", "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ "DEFINING THE VARIABLES...\na", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], " = allocation to male function by the ith hermaphrodite in the population. \ \na = average allocation to male function in the remaining part of the \ population, excluding our target individual\nR = Total resource base for \ reproduction\nk = the number of mates\nV = The reproductive value though male \ fuction\nW", StyleBox["m", FontVariations->{"CompatibilityType"->"Subscript"}], " = Fitness through male function\nW", StyleBox["f", FontVariations->{"CompatibilityType"->"Subscript"}], " = Fitness though female function (assuming Bateman's principle).\nW", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], " = Fitness of the ith individual (Wf + Wm)" }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[BoxData[{ \(k =. \), "\n", \(a =. \), "\n", \(ai =. \), "\n", \(R =. \), "\n", \(V =. \)}], "Input"], Cell[TextData[{ "\nFIRST WE DEFINE FITNESS THROUGH FEMALE FUNCTION, W", StyleBox["f.", FontVariations->{"CompatibilityType"->"Subscript"}], "\n" }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\" \ This will store W", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]], StyleBox["f", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1], FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[" in memory)", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Wf = R*(1 - ai)", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\((1 - ai)\)\ R\)], "Output"] }, Open ]], Cell[TextData[{ "NEXT DEFINE FITNESS THROUGH MALE FUNCTION, W", StyleBox["m. ", FontVariations->{"CompatibilityType"->"Subscript"}], StyleBox[ "V is the reproductive value of male function, which will be defined \ shortly.", FontColor->RGBColor[1, 0, 0]], "\n" }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Wm = V*R*ai", "Input", AspectRatioFixed->True], Cell[BoxData[ \(ai\ R\ V\)], "Output"] }, Open ]], Cell[TextData[ "\nNOW DEFINE THE VARIABLE, V, AS THE RATIO OF EGGS IN THE POPULATION TO \ SPERM IN THE POPULATION.\n"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["V = (k*(1 - a))/((k - 1)*a + ai)", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\(\((1 - a)\)\ k\)\/\(ai + a\ \((\(-1\) + k)\)\)\)], "Output"] }, Open ]], Cell[TextData[ "\nTOTAL FITNESS OF THE INDIVIDUAL IS THE SUM OF FITNESS THROUGH FEMALE + \ MALE FUNCTION.\n"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Wi = Wf + Wm", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\((1 - ai)\)\ R + \(\((1 - a)\)\ ai\ k\ R\)\/\(ai + a\ \((\(-1\) + \ k)\)\)\)], "Output"] }, Open ]], Cell[TextData[ "\nNOW CALCULATE THE FIRST DERIVATIVE OF INDIVIDUAL FITNESS WITH RESPECT TO \ ALLOCATION TO MALE FUNCTION.\n"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Firstder = D[Wi, ai]", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\(-R\) - \(\((1 - a)\)\ ai\ k\ R\)\/\((ai + a\ \((\(-1\) + k)\))\)\^2 + \ \(\((1 - a)\)\ k\ R\)\/\(ai + a\ \((\(-1\) + k)\)\)\)], "Output"] }, Open ]], Cell[TextData[ "\nCALCULATE THE SECOND DERIVATIVE OF INDIVIDUAL FITNESS AS A FUNCTION OF ITS \ ALLOCATION TO MALE FUNCTION. Remember, local stability requires a negative \ second derivative\n"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Secondder = D[Firstder, ai]", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\(2\ \((1 - a)\)\ ai\ k\ R\)\/\((ai + a\ \((\(-1\) + k)\))\)\^3 - \(2\ \ \((1 - a)\)\ k\ R\)\/\((ai + a\ \((\(-1\) + k)\))\)\^2\)], "Output"] }, Open ]], Cell[TextData["\nSIMPLIFY THE SECOND DERIVATIVE. "], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Simplify [Secondder]", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\(2\ \((\(-1\) + a)\)\ a\ \((\(-1\) + k)\)\ k\ R\)\/\((ai + a\ \ \((\(-1\) + k)\))\)\^3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(CSS = \[PartialD]\_\(a, ai\)Wi\)], "Input"], Cell[BoxData[ \(\(ai\ k\ R\)\/\((ai + a\ \((\(-1\) + k)\))\)\^2 - \(k\ R\)\/\(ai + a\ \ \((\(-1\) + k)\)\) + \(2\ \((1 - a)\)\ ai\ \((\(-1\) + k)\)\ k\ R\)\/\((ai + \ a\ \((\(-1\) + k)\))\)\^3 - \(\((1 - a)\)\ \((\(-1\) + k)\)\ k\ R\)\/\((ai + \ a\ \((\(-1\) + k)\))\)\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[CSS]\)], "Input"], Cell[BoxData[ \(\(-\(\(\((\(-1\) + k)\)\ k\ \((\(-ai\) + a\ \((\(-1\) + 2\ ai + k)\))\)\ R\)\/\((ai + a\ \((\(-1\) + k)\))\)\^3\)\)\)], \ "Output"] }, Open ]], Cell[TextData[{ "\nNote that the second derivative is less that zero when the numerator is \ negative, which is true whenever k > 1 AND a < 1. Hence for k > 1 (i.e., \ more than one mate) and a < 1 (i.e., less than 100% allocation to male \ function in the population), we can find a locally stable ESS by setting a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], " = a and solving for the case when the first derivative equal to zero.\n\n\ SET a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], " = a. REMEMBER WHEN THE POPULATION IS AT THE ESS, INDIVIDUAL FITNESS \ SHOULD BE MAXIMIZED AT THE ESS.\n\n" }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["\<\ ai = astar a = astar\ \>", "Input", AspectRatioFixed->True], Cell[BoxData[ \(astar\)], "Output"], Cell[BoxData[ \(astar\)], "Output"] }, Open ]], Cell[TextData[ "\nSET THE FIRST DERIVATIVE EQUAL TO ZERO AND SOLVE FOR a. \n"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Solve [Firstder == 0, astar]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{astar \[Rule] \(\(-1\) + k\)\/\(\(-1\) + 2\ k\)}}\)], "Output"] }, Open ]], Cell[TextData[{ "\nHence the allocation to male function, a, at \nthe ESS is:\n\n", StyleBox[" a = (k-1)/(2k - 1)", FontColor->RGBColor[1, 0, 0]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[StyleBox["Now set the population allocation, a, at the ESS", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]]], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["\<\ astar = (k - 1)/(2*k -1)\ \>", "Input", AspectRatioFixed->True], Cell[BoxData[ \(\(\(-1\) + k\)\/\(\(-1\) + 2\ k\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[Secondder]\)], "Input"], Cell[BoxData[ \(\(\((2 - 4\ k)\)\ R\)\/\(\((\(-1\) + k)\)\ k\)\)], "Output"] }, Open ]], Cell[TextData[StyleBox["\nNote that the second derivative is negative, so our \ solution for a* is evolutionarily stable\n", FontFamily->"Helvetica", FontWeight->"Bold"]], "Text", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[CSS]\)], "Input"], Cell[BoxData[ \(\(\((\(-3\) + 8\ k - 4\ k\^2)\)\ R\)\/\(\((\(-1\) + k)\)\ k\)\)], \ "Output"] }, Open ]], Cell[TextData[StyleBox["\nThe solution is also convergence stable. (don't \ worry if this does not make sense. I did not cover it.)\nNow let the \ individual allocation, ai, be a variable again. So (ai) is no longer equal \ to (a). The purpose is to graph individual fitness as a function of ai when \ the population is at the ESS. We would expect that Wi is maximized under \ this condition when ai converges on a.\n\nI'm also going to set the Resources \ equal to 1 unit.\n", FontFamily->"Helvetica", FontWeight->"Bold"]], "Text", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["\<\ ai = . R=1\ \>", "Input", AspectRatioFixed->True], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[TextData[StyleBox[ "\nNow, for the crux of the bisquit. Let there be two mates (k = 2).\n", FontFamily->"Helvetica", FontWeight->"Bold"]], "Text", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["k=2", "Input", AspectRatioFixed->True], Cell[BoxData[ \(2\)], "Output"] }, Open ]], Cell[TextData[ "The ESS can be found for two mates by simplifying the population allocation, \ a."], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Simplify [astar]", "Input", AspectRatioFixed->True], Cell[BoxData[ \(1\/3\)], "Output"] }, Open ]], Cell[TextData[{ "Hence, the ESS is at 0.333.\n\nNow, let's plot the relationship between \ fitness through ", StyleBox["male", FontVariations->{"Underline"->True}], " function and the allocation by the ith individual to male function." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wm}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["m", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 0.588604 [ [.21429 .00222 -9 -9 ] [.21429 .00222 9 0 ] [.40476 .00222 -9 -9 ] [.40476 .00222 9 0 ] [.59524 .00222 -9 -9 ] [.59524 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [1.025 .01472 0 -6 ] [1.025 .01472 52 6 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [.02381 .64303 -26.0625 0 ] [.02381 .64303 26.0625 12 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(0.2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(0.4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(0.6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(0.8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(1)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -10 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87.0625 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (m) show 99.125 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.125 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .09986 L .10458 .17389 L .14415 .23044 L .18221 .27595 L .22272 .31703 L .26171 .3509 L .30316 .38206 L .34309 .40824 L .3815 .4305 L .42237 .45156 L .46172 .46969 L .49955 .48542 L .53984 .5006 L .57861 .51389 L .61984 .52678 L .65954 .53814 L .69774 .54821 L .73838 .55811 L .77751 .56693 L .81909 .57562 L .85916 .5834 L .89771 .59039 L .93871 .59735 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{319, 197.188}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgooooo`03o`000?oo oooooooo00Cooooo000Jooooo`03o`000?oooooooooo0?3ooooo1?l00005ooooo`03o`000?oooooo oooo00Wooooo00Go0000ooooooooooooooooo`000003ooooo`Go00001Oooool00ol0003ooooooooo o`02ooooo`03o`000?oooooooooo00?ooooo000Jooooo`03o`000?oooooooooo0>oooooo00Co0000 oooooooooooo00001Oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00;ooooo00?o 0000ooooooooool00oooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00?ooooo00?o 0000ooooooooool00oooool001CooooolOl00008ooooo`?o00001Oooool00ol0003oooooooooo`09 ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`04 ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool00oooool001[ooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Wooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02Oooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Wooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Wooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00_ooooo00Co0000oooo oooooooo00001?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00?ooooo00?o0000 ooooooooool00oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Cooooo00?o0000 ooooooooool00oooool001[ooooo0_l0000[ooooo`03o`000?oooooooooo02_ooooo00?o0000oooo ooooool0:oooool00ol0003oooooooooo`0Zooooo`03o`000?oooooooooo02_ooooo00?o0000oooo ooooool03?ooool2o`0000Gooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`04oooo o`03o`000?oooooooooo00?o00001Oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo 00Cooooo000Jooooo`;o0000moooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Ko oooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Go oooo000Jooooo`03o`000?oooooo00000?Kooooo00?o0000ooooooooool02Oooool00ol0003ooooo ooooo`0:ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool02oooool001[ooooo00?o 0000ooooool00000oooooolSooooo`006_ooool00ol0003oooooo`00003oooooob?ooooo000Joooo o`04o`000?ooooooooooo`000?oooooo8_ooool001[ooooo00Co0000oooooooooooo0000oooooolR ooooo`006_ooool01Ol0003ooooooooooooooooo00000?oooooo8Oooool001[ooooo00Go0000oooo ooooooooooooo`00003oooooob7ooooo000Jooooo`03o`000?oooooooooo00;ooooo00?o0000oooo ooooool0oooooolNooooo`006_ooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo0?oo oooo7_ooool001[ooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`3ooooooakooooo 000Jooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0oooooolMooooo`006_ooool0 0ol0003oooooooooo`03ooooo`03o`000?oooooooooo0?oooooo7Oooool001[ooooo00?o0000oooo ooooool01?ooool00ol0003oooooooooo`3ooooooacooooo000Jooooo`03o`000?oooooooooo00Co oooo00?o0000ooooooooool0oooooolLooooo`006_ooool00ol0003oooooooooo`05ooooo`03o`00 0?oooooooooo0?oooooo6oooool001[ooooo00?o0000ooooooooool01Oooool00ol0003ooooooooo o`3ooooooa_ooooo000Jooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool0oooooolK ooooo`006_ooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo0?oooooo6_ooool001[o oooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`3ooooooa[ooooo000Jooooo`03o`00 0?oooooooooo00Oooooo00?o0000ooooooooool0oooooolIooooo`006_ooool00ol0003ooooooooo o`07ooooo`03o`000?oooooooooo0?oooooo6Oooool001[ooooo00?o0000ooooooooool02?ooool0 0ol0003oooooooooo`3ooooooaSooooo0007ooooo`;o00001?ooool01?l0003oooooooooooooool5 o`0000Cooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`3ooooooaOooooo0006oooo o`04o`000?ooooooooooo`0000Sooooo00Co0000oooooooooooo00001?ooool00ol0003ooooooooo o`09ooooo`03o`000?oooooooooo0?oooooo5oooool000Kooooo00Co0000oooooooooooo00002Ooo ool00ol0003oooooooooo`04ooooo`;o00002oooool00ol0003oooooooooo`3ooooooaKooooo0006 ooooo`04o`000?ooooooooooo`0000[ooooo00?o0000ooooooooool00oooool00ol0003ooooooooo o`0:ooooo`03o`000?oooooooooo0?oooooo5_ooool000Kooooo00Co0000oooooooooooo00001ooo ool01Ol0003ooooooooooooooooo000000Cooooo00?o0000ooooooooool02oooool00ol0003ooooo ooooo`3ooooooaGooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo00Go0000oooooooooooo ooooo`000004ooooo`03o`000?oooooooooo00cooooo00?o0000ooooooooool0oooooolDooooo`00 1oooool2o`0000Wooooo0ol00005ooooo`03o`000?oooooooooo00cooooo00?o0000ooooooooool0 oooooolDooooo`006_ooool00ol0003oooooooooo`0=ooooo`03o`000?oooooooooo0?oooooo4ooo ool001[ooooo00?o0000ooooooooool03Oooool00ol0003oooooooooo`3ooooooa?ooooo000Joooo o`03o`000?oooooooooo00kooooo00?o0000ooooooooool0oooooolBooooo`006_ooool00ol0003o ooooooooo`0?ooooo`03o`000?oooooooooo0?oooooo4Oooool001[ooooo00?o0000ooooooooool0 3oooool00ol0003oooooooooo`3ooooooa7ooooo000Jooooo`03o`000?oooooooooo013ooooo00?o 0000ooooooooool0ooooool@ooooo`006_ooool00ol0003oooooooooo`0@ooooo`03o`000?oooooo oooo0?oooooo4?ooool001[ooooo00?o0000ooooooooool04Oooool00ol0003oooooooooo`3ooooo o`oooooo000Jooooo`03o`000?oooooooooo01;ooooo00?o0000ooooooooool0ooooool>ooooo`00 6_ooool00ol0003oooooooooo`0Booooo`03o`000?oooooooooo0?oooooo3_ooool001[ooooo00?o 0000ooooooooool04oooool00ol0003oooooooooo`3oooooo`gooooo000Jooooo`03o`000?oooooo oooo01Cooooo00?o0000ooooooooool0ooooool_ooooo000Jooooo`03o`000?oooooooooo03Gooooo00?o0000ooooooooool0j_ooool0 01[ooooo00?o0000ooooooooool0=_ooool2o`000>[ooooo0007ooooo`;o00001?ooool00ol0003o ooooooooo`02ooooo`?o00001Oooool00ol0003oooooooooo`0hooooo`03o`000?oooooooooo0>Oo oooo0006ooooo`04o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`000004oooo o`03o`000?oooooooooo03Wooooo0_l0003Wooooo`001_ooool01?l0003oooooooooool00007oooo o`05o`000?ooooooooooooooool000001?ooool00ol0003oooooooooo`0kooooo`03o`000?oooooo oooo0>Cooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo1?l00005ooooo`;o0000?Oooool0 0ol0003oooooooooo`3Sooooo`001_ooool01?l0003oooooooooool00007ooooo`03o`000?oooooo oooo00Kooooo00?o0000ooooooooool0?Oooool2o`000>?ooooo0006ooooo`04o`000?oooooooooo o`0000Sooooo00?o0000ooooooooool01Oooool00ol0003oooooooooo`0oooooo`03o`000?oooooo oooo0>3ooooo0007ooooo`;o00002_ooool2o`0000Gooooo00?o0000ooooooooool0@?ooool2o`00 0>3ooooo000Jooooo`03o`000?oooooooooo04;ooooo00?o0000ooooooooool0gOooool001[ooooo 00?o0000ooooooooool0@oooool2o`000=gooooo000Jooooo`03o`000?oooooooooo04Gooooo00?o 0000ooooooooool0f_ooool001[ooooo00?o0000ooooooooool0A_ooool2o`000=[ooooo000Joooo o`03o`000?oooooooooo04Sooooo00?o0000ooooooooool0eoooool001[ooooo00?o0000oooooooo ool0BOooool2o`000=Oooooo000Jooooo`03o`000?oooooooooo04_ooooo00?o0000ooooooooool0 e?ooool001[ooooo00?o0000ooooooooool0C?ooool2o`000=Cooooo000Jooooo`03o`000?oooooo oooo04kooooo00?o0000ooooooooool0dOooool001[ooooo00?o0000ooooooooool0Coooool2o`00 0=7ooooo000Jooooo`03o`000?oooooooooo057ooooo00?o0000ooooooooool0c_ooool001[ooooo 00?o0000ooooooooool0D_ooool2o`000ooooo`?o0000 TOooool001[ooooo00?o0000ooooooooool0TOooool3o`0008kooooo000Jooooo`03o`000?oooooo oooo09Cooooo1?l0002:ooooo`006_ooool00ol0003oooooooooo`2Hooooo`Go0000QOooool001[o oooo00?o0000ooooooooool0WOooool5o`00083ooooo000Jooooo`03o`000?oooooooooo0:;ooooo 1Ol0001kooooo`006_ooool00ol0003oooooooooo`2Wooooo`Co0000Moooool001[ooooo00?o0000 ooooooooool0Zoooool5o`0007;ooooo000Jooooo`03o`000?oooooooooo0;3ooooo1?l0001^oooo o`006_ooool00ol0003oooooooooo`2dooooo`?o0000Joooool001[ooooo00?o0000ooooooooool0 ]oooool3o`0006Sooooo000Jooooo`03o`000?oooooooooo0;[ooooo1ol0001Qooooo`006_ooool0 0ol0003oooooooooo`31ooooo`Oo0000F_ooool001[ooooo00?o0000ooooooooool0b?ooool5o`00 05Gooooo000Jooooo`03o`000?oooooooooo0ooooo`03o`000?oooooooooo0?oooooo3oooool000?ooooo00?o 0000ooooool000001_ooool00ol0003oooooooooo`09ooooo`05o`000?ooooooooooooooool00000 0oooool01Ol0003oooooo`000?oooooo000000Gooooo00?o0000ooooooooool00_ooool00ol0003o ooooooooo`3oooooo`kooooo0003ooooo`03o`000?oooooo000000Gooooo00?o0000ooooooooool0 2Oooool00ol0003oooooooooo`02ooooo`09o`000?ooooooooooooooool0003oooooo`000?oooooo 000000Cooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`3oooooo`kooooo0003oooo o`03o`000?oooooo000000Gooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`02oooo o`09o`000?ooooooooooooooool0003oooooo`000?oooooo000000Cooooo00?o0000ooooooooool0 0oooool00ol0003oooooooooo`3oooooo`kooooo0002ooooo`05o`000?oooooo0000ooooool00000 0oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00?ooooo00Wo0000oooooooooooo ooooo`000?oooooo0000ooooool000000oooool00ol0003oooooooooo`04ooooo`03o`000?oooooo oooo0?oooooo3_ooool000;ooooo00Go0000ooooool0003oooooo`000003ooooo`03o`000?oooooo oooo00Wooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`02o`000003ooooool0003o oooo00?ooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`3oooooo`oooooo0002oooo o`05o`000?oooooo0000ooooool000000_ooool00ol0003oooooooooo`09ooooo`03o`000?oooooo oooo00Kooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`03ooooo`03o`000?oooooo oooo0?oooooo4?ooool000;ooooo1_l000000ooooooo0000ooooo`0:ooooo`03o`000?oooooooooo 00oooooo00?o0000ooooooooool0oooooolFooooo`00oooooom0ooooo`00oooooom0ooooo`00oooo oom0ooooo`00oooooom0ooooo`00oooooom0ooooo`00oooooom0ooooo`00oooooom0ooooo`00oooo oom0ooooo`00oooooom0ooooo`00oooooom0ooooo`00oooooom0ooooo`00oooooom0ooooo`00\ \>"], ImageRangeCache->{{{0, 318}, {196.188, 0}} -> {-0.114195, -0.161657, \ 0.00438139, 0.00708924}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "\nRight! Diminishing returns, just as expected.\n\n\nNow, let's plot the \ relationship between fitness through ", StyleBox["female", FontVariations->{"Underline"->True}], " function and the allocation by the ith individual to male function.\n" }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wf}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["f", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 0.588604 [ [.21429 .00222 -9 -9 ] [.21429 .00222 9 0 ] [.40476 .00222 -9 -9 ] [.40476 .00222 9 0 ] [.59524 .00222 -9 -9 ] [.59524 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [1.025 .01472 0 -6 ] [1.025 .01472 52 6 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [.02381 .64303 -26 0 ] [.02381 .64303 26 12 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(0.2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(0.4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(0.6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(0.8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(1)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -10 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (f) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .57944 L .10458 .5534 L .14415 .52894 L .18221 .50542 L .22272 .48039 L .26171 .45629 L .30316 .43067 L .34309 .406 L .3815 .38225 L .42237 .357 L .46172 .33268 L .49955 .30929 L .53984 .2844 L .57861 .26043 L .61984 .23495 L .65954 .21041 L .69774 .18681 L .73838 .16169 L .77751 .13751 L .81909 .11181 L .85916 .08704 L .89771 .06322 L .93871 .03788 L .97619 .01472 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{278.062, 171.875}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg?ooool2o`0000Cooooo00Co0000oooooooooooooooo1Ol0000Goooo o`;o00001?ooool00ol0003oooooooooo`03ooooo`?o00005oooool2o`0000Cooooo00?o0000oooo ooooool00_ooool3o`0001Sooooo0_l00004ooooo`03o`000?oooooooooo00;ooooo0ol0000Moooo o`?o0000?_ooool003Oooooo00Co0000oooooooooooo00002?ooool01?l0003oooooooooool0000F ooooo`04o`000?ooooooooooo`0000[ooooo00?o0000ooooooooool05Oooool01?l0003ooooooooo ool00007ooooo`05o`000?ooooooooooooooool000005_ooool01?l0003oooooooooool00007oooo o`05o`000?ooooooooooooooool000007Oooool00ol0003oooooooooo`0mooooo`00=oooool01?l0 003oooooooooool00009ooooo`03o`000?oooooooooo01Kooooo00Co0000oooooooooooo00001ooo ool5o`0001Kooooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo000001Ko oooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo000001gooooo00?o0000 ooooooooool0?Oooool003Oooooo00Co0000oooooooooooo00002_ooool00ol0003oooooooooo`0E ooooo`04o`000?ooooooooooo`0000Oooooo00Co0000oooooooooooo00005oooool01?l0003ooooo ooooool00007ooooo`Co00005oooool01?l0003oooooooooool00008ooooo`?o00007_ooool00ol0 003oooooooooo`0mooooo`00=oooool01?l0003oooooooooool00007ooooo`05o`000?oooooooooo ooooool000005_ooool01?l0003oooooooooool00008ooooo`03o`000?oooooo000001Oooooo00Co 0000oooooooooooo00001oooool00ol0003oooooooooo`0Hooooo`04o`000?ooooooooooo`0000Oo oooo00Go0000ooooooooooooooooo`00000Mooooo`03o`000?oooooooooo03gooooo000gooooo`04 o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`00000Fooooo`04o`000?oooooo ooooo`0000Wooooo0_l0000Gooooo`04o`000?ooooooooooo`0000Sooooo00?o0000ooooooooool0 5oooool01?l0003oooooooooool00007ooooo`05o`000?ooooooooooooooool000007?ooool2o`00 03oooooo000hooooo`;o00002Oooool3o`0001Sooooo0_l0000;ooooo`03o`000?oooooooooo01Ko oooo0_l0000:ooooo`;o00006?ooool2o`0000Wooooo0ol0000Nooooo`03o`000?oooooooooo02Ko oooo00?o0000ooooooooool03?ooool00ol0003oooooooooo`05ooooo`006_ooool00ol0003ooooo ooooo`3Cooooo`Go00002Oooool00ol0003oooooooooo`0>ooooo`03o`000?oooooooooo00Cooooo 000Jooooo`03o`000?oooooooooo0ooooo`006_ooool00ol0003ooooooooo o`2Xooooo`03o`000?oooooooooo04kooooo000Jooooo`03o`000?oooooooooo0:Kooooo0_l0001A ooooo`006_ooool00ol0003oooooooooo`2Uooooo`03o`000?oooooooooo057ooooo000Jooooo`03 o`000?oooooooooo0:Cooooo00?o0000ooooooooool0D_ooool001[ooooo00?o0000ooooooooool0 X_ooool2o`0005Gooooo000Jooooo`03o`000?oooooooooo0:7ooooo00?o0000ooooooooool0EOoo ool001[ooooo00?o0000ooooooooool0Woooool2o`0005Sooooo000Jooooo`03o`000?oooooooooo 09gooooo0_l0001Jooooo`006_ooool00ol0003oooooooooo`2Looooo`03o`000?oooooooooo05[o oooo000Jooooo`03o`000?oooooooooo09[ooooo0_l0001Mooooo`001oooool2o`0000Cooooo00Co 0000oooooooooooooooo1Ol00004ooooo`03o`000?oooooooooo09Sooooo0_l0001Oooooo`001_oo ool01?l0003oooooooooool00008ooooo`04o`000?ooooooooooo`0000Cooooo00?o0000oooooooo ool0U_ooool2o`00067ooooo0006ooooo`04o`000?ooooooooooo`0000Wooooo00?o0000oooooooo ool01?ooool00ol0003oooooooooo`2Eooooo`03o`000?oooooooooo067ooooo0006ooooo`04o`00 0?ooooooooooo`0000[ooooo00?o0000ooooooooool00oooool2o`0009Cooooo0_l0001Tooooo`00 1_ooool01?l0003oooooooooool00007ooooo`05o`000?ooooooooooooooool000001?ooool00ol0 003oooooooooo`2Aooooo`;o0000I_ooool000Kooooo00Co0000oooooooooooo00001oooool01Ol0 003ooooooooooooooooo000000Cooooo00?o0000ooooooooool0T?ooool00ol0003oooooooooo`1V ooooo`001oooool2o`0000Wooooo0ol00005ooooo`03o`000?oooooooooo08kooooo0_l0001Yoooo o`006_ooool00ol0003oooooooooo`2=ooooo`03o`000?oooooooooo06Wooooo000Jooooo`03o`00 0?oooooooooo08cooooo00?o0000ooooooooool0J_ooool001[ooooo00?o0000ooooooooool0R_oo ool2o`0006gooooo000Jooooo`03o`000?oooooooooo08Sooooo0_l0001_ooooo`006_ooool00ol0 003oooooooooo`26ooooo`;o0000LOooool001[ooooo00?o0000ooooooooool0QOooool00ol0003o ooooooooo`1aooooo`006_ooool00ol0003oooooooooo`23ooooo`;o0000M?ooool001[ooooo00?o 0000ooooooooool0POooool2o`0007Kooooo000Jooooo`03o`000?oooooooooo07oooooo0_l0001h ooooo`006_ooool00ol0003oooooooooo`1nooooo`03o`000?oooooooooo07Sooooo000Jooooo`03 o`000?oooooooooo07cooooo0_l0001kooooo`006_ooool00ol0003oooooooooo`1jooooo`;o0000 OOooool001[ooooo00?o0000ooooooooool0NOooool00ol0003oooooooooo`1mooooo`006_ooool0 0ol0003oooooooooo`1gooooo`;o0000P?ooool001[ooooo00?o0000ooooooooool0MOooool2o`00 08;ooooo000Jooooo`03o`000?oooooooooo07Cooooo00?o0000ooooooooool0P_ooool001[ooooo 00?o0000ooooooooool0L_ooool2o`0008Gooooo0007ooooo`;o00001?ooool00ol0003ooooooooo o`03ooooo`?o00001?ooool00ol0003oooooooooo`1aooooo`03o`000?oooooooooo08Gooooo0006 ooooo`04o`000?ooooooooooo`0000[ooooo00?o0000ooooooooool00oooool00ol0003ooooooooo o`1_ooooo`;o0000R?ooool000Kooooo00Co0000oooooooooooo00001oooool5o`0000Cooooo0_l0 001^ooooo`;o0000R_ooool000Kooooo00Co0000oooooooooooo00001oooool01?l0003ooooooooo ool00005ooooo`03o`000?oooooooooo06cooooo00?o0000ooooooooool0R_ooool000Kooooo00Co 0000oooooooooooo00002?ooool00ol0003oooooo`000005ooooo`03o`000?oooooooooo06[ooooo 0_l0002=ooooo`001_ooool01?l0003oooooooooool00009ooooo`;o00001Oooool00ol0003ooooo ooooo`1Yooooo`03o`000?oooooooooo08gooooo0007ooooo`;o00002oooool00ol0003ooooooooo o`03ooooo`03o`000?oooooooooo06Oooooo0_l0002@ooooo`006_ooool00ol0003oooooooooo`1U ooooo`;o0000T_ooool001[ooooo00?o0000ooooooooool0I?ooool00ol0003oooooooooo`2Boooo o`006_ooool00ol0003oooooooooo`1Rooooo`;o0000UOooool001[ooooo00?o0000ooooooooool0 HOooool00ol0003oooooooooo`2Eooooo`006_ooool00ol0003oooooooooo`1Oooooo`;o0000V?oo ool001[ooooo00?o0000ooooooooool0GOooool2o`0009[ooooo000Jooooo`03o`000?oooooooooo 05cooooo00?o0000ooooooooool0V_ooool001[ooooo00?o0000ooooooooool0F_ooool2o`0009go oooo000Jooooo`03o`000?oooooooooo05Wooooo00?o0000ooooooooool0WOooool001[ooooo00?o 0000ooooooooool0Eoooool2o`000:3ooooo000Jooooo`03o`000?oooooooooo05Kooooo00?o0000 ooooooooool0X?ooool001[ooooo00?o0000ooooooooool0EOooool00ol0003oooooooooo`2Qoooo o`006_ooool00ol0003oooooooooo`1Cooooo`;o0000Y?ooool001[ooooo00?o0000ooooooooool0 DOooool2o`000:Kooooo000Jooooo`03o`000?oooooooooo04oooooo0_l0002Xooooo`006_ooool0 0ol0003oooooooooo`1=ooooo`;o0000Z_ooool000Oooooo0_l00004ooooo`03o`000?oooooooooo 00;ooooo0ol00005ooooo`03o`000?oooooooooo04_ooooo0_l0002/ooooo`001_ooool01?l0003o ooooooooool00007ooooo`05o`000?ooooooooooooooool000001?ooool00ol0003oooooooooo`1: ooooo`03o`000?oooooooooo0:cooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo00Go0000 ooooooooooooooooo`000004ooooo`03o`000?oooooooooo04Sooooo0_l0002_ooooo`001_ooool0 1?l0003oooooooooool00007ooooo`Co00001Oooool2o`0004Oooooo0_l0002aooooo`001_ooool0 1?l0003oooooooooool00007ooooo`03o`000?oooooooooo00Kooooo00?o0000ooooooooool0AOoo ool00ol0003oooooooooo`2aooooo`001_ooool01?l0003oooooooooool00008ooooo`03o`000?oo oooooooo00Gooooo00?o0000ooooooooool0@oooool2o`000;Cooooo0007ooooo`;o00002_ooool2 o`0000Gooooo00?o0000ooooooooool0@_ooool00ol0003oooooooooo`2dooooo`006_ooool00ol0 003oooooooooo`10ooooo`;o0000]oooool001[ooooo00?o0000ooooooooool0?_ooool2o`000;Wo oooo000Jooooo`03o`000?oooooooooo03gooooo00?o0000ooooooooool0^Oooool001[ooooo00?o 0000ooooooooool0>oooool2o`000;cooooo000Jooooo`03o`000?oooooooooo03[ooooo00?o0000 ooooooooool0_?ooool001[ooooo00?o0000ooooooooool0>?ooool2o`000;oooooo000Jooooo`03 o`000?oooooooooo03Kooooo0_l00031ooooo`006_ooool00ol0003oooooooooo`0eooooo`03o`00 0?oooooooooo0<7ooooo000Jooooo`03o`000?oooooooooo03?ooooo0_l00034ooooo`006_ooool0 0ol0003oooooooooo`0booooo`03o`000?oooooooooo07ooooo000Jooooo`03o`000?oooooo oooo01?ooooo0_l0003Tooooo`006_ooool00ol0003oooooooooo`0Aooooo`;o0000i_ooool001[o oooo00?o0000ooooooooool04?ooool00ol0003oooooooooo`3Vooooo`006_ooool00ol0003ooooo ooooo`0>ooooo`;o0000jOooool001[ooooo00?o0000ooooooooool03?ooool2o`000>_ooooo000J ooooo`03o`000?oooooooooo00_ooooo00?o0000ooooooooool0joooool001[ooooo00?o0000oooo ooooool02Oooool2o`000>kooooo000Jooooo`03o`000?oooooooooo00Sooooo00?o0000oooooooo ool0k_ooool001[ooooo00?o0000ooooooooool01_ooool2o`000?7ooooo000Jooooo`03o`000?oo oooooooo00Gooooo00?o0000ooooooooool0lOooool001[ooooo00?o0000ooooooooool00oooool2 o`000?Cooooo000Jooooo`04o`000?ooooooooooooooo`;o0000m_ooool001;ooooo0ol00005oooo o`04o`000?ooooooooooo`000?Sooooo000Cooooo`03o`000?oooooooooo00Cooooo0ol0003ioooo o`004oooool00ol0003oooooooooo`04ooooo`;o0000n_ooool001?ooooo00?o0000ooooooooool0 1?ooool00ol0003oooooooooo`3iooooo`004oooool00ol0003oooooooooo`04ooooo`03o`000?oo oooooooo0?Wooooo000Booooo`;o00001_ooool00ol0003oooooooooo`3iooooo`004oooool00ol0 003oooooooooo`3oooooo`7ooooo003ooooooaOooooo003ooooooaOooooo003ooooooaOooooo003o oooooaOooooo003ooooooaOooooo000Nooooo`03o`000?oooooooooo00cooooo00?o0000oooooooo ool0i_ooool000oooooo1Ol00009ooooo`03o`000?oooooooooo00kooooo00?o0000ooooooooool0 iOooool000?ooooo00?o0000ooooool000001_ooool00ol0003oooooooooo`09ooooo`05o`000?oo ooooooooooooool000000oooool5o`0000Gooooo00?o0000ooooooooool00_ooool00ol0003ooooo ooooo`3Tooooo`000oooool00ol0003oooooo`000005ooooo`03o`000?oooooooooo00Wooooo00?o 0000ooooooooool00_ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Cooooo00?o 0000ooooooooool00oooool00ol0003oooooooooo`3Tooooo`000oooool00ol0003oooooo`000005 ooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`03 ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`3T ooooo`000_ooool01Ol0003oooooo`000?oooooo000000?ooooo00?o0000ooooooooool02Oooool0 0ol0003oooooooooo`03ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool00oooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo0>Cooooo0002ooooo`05o`000?oooooo0000 ooooool000000oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Cooooo00Co0000 oooooooooooooooo1?l00003ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0iOoo ool000;ooooo00Go0000ooooool0003oooooo`000002ooooo`03o`000?oooooooooo00Wooooo00?o 0000ooooooooool01_ooool01Ol0003ooooooooooooooooo000000Cooooo00?o0000ooooooooool0 0oooool00ol0003oooooooooo`3Vooooo`000_ooool6o`000003ooooool0003ooooo00[ooooo00?o 0000ooooooooool02oooool2o`0000;ooooo00?o0000ooooooooool0k?ooool00?oooooo5oooool0 0?oooooo5oooool00?oooooo5oooool00?oooooo5oooool00?oooooo5oooool00?oooooo5oooool0 0?oooooo5oooool00?oooooo5oooool00?oooooo5oooool00?oooooo5oooool00?oooooo5oooool0 0?oooooo5oooool00?oooooo5oooool00001\ \>"], ImageRangeCache->{{{0, 277.062}, {170.875, 0}} -> {-0.137312, -0.194121, \ 0.00528105, 0.00854492}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ Right! Linear increase in fitness with increasing allocation to female \ function. (This is a consequence of our assumtion that female function is \ limited only by resources.) REMEMBER: allocation to female fitness increases \ from right to left; it's equal to 1 - ai. Bueno, Now let's plot the relationship between total fitness and the \ allocation by the ith individual to male function. It should be hump shaped. \ \>", "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wi}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 -1.7511 1.76581 [ [.21429 .00222 -9 -9 ] [.21429 .00222 9 0 ] [.40476 .00222 -9 -9 ] [.40476 .00222 9 0 ] [.59524 .00222 -9 -9 ] [.59524 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [1.025 .01472 0 -6 ] [1.025 .01472 52 6 ] [.01131 .10301 -24 -4.5 ] [.01131 .10301 0 4.5 ] [.01131 .1913 -18 -4.5 ] [.01131 .1913 0 4.5 ] [.01131 .27959 -24 -4.5 ] [.01131 .27959 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .45617 -24 -4.5 ] [.01131 .45617 0 4.5 ] [.01131 .54446 -18 -4.5 ] [.01131 .54446 0 4.5 ] [.02381 .64303 -26 0 ] [.02381 .64303 26 12 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(0.2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(0.4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(0.6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(0.8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(1)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -10 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .10301 m .03006 .10301 L s [(1.05)] .01131 .10301 1 0 Mshowa .02381 .1913 m .03006 .1913 L s [(1.1)] .01131 .1913 1 0 Mshowa .02381 .27959 m .03006 .27959 L s [(1.15)] .01131 .27959 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(1.2)] .01131 .36788 1 0 Mshowa .02381 .45617 m .03006 .45617 L s [(1.25)] .01131 .45617 1 0 Mshowa .02381 .54446 m .03006 .54446 L s [(1.3)] .01131 .54446 1 0 Mshowa .125 Mabswid .02381 .03237 m .02756 .03237 L s .02381 .05003 m .02756 .05003 L s .02381 .06769 m .02756 .06769 L s .02381 .08535 m .02756 .08535 L s .02381 .12066 m .02756 .12066 L s .02381 .13832 m .02756 .13832 L s .02381 .15598 m .02756 .15598 L s .02381 .17364 m .02756 .17364 L s .02381 .20895 m .02756 .20895 L s .02381 .22661 m .02756 .22661 L s .02381 .24427 m .02756 .24427 L s .02381 .26193 m .02756 .26193 L s .02381 .29725 m .02756 .29725 L s .02381 .3149 m .02756 .3149 L s .02381 .33256 m .02756 .33256 L s .02381 .35022 m .02756 .35022 L s .02381 .38554 m .02756 .38554 L s .02381 .40319 m .02756 .40319 L s .02381 .42085 m .02756 .42085 L s .02381 .43851 m .02756 .43851 L s .02381 .47383 m .02756 .47383 L s .02381 .49148 m .02756 .49148 L s .02381 .50914 m .02756 .50914 L s .02381 .5268 m .02756 .5268 L s .02381 .56212 m .02756 .56212 L s .02381 .57978 m .02756 .57978 L s .02381 .59743 m .02756 .59743 L s .02381 .61509 m .02756 .61509 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .19853 L .10458 .34249 L .14415 .43877 L .18221 .50474 L .20178 .5305 L .22272 .55285 L .24402 .57071 L .26416 .58356 L .27386 .58847 L .28414 .59284 L .29377 .5962 L .30258 .59866 L .31199 .60069 L .31718 .60156 L .32211 .60221 L .32665 .60268 L .33086 .603 L .33329 .60313 L .33548 .60322 L .3367 .60326 L .33802 .60329 L .33927 .60331 L .34041 .60332 L .34167 .60332 L .34287 .60331 L .34394 .6033 L .34511 .60328 L .34638 .60324 L .34773 .6032 L .35015 .60309 L .35238 .60297 L .35447 .60282 L .35924 .6024 L .36442 .60181 L .36918 .60114 L .3799 .59921 L .39882 .59445 L .41952 .5874 L .46008 .56859 L .49913 .54504 L .54063 .51499 L .58061 .48183 L .61908 .44655 L .65999 .40581 L .6994 .36386 L .73728 .32127 L .77762 .27378 L .81645 .22619 L .85772 .1738 L Mistroke .89749 .12175 L .93573 .07036 L .97619 .01472 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{229.625, 141.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgGooooo003Uooooo`00iOooool00>Gooooo003Uooooo`00iOooool00>Gooooo003Uooooo`00iOoo ool00>Gooooo003Uooooo`00;oooool2o`0000Cooooo00Co0000oooooooooooooooo1Ol0000>oooo o`;o00001?ooool00ol0003oooooooooo`03ooooo`?o00003Oooool2o`0000Cooooo00?o0000oooo ooooool00_ooool3o`0000oooooo0_l00004ooooo`03o`000?oooooooooo00;ooooo0ol0000Doooo o`?o0000>oooool002kooooo00Co0000oooooooooooo00002?ooool01?l0003oooooooooool0000= ooooo`04o`000?ooooooooooo`0000[ooooo00?o0000ooooooooool02oooool01?l0003ooooooooo ool00007ooooo`05o`000?ooooooooooooooool000003Oooool01?l0003oooooooooool00007oooo o`05o`000?ooooooooooooooool000005?ooool00ol0003oooooooooo`0jooooo`00;_ooool01?l0 003oooooooooool00009ooooo`03o`000?oooooooooo00gooooo00Co0000oooooooooooo00001ooo ool5o`0000cooooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo000000go oooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo000001Cooooo00?o0000 ooooooooool0>_ooool002kooooo00Co0000oooooooooooo00002_ooool00ol0003oooooooooo`0< ooooo`04o`000?ooooooooooo`0000Oooooo00Co0000oooooooooooo00003Oooool01?l0003ooooo ooooool00007ooooo`Co00003_ooool01?l0003oooooooooool00008ooooo`?o00005Oooool00ol0 003oooooooooo`0jooooo`00;_ooool01?l0003oooooooooool00007ooooo`05o`000?oooooooooo ooooool000003Oooool01?l0003oooooooooool00008ooooo`03o`000?oooooo000000gooooo00Co 0000oooooooooooo00001oooool00ol0003oooooooooo`0?ooooo`04o`000?ooooooooooo`0000Oo oooo00Go0000ooooooooooooooooo`00000Dooooo`03o`000?oooooooooo03[ooooo000^ooooo`04 o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`00000=ooooo`04o`000?oooooo ooooo`0000Wooooo0_l0000=ooooo`04o`000?ooooooooooo`0000Sooooo00?o0000ooooooooool0 3_ooool01?l0003oooooooooool00007ooooo`05o`000?ooooooooooooooool000004oooool2o`00 03cooooo000_ooooo`;o00002Oooool3o`0000oooooo0_l0000;ooooo`03o`000?oooooooooo00co oooo0_l0000:ooooo`;o00003oooool2o`0000Wooooo0ol0000Eooooo`03o`000?oooooooooo02?o oooo00?o0000ooooooooool03?ooool00ol0003oooooooooo`05ooooo`00_oooool5o`0000Wooooo 00?o0000ooooooooool03_ooool00ol0003oooooooooo`04ooooo`006_ooool00ol0003ooooooooo o`2Fooooo`Co00001Oooool00ol0003oooooooooo`09ooooo`05o`000?ooooooooooooooool00000 0oooool5o`0000Gooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`03ooooo`006_oo ool00ol0003oooooooooo`2Eooooo`04o`000?ooooooooooo`0000Gooooo00?o0000ooooooooool0 2Oooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0 1?ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00?ooooo000FoooooiOo00001_oo ool3o`0000Gooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`02ooooo`03o`000?oo oooooooo00?ooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`03ooooo`03o`000?oo oooooooo00?ooooo000Jooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`06ooooo`04o`000?ooooooooooo`0000Cooooo00?o0000ooooooooool02Ooo ool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool00ooo ool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00?ooooo000Jooooo`03o`000?oooooo oooo08_ooooo00?o0000ooooooooool02?ooool2o`0000Gooooo00?o0000ooooooooool02Oooool0 0ol0003oooooooooo`04ooooo`03o`000?oooooooooo00?o00001Oooool00ol0003oooooooooo`03 ooooo`03o`000?oooooooooo00Cooooo000Jooooo`03o`000?oooooooooo08[ooooo00?o0000oooo ooooool03oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Kooooo00?o0000oooo ooooool01_ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Gooooo000Jooooo`;o 0000Roooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo00Wooooo00?o0000oooooooo ool02_ooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo00_ooooo000Jooooo`;o0000 R_ooool00ol0003oooooooooo`0looooo`006_ooool2o`0008Wooooo00?o0000ooooooooool0?Ooo ool001[ooooo0_l00029ooooo`03o`000?oooooooooo03gooooo000Jooooo`;o0000R?ooool00ol0 003oooooooooo`0nooooo`006_ooool00ol0003oooooo`000026ooooo`03o`000?oooooooooo03oo oooo000Jooooo`03o`000?oooooo000008Kooooo00?o0000ooooooooool0?oooool00004ooooool0 003o0000o`0000Cooooo00?o0000ooooooooool00oooool2o`0000?ooooo0ol00004ooooo`03o`00 0?oooooo000008Gooooo00?o0000ooooooooool0@?ooool000;ooooo00?o0000ooooooooool02?oo ool01_l0003oooooooooool0003oooooo`0000?ooooo00Oo0000ooooooooooooooooo`000?oooooo 000008Cooooo00?o0000ooooooooool0@Oooool000;ooooo00?o0000ooooooooool02?ooool01?l0 003oooooooooool00005ooooo`07o`000?ooooooooooooooool0003oooooo`000023ooooo`03o`00 0?oooooooooo04;ooooo0002ooooo`03o`000?oooooooooo00Sooooo00Co0000oooooooooooo0000 1Oooool01ol0003ooooooooooooooooo0000ooooool00000P_ooool00ol0003oooooooooo`13oooo o`000_ooool00ol0003oooooooooo`08ooooo`05o`000?ooooooooooo`000?ooool01?l00004oooo o`04o`000?ooooooooooo`00083ooooo00?o0000ooooooooool0A?ooool00003ooooool0003o0000 00[ooooo00Ko0000oooooooooooo0000ooooool00007ooooo`04o`000?ooooooooooo`0007oooooo 00?o0000ooooooooool0AOooool000;ooooo00?o0000ooooooooool02Oooool2o`0000;ooooo1Ol0 0003ooooo`04o`000?ooooooooooo`0007oooooo00?o0000ooooooooool0AOooool001[ooooo00Co 0000oooooooooooo0000O_ooool00ol0003oooooooooo`16ooooo`006_ooool01?l0003ooooooooo ool0001mooooo`03o`000?oooooooooo04Oooooo000Jooooo`04o`000?ooooooooooo`0007cooooo 00?o0000ooooooooool0B?ooool001[ooooo00Go0000ooooooooooooooooo`00001kooooo`03o`00 0?oooooooooo04Sooooo000Jooooo`05o`000?ooooooooooooooool00000N_ooool00ol0003ooooo ooooo`19ooooo`006_ooool01Ol0003ooooooooooooooooo000007Wooooo00?o0000ooooooooool0 B_ooool000Oooooo0ol00004ooooo`03o`000?oooooooooo00;ooooo0ol00004ooooo`05o`000?oo ooooooooooooool00000N?ooool00ol0003oooooooooo`1;ooooo`002?ooool00ol0003ooooooooo o`09ooooo`03o`000?oooooooooo00?ooooo00Go0000ooooooooooooooooo`00001hooooo`03o`00 0?oooooooooo04_ooooo0008ooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool00ooo ool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo07Cooooo00?o0000ooooooooool0C?oo ool000Sooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`03ooooo`03o`000?oooooo oooo00;ooooo00?o0000ooooooooool0Loooool00ol0003oooooooooo`1=ooooo`002?ooool00ol0 003oooooooooo`09ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool00_ooool00ol0 003oooooooooo`1booooo`03o`000?oooooooooo04kooooo0007ooooo`;o00002_ooool2o`0000Go oooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`1booooo`03o`000?oooooooooo04ko oooo0008ooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool00oooool00ol0003ooooo ooooo`02ooooo`03o`000?oooooooooo077ooooo00?o0000ooooooooool0Coooool001[ooooo00?o 0000ooooooooool00oooool00ol0003oooooooooo`1_ooooo`03o`000?oooooooooo053ooooo000J ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0K_ooool00ol0003oooooooooo`1A ooooo`006_ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo06kooooo00?o0000oooo ooooool0DOooool001[ooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`1/ooooo`03 o`000?oooooooooo05;ooooo000Jooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool0 Joooool00ol0003oooooooooo`1Cooooo`006_ooool00ol0003oooooooooo`04ooooo`03o`000?oo oooooooo06[ooooo00?o0000ooooooooool0E?ooool001[ooooo00?o0000ooooooooool01Oooool0 0ol0003oooooooooo`1Xooooo`03o`000?oooooooooo05Gooooo00001?oooooo0000o`000?l00004 ooooo`03o`000?oooooooooo00;ooooo0ol00003ooooo`?o00001?ooool00ol0003oooooooooo`05 ooooo`03o`000?oooooooooo06Oooooo00?o0000ooooooooool0E_ooool000;ooooo00?o0000oooo ooooool02Oooool01Ol0003ooooooooooooooooo000000?ooooo00Go0000ooooooooooooooooo`00 0007ooooo`03o`000?oooooooooo06Kooooo00?o0000ooooooooool0Eoooool000;ooooo00?o0000 ooooooooool02Oooool00ol0003oooooooooo`05ooooo`05o`000?ooooooooooooooool000002?oo ool00ol0003oooooooooo`1Uooooo`03o`000?oooooooooo05Oooooo0002ooooo`03o`000?oooooo oooo00Wooooo00?o0000ooooooooool01Oooool01Ol0003ooooooooooooooooo000000Sooooo00?o 0000ooooooooool0I?ooool00ol0003oooooooooo`1Hooooo`000_ooool00ol0003oooooooooo`09 ooooo`04o`000?ooooooooooooooo`Co00001?ooool00ol0003oooooooooo`06ooooo`03o`000?oo oooooooo06?ooooo00?o0000ooooooooool0FOooool00003ooooool0003o000000[ooooo0_l00003 ooooo`03o`000?oooooooooo00Gooooo00?o0000ooooooooool01oooool00ol0003oooooooooo`1Q ooooo`03o`000?oooooooooo05[ooooo0002ooooo`03o`000?oooooooooo00Wooooo00Co0000oooo oooooooooooo1Ol00003ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool0H?ooool0 0ol0003oooooooooo`1Kooooo`006_ooool00ol0003oooooooooo`07ooooo`03o`000?oooooooooo 05oooooo00?o0000ooooooooool0G?ooool001[ooooo00?o0000ooooooooool02?ooool00ol0003o ooooooooo`1Mooooo`03o`000?oooooooooo05gooooo000Jooooo`03o`000?oooooooooo00Sooooo 00?o0000ooooooooool0GOooool00ol0003oooooooooo`1Mooooo`006_ooool00ol0003ooooooooo o`08ooooo`03o`000?oooooooooo05cooooo00?o0000ooooooooool0G_ooool001[ooooo00?o0000 ooooooooool02Oooool00ol0003oooooooooo`1Jooooo`03o`000?oooooooooo05oooooo000Joooo o`03o`000?oooooooooo00Wooooo00?o0000ooooooooool0FOooool00ol0003oooooooooo`1Poooo o`001oooool3o`0000Cooooo00Co0000oooooooooooooooo1Ol00003ooooo`03o`000?oooooooooo 00Wooooo00?o0000ooooooooool0F?ooool00ol0003oooooooooo`1Qooooo`002?ooool00ol0003o ooooooooo`08ooooo`04o`000?ooooooooooo`0000?ooooo00?o0000ooooooooool02_ooool00ol0 003oooooooooo`1Fooooo`03o`000?oooooooooo06;ooooo0008ooooo`03o`000?oooooooooo00Wo oooo00?o0000ooooooooool00oooool00ol0003oooooooooo`0:ooooo`03o`000?oooooooooo05Go oooo00?o0000ooooooooool0Hoooool000Sooooo00?o0000ooooooooool02_ooool00ol0003ooooo ooooo`02ooooo`03o`000?oooooooooo00_ooooo00?o0000ooooooooool0Doooool00ol0003ooooo ooooo`1Tooooo`002?ooool00ol0003oooooooooo`07ooooo`05o`000?ooooooooooooooool00000 0oooool00ol0003oooooooooo`0;ooooo`03o`000?oooooooooo05;ooooo00?o0000ooooooooool0 IOooool000Oooooo0_l00009ooooo`05o`000?ooooooooooooooool000000oooool00ol0003ooooo ooooo`0;ooooo`03o`000?oooooooooo057ooooo00?o0000ooooooooool0I_ooool000Sooooo00?o 0000ooooooooool02?ooool3o`0000Cooooo00?o0000ooooooooool03?ooool00ol0003ooooooooo o`1?ooooo`03o`000?oooooooooo06Oooooo000Jooooo`03o`000?oooooooooo00cooooo00?o0000 ooooooooool0C_ooool00ol0003oooooooooo`1Xooooo`006_ooool00ol0003oooooooooo`0=oooo o`03o`000?oooooooooo04cooooo00?o0000ooooooooool0JOooool001[ooooo00?o0000oooooooo ool03Oooool00ol0003oooooooooo`1;ooooo`03o`000?oooooooooo06[ooooo000Jooooo`03o`00 0?oooooooooo00kooooo00?o0000ooooooooool0BOooool00ol0003oooooooooo`1[ooooo`006_oo ool00ol0003oooooooooo`0>ooooo`03o`000?oooooooooo04Sooooo00?o0000ooooooooool0K?oo ool001[ooooo00?o0000ooooooooool03_ooool00ol0003oooooooooo`17ooooo`03o`000?oooooo oooo06gooooo00001?oooooo0000o`000?l00004ooooo`04o`000?ooooooooooooooo`Go00000_oo ool3o`0000Cooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`15ooooo`03o`000?oo oooooooo06kooooo0002ooooo`03o`000?oooooooooo00Sooooo00Ko0000oooooooooooo0000oooo ool00003ooooo`05o`000?ooooooooooooooool000004Oooool00ol0003oooooooooo`13ooooo`;o 0000LOooool000;ooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`05ooooo`05o`00 0?ooooooooooooooool000004_ooool00ol0003oooooooooo`11ooooo`03o`000?oooooooooo077o oooo0002ooooo`03o`000?oooooooooo00[ooooo00?o0000ooooooooool01?ooool01Ol0003ooooo oooooooooooo000001;ooooo00?o0000ooooooooool0@?ooool00ol0003oooooooooo`1booooo`00 0_ooool00ol0003oooooooooo`07ooooo`06o`000?ooooooooooooooool0003ooooo1?l00004oooo o`03o`000?oooooooooo017ooooo00?o0000ooooooooool0?_ooool00ol0003oooooooooo`1coooo o`0000?oooooo`000?l000002Oooool01ol0003ooooooooooooooooo0000ooooool000001oooool0 0ol0003oooooooooo`0Aooooo`03o`000?oooooooooo03gooooo00?o0000ooooooooool0M?ooool0 00;ooooo00?o0000ooooooooool02?ooool3o`0000;ooooo1Ol00003ooooo`03o`000?oooooooooo 01;ooooo00?o0000ooooooooool0>_ooool2o`0007Oooooo000Jooooo`03o`000?oooooooooo01;o oooo00?o0000ooooooooool0>Oooool00ol0003oooooooooo`1gooooo`006_ooool00ol0003ooooo ooooo`0Cooooo`03o`000?oooooooooo03Oooooo00?o0000ooooooooool0N?ooool001[ooooo00?o 0000ooooooooool04oooool00ol0003oooooooooo`0fooooo`03o`000?oooooooooo07Wooooo000J ooooo`03o`000?oooooooooo01Cooooo00?o0000ooooooooool0=?ooool00ol0003oooooooooo`1j ooooo`006_ooool00ol0003oooooooooo`0Dooooo`03o`000?oooooooooo03;ooooo0_l0001moooo o`006_ooool00ol0003oooooooooo`0Eooooo`03o`000?oooooooooo033ooooo00?o0000oooooooo ool0OOooool000Oooooo0ol00004ooooo`03o`000?oooooooooo00;ooooo0ol00004ooooo`03o`00 0?oooooooooo01Kooooo00?o0000ooooooooool0;_ooool00ol0003oooooooooo`1nooooo`002?oo ool00ol0003oooooooooo`07ooooo`05o`000?ooooooooooooooool000000oooool00ol0003ooooo ooooo`0Gooooo`03o`000?oooooooooo02cooooo00?o0000ooooooooool0Ooooool000Sooooo00?o 0000ooooooooool02oooool01Ol0003ooooooooooooooooo000001[ooooo00?o0000ooooooooool0 :_ooool00ol0003oooooooooo`20ooooo`002?ooool00ol0003oooooooooo`09ooooo`;o00001?oo ool00ol0003oooooooooo`0Iooooo`03o`000?oooooooooo02Oooooo0_l00023ooooo`002?ooool0 0ol0003oooooooooo`0;ooooo`05o`000?ooooooooooooooool000007?ooool2o`0002Kooooo00?o 0000ooooooooool0Poooool000Oooooo0_l00009ooooo`05o`000?ooooooooooooooool000000ooo ool00ol0003oooooooooo`0Looooo`03o`000?oooooooooo027ooooo0_l00026ooooo`002?ooool0 0ol0003oooooooooo`08ooooo`?o00001?ooool00ol0003oooooooooo`0Mooooo`03o`000?oooooo oooo01oooooo00?o0000ooooooooool0Q_ooool001[ooooo00?o0000ooooooooool07_ooool2o`00 01gooooo0_l00029ooooo`006_ooool00ol0003oooooooooo`0Pooooo`03o`000?oooooooooo01Oo oooo0ol0002;ooooo`006_ooool00ol0003oooooooooo`0Qooooo`03o`000?oooooooooo01?ooooo 0ol0002>ooooo`006_ooool00ol0003oooooooooo`0Rooooo`?o00003oooool3o`00097ooooo000J ooooo`03o`000?oooooooooo02Gooooo1Ol00006ooooo`Co0000U?ooool001[ooooo00?o0000oooo ooooool0:Oooool8o`0009Oooooo000Jooooo`03o`000?oooooooooo0Gooooo003Uooooo`00iOooool001kooooo00?o 0000ooooooooool03?ooool00ol0003oooooooooo`2eooooo`003oooool5o`0000Wooooo00?o0000 ooooooooool03_ooool00ol0003oooooooooo`2dooooo`000oooool00ol0003oooooo`000006oooo o`03o`000?oooooooooo00Wooooo00Go0000ooooooooooooooooo`000003ooooo`Go00001Oooool0 0ol0003oooooooooo`02ooooo`03o`000?oooooooooo0;?ooooo0003ooooo`03o`000?oooooo0000 00Gooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo 00?ooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo 0;?ooooo0003ooooo`03o`000?oooooo000000Gooooo00?o0000ooooooooool02Oooool00ol0003o ooooooooo`02ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool01?ooool00ol0003o ooooooooo`03ooooo`03o`000?oooooooooo0;?ooooo0002ooooo`05o`000?oooooo0000ooooool0 00000oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00?ooooo00?o0000oooooooo ool00oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Cooooo00?o0000oooooooo ool0/oooool000;ooooo00Go0000ooooool0003oooooo`000003ooooo`03o`000?oooooooooo00Wo oooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`03o`0000Gooooo00?o0000oooooooo ool00oooool00ol0003oooooooooo`2dooooo`000_ooool01Ol0003oooooo`000?oooooo000000;o oooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Ko oooo00?o0000ooooooooool00oooool00ol0003oooooooooo`2eooooo`000_ooool6o`000003oooo ool0003ooooo00[ooooo00?o0000ooooooooool02_ooool00ol0003oooooooooo`02ooooo`03o`00 0?oooooooooo0;_ooooo003Uooooo`00iOooool00>Gooooo003Uooooo`00iOooool00>Gooooo003U ooooo`00iOooool00>Gooooo003Uooooo`00iOooool00>Gooooo003Uooooo`00\ \>"], ImageRangeCache->{{{0, 228.625}, {140.938, 0}} -> {-0.181467, 0.91476, \ 0.00697932, 0.00376426}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "Note that individual fitness, Wi, is maximal when a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], " = a = 0.33. That is when the individual allocation is at the ESS.\n\n\n\n\ Now let's let the local mating population be large, say 100 mates." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["k=100", "Input", AspectRatioFixed->True], Cell[BoxData[ \(100\)], "Output"] }, Open ]], Cell[TextData[ "The new ESS for 100 mates is found by simplifying the parameter, a."], "Text",\ Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Simplify [a]", "Input", AspectRatioFixed->True], Cell[BoxData[ \(99\/199\)], "Output"] }, Open ]], Cell[TextData[{ "\nHence, the ESS is at 99/199, which is about 1/2.\n\nNow, as previously, \ let's first plot the relationship between fitness through ", StyleBox["male", FontVariations->{"Underline"->True}], " function and the allocation by the ith individual to male function." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wm}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["m", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 0.588604 [ [.21429 .00222 -9 -9 ] [.21429 .00222 9 0 ] [.40476 .00222 -9 -9 ] [.40476 .00222 9 0 ] [.59524 .00222 -9 -9 ] [.59524 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [1.025 .01472 0 -6 ] [1.025 .01472 52 6 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [.02381 .64303 -26.0625 0 ] [.02381 .64303 26.0625 12 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(0.2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(0.4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(0.6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(0.8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(1)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -10 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87.0625 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (m) show 99.125 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.125 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .03906 L .10458 .06556 L .14415 .09041 L .18221 .11426 L .22272 .13961 L .26171 .16397 L .30316 .18982 L .34309 .21468 L .3815 .23856 L .42237 .26392 L .46172 .2883 L .49955 .3117 L .53984 .33657 L .57861 .36047 L .61984 .38584 L .65954 .41024 L .69774 .43366 L .73838 .45855 L .77751 .48247 L .81909 .50785 L .85916 .53226 L .89771 .5557 L .93871 .5806 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{315.562, 195.062}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgooooo`03o`000?oo oooooooo00Cooooo000Jooooo`03o`000?oooooooooo0>cooooo1?l00005ooooo`03o`000?oooooo oooo00Wooooo00Go0000ooooooooooooooooo`000003ooooo`Go00001Oooool00ol0003ooooooooo o`02ooooo`03o`000?oooooooooo00?ooooo000Jooooo`03o`000?oooooooooo0>_ooooo00Co0000 oooooooooooo00001Oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00;ooooo00?o 0000ooooooooool00oooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00?ooooo00?o 0000ooooooooool00oooool001CoooookOl00008ooooo`?o00001Oooool00ol0003oooooooooo`09 ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`04 ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool00oooool001[ooooo00?o0000oooo ool000002?ooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02Oooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Wooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02Oooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool02?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00[ooooo00Co0000oooo oooooooo00001?ooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00?ooooo00?o0000 ooooooooool00oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Cooooo00?o0000 ooooooooool00oooool001[ooooo00?o0000ooooooooool00_l0000Xooooo`03o`000?oooooooooo 02[ooooo00?o0000ooooooooool0:_ooool00ol0003oooooooooo`0Zooooo`03o`000?oooooooooo 02[ooooo00?o0000ooooooooool02oooool2o`0000Gooooo00?o0000ooooooooool02Oooool00ol0 003oooooooooo`04ooooo`03o`000?oooooooooo00?o00001Oooool00ol0003oooooooooo`03oooo o`03o`000?oooooooooo00Cooooo000Jooooo`03o`000?oooooooooo00;ooooo00?o0000oooooooo ool0kOooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00Kooooo00?o0000oooooooo ool01_ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Gooooo000Jooooo`03o`00 0?oooooooooo00?ooooo0_l0003]ooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool0 2_ooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo00_ooooo000Jooooo`03o`000?oo oooooooo00Gooooo00?o0000ooooooooool0oooooolGooooo`006_ooool00ol0003oooooooooo`06 ooooo`;o0000oooooolGooooo`006_ooool00ol0003oooooooooo`08ooooo`;o0000oooooolEoooo o`006_ooool00ol0003oooooooooo`0:ooooo`03o`000?oooooooooo0?oooooo4_ooool001[ooooo 00?o0000ooooooooool02oooool2o`000?oooooo4_ooool001[ooooo00?o0000ooooooooool03Ooo ool2o`000?oooooo4?ooool001[ooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`3o ooooo`gooooo000Jooooo`03o`000?oooooooooo013ooooo0_l0003oooooo`gooooo000Jooooo`03 o`000?oooooooooo01;ooooo00?o0000ooooooooool0ooooool:ooooo`006_ooool00ol0003ooooo ooooo`0Cooooo`;o0000ooooool:ooooo`006_ooool00ol0003oooooooooo`0Eooooo`03o`000?oo oooooooo0?oooooo1oooool001[ooooo00?o0000ooooooooool05_ooool2o`000?oooooo1oooool0 01[ooooo00?o0000ooooooooool06?ooool00ol0003oooooooooo`3oooooo`Cooooo000Jooooo`03 o`000?oooooooooo01Wooooo0_l0003oooooo`Cooooo000Jooooo`03o`000?oooooooooo01_ooooo 00?o0000ooooooooool0ooooool1ooooo`006_ooool00ol0003oooooooooo`0Looooo`;o0000oooo ool1ooooo`006_ooool00ol0003oooooooooo`0Nooooo`03o`000?oooooooooo0?gooooo000Joooo o`03o`000?oooooooooo01oooooo0_l0003mooooo`006_ooool00ol0003oooooooooo`0Qooooo`03 o`000?oooooooooo0?[ooooo000Jooooo`03o`000?oooooooooo02;ooooo0_l0003jooooo`006_oo ool00ol0003oooooooooo`0Tooooo`;o0000n?ooool000Oooooo0_l00004ooooo`04o`000?oooooo ooooooooo`Go00001?ooool00ol0003oooooooooo`0Vooooo`03o`000?oooooooooo0?Gooooo0006 ooooo`04o`000?ooooooooooo`0000Sooooo00Co0000oooooooooooo00001?ooool00ol0003ooooo ooooo`0Wooooo`;o0000mOooool000Kooooo00Co0000oooooooooooo00002Oooool00ol0003ooooo ooooo`04ooooo`;o0000:_ooool2o`000??ooooo0006ooooo`04o`000?ooooooooooo`0000[ooooo 00?o0000ooooooooool00oooool00ol0003oooooooooo`0[ooooo`03o`000?oooooooooo0?3ooooo 0006ooooo`04o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`000004ooooo`03 o`000?oooooooooo02cooooo0_l0003`ooooo`001_ooool01?l0003oooooooooool00007ooooo`05 o`000?ooooooooooooooool000001?ooool00ol0003oooooooooo`0^ooooo`;o0000k_ooool000Oo oooo0_l00009ooooo`?o00001Oooool00ol0003oooooooooo`0`ooooo`;o0000k?ooool001[ooooo 00?o0000ooooooooool0<_ooool00ol0003oooooooooo`3Yooooo`006_ooool00ol0003ooooooooo o`0cooooo`;o0000jOooool001[ooooo00?o0000ooooooooool0=Oooool2o`000>Oooooo000Joooo o`03o`000?oooooooooo03Oooooo00?o0000ooooooooool0i?ooool001[ooooo00?o0000oooooooo ool0>?ooool2o`000>Cooooo000Jooooo`03o`000?oooooooooo03[ooooo00?o0000ooooooooool0 hOooool001[ooooo00?o0000ooooooooool0>oooool00ol0003oooooooooo`3Pooooo`006_ooool0 0ol0003oooooooooo`0looooo`;o0000h?ooool001[ooooo00?o0000ooooooooool0?_ooool00ol0 003oooooooooo`3Mooooo`006_ooool00ol0003oooooooooo`0oooooo`;o0000gOooool001[ooooo 00?o0000ooooooooool0@Oooool2o`000=_ooooo000Jooooo`03o`000?oooooooooo04?ooooo0_l0 003Iooooo`006_ooool00ol0003oooooooooo`15ooooo`03o`000?oooooooooo0=Kooooo000Joooo o`03o`000?oooooooooo04Kooooo0_l0003Fooooo`006_ooool00ol0003oooooooooo`18ooooo`;o 0000e?ooool001[ooooo00?o0000ooooooooool0B_ooool00ol0003oooooooooo`3Aooooo`006_oo ool00ol0003oooooooooo`1;ooooo`;o0000dOooool001[ooooo00?o0000ooooooooool0COooool0 0ol0003oooooooooo`3>ooooo`006_ooool00ol0003oooooooooo`1>ooooo`;o0000c_ooool001[o oooo00?o0000ooooooooool0D?ooool00ol0003oooooooooo`3;ooooo`001oooool2o`0000Cooooo 00?o0000ooooooooool00oooool3o`0000Cooooo00?o0000ooooooooool0DOooool2o`000<_ooooo 0006ooooo`04o`000?ooooooooooo`0000[ooooo00?o0000ooooooooool00oooool00ol0003ooooo ooooo`1Cooooo`;o0000bOooool000Kooooo00Co0000oooooooooooo00001oooool5o`0000Cooooo 00?o0000ooooooooool0EOooool00ol0003oooooooooo`36ooooo`001_ooool01?l0003ooooooooo ool00007ooooo`04o`000?ooooooooooo`0000Gooooo0_l0001Gooooo`;o0000a_ooool000Kooooo 00Co0000oooooooooooo00002?ooool00ol0003oooooo`000005ooooo`03o`000?oooooooooo05So oooo0_l00034ooooo`001_ooool01?l0003oooooooooool00009ooooo`;o00001Oooool00ol0003o ooooooooo`1Jooooo`03o`000?oooooooooo0<7ooooo0007ooooo`;o00002oooool00ol0003ooooo ooooo`03ooooo`03o`000?oooooooooo05_ooooo0_l00031ooooo`006_ooool00ol0003ooooooooo o`1Mooooo`03o`000?oooooooooo0;kooooo000Jooooo`03o`000?oooooooooo05kooooo0_l0002n ooooo`006_ooool00ol0003oooooooooo`1Pooooo`03o`000?oooooooooo0;_ooooo000Jooooo`03 o`000?oooooooooo067ooooo0_l0002kooooo`006_ooool00ol0003oooooooooo`1Sooooo`03o`00 0?oooooooooo0;Sooooo000Jooooo`03o`000?oooooooooo06Cooooo0_l0002hooooo`006_ooool0 0ol0003oooooooooo`1Vooooo`;o0000]_ooool001[ooooo00?o0000ooooooooool0J?ooool2o`00 0;Cooooo000Jooooo`03o`000?oooooooooo06[ooooo00?o0000ooooooooool0/Oooool001[ooooo 00?o0000ooooooooool0Joooool2o`000;7ooooo000Jooooo`03o`000?oooooooooo06gooooo0_l0 002_ooooo`006_ooool00ol0003oooooooooo`1_ooooo`03o`000?oooooooooo0:cooooo000Joooo o`03o`000?oooooooooo073ooooo0_l0002/ooooo`006_ooool00ol0003oooooooooo`1booooo`03 o`000?oooooooooo0:Wooooo000Jooooo`03o`000?oooooooooo07?ooooo0_l0002Yooooo`006_oo ool00ol0003oooooooooo`1eooooo`03o`000?oooooooooo0:Kooooo000Jooooo`03o`000?oooooo oooo07Kooooo0_l0002Vooooo`006_ooool00ol0003oooooooooo`1hooooo`;o0000Y?ooool001[o oooo00?o0000ooooooooool0N_ooool00ol0003oooooooooo`2Qooooo`006_ooool00ol0003ooooo ooooo`1kooooo`;o0000XOooool001[ooooo00?o0000ooooooooool0OOooool2o`0009oooooo0007 ooooo`;o00001?ooool00ol0003oooooooooo`02ooooo`?o00001Oooool00ol0003oooooooooo`1o ooooo`03o`000?oooooooooo09cooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo00Go0000 ooooooooooooooooo`000004ooooo`03o`000?oooooooooo083ooooo0_l0002Looooo`001_ooool0 1?l0003oooooooooool00007ooooo`05o`000?ooooooooooooooool000001?ooool00ol0003ooooo ooooo`22ooooo`03o`000?oooooooooo09Wooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo 1?l00005ooooo`;o0000Q?ooool2o`0009Wooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`25ooooo`03o`000?oooooooooo09Kooooo 0006ooooo`04o`000?ooooooooooo`0000Sooooo00?o0000ooooooooool01Oooool00ol0003ooooo ooooo`26ooooo`;o0000U_ooool000Oooooo0_l0000:ooooo`;o00001Oooool00ol0003ooooooooo o`28ooooo`03o`000?oooooooooo09?ooooo000Jooooo`03o`000?oooooooooo08Wooooo0_l0002C ooooo`006_ooool00ol0003oooooooooo`2;ooooo`;o0000TOooool001[ooooo00?o0000oooooooo ool0SOooool00ol0003oooooooooo`2>ooooo`006_ooool00ol0003oooooooooo`2>ooooo`;o0000 S_ooool001[ooooo00?o0000ooooooooool0T?ooool2o`0008cooooo000Jooooo`03o`000?oooooo oooo09;ooooo00?o0000ooooooooool0ROooool001[ooooo00?o0000ooooooooool0Toooool2o`00 08Wooooo000Jooooo`03o`000?oooooooooo09Gooooo0_l00027ooooo`006_ooool00ol0003ooooo ooooo`2Gooooo`;o0000QOooool001[ooooo00?o0000ooooooooool0VOooool00ol0003ooooooooo o`22ooooo`006_ooool00ol0003oooooooooo`2Jooooo`;o0000P_ooool001[ooooo00?o0000oooo ooooool0W?ooool2o`00083ooooo000Jooooo`03o`000?oooooooooo09kooooo00?o0000oooooooo ool0OOooool001[ooooo00?o0000ooooooooool0Woooool2o`0007gooooo000Jooooo`03o`000?oo oooooooo0:7ooooo00?o0000ooooooooool0N_ooool001[ooooo00?o0000ooooooooool0X_ooool2 o`0007[ooooo000Jooooo`03o`000?oooooooooo0:Cooooo00?o0000ooooooooool0Moooool001[o oooo00?o0000ooooooooool0YOooool2o`0007Oooooo000Jooooo`03o`000?oooooooooo0:Oooooo 0_l0001eooooo`006_ooool00ol0003oooooooooo`2Yooooo`03o`000?oooooooooo07;ooooo000J ooooo`03o`000?oooooooooo0:[ooooo0_l0001booooo`001oooool2o`0000Cooooo00?o0000oooo ooooool00_ooool3o`0000Gooooo00?o0000ooooooooool0[?ooool2o`00073ooooo0006ooooo`04 o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`000004ooooo`03o`000?oooooo oooo0:kooooo00?o0000ooooooooool0KOooool000Kooooo00Co0000oooooooooooo00001oooool0 1Ol0003ooooooooooooooooo000000Cooooo0_l0002`ooooo`;o0000KOooool000Kooooo00Co0000 oooooooooooo00002?ooool3o`0000Gooooo00?o0000ooooooooool0/Oooool00ol0003ooooooooo o`1Zooooo`001_ooool01?l0003oooooooooool00007ooooo`05o`000?ooooooooooooooool00000 1?ooool00ol0003oooooooooo`2booooo`;o0000J_ooool000Kooooo00Co0000oooooooooooo0000 1oooool01Ol0003ooooooooooooooooo000000Cooooo00?o0000ooooooooool0]?ooool00ol0003o ooooooooo`1Wooooo`001oooool2o`0000Wooooo0ol00005ooooo`03o`000?oooooooooo0;Gooooo 0_l0001Wooooo`006_ooool00ol0003oooooooooo`2gooooo`03o`000?oooooooooo06Cooooo000J ooooo`03o`000?oooooooooo0;Sooooo0_l0001Tooooo`006_ooool00ol0003oooooooooo`2joooo o`;o0000H_ooool001[ooooo00?o0000ooooooooool0_?ooool2o`00063ooooo000Jooooo`03o`00 0?oooooooooo0;kooooo0_l0001Nooooo`006_ooool00ol0003oooooooooo`30ooooo`;o0000G?oo ool001[ooooo00?o0000ooooooooool0`_ooool2o`0005[ooooo000Jooooo`03o`000?oooooooooo 0"], ImageRangeCache->{{{0, 314.562}, {194.062, 0}} -> {-0.115854, -0.163968, \ 0.00444507, 0.00719228}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "\nYes indeed. Virtually linear gains through male function when the local \ mating population is large.\n\nNow, let's plot the relationship between \ fitness through ", StyleBox["female", FontVariations->{"Underline"->True}], " function and the allocation by the ith indiviudal to male function." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wf}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["f", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 0.588604 [ [.21429 .00222 -9 -9 ] [.21429 .00222 9 0 ] [.40476 .00222 -9 -9 ] [.40476 .00222 9 0 ] [.59524 .00222 -9 -9 ] [.59524 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [1.025 .01472 0 -6 ] [1.025 .01472 52 6 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [.02381 .64303 -26 0 ] [.02381 .64303 26 12 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(0.2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(0.4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(0.6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(0.8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(1)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -10 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (f) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .57944 L .10458 .5534 L .14415 .52894 L .18221 .50542 L .22272 .48039 L .26171 .45629 L .30316 .43067 L .34309 .406 L .3815 .38225 L .42237 .357 L .46172 .33268 L .49955 .30929 L .53984 .2844 L .57861 .26043 L .61984 .23495 L .65954 .21041 L .69774 .18681 L .73838 .16169 L .77751 .13751 L .81909 .11181 L .85916 .08704 L .89771 .06322 L .93871 .03788 L .97619 .01472 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{292.625, 180.875}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgoooool2o`0000Cooooo00Co0000oooooooooooooooo1Ol0000Joooo o`;o00001?ooool00ol0003oooooooooo`03ooooo`?o00006Oooool2o`0000Cooooo00?o0000oooo ooooool00_ooool3o`0001_ooooo0_l00004ooooo`03o`000?oooooooooo00;ooooo0ol0000Poooo o`?o0000?_ooool003[ooooo00Co0000oooooooooooo00002?ooool01?l0003oooooooooool0000I ooooo`04o`000?ooooooooooo`0000[ooooo00?o0000ooooooooool05oooool01?l0003ooooooooo ool00007ooooo`05o`000?ooooooooooooooool000006Oooool01?l0003oooooooooool00007oooo o`05o`000?ooooooooooooooool000008?ooool00ol0003oooooooooo`0mooooo`00>_ooool01?l0 003oooooooooool00009ooooo`03o`000?oooooooooo01Wooooo00Co0000oooooooooooo00001ooo ool5o`0001Sooooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo000001Wo oooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo0000023ooooo00?o0000 ooooooooool0?Oooool003[ooooo00Co0000oooooooooooo00002_ooool00ol0003oooooooooo`0H ooooo`04o`000?ooooooooooo`0000Oooooo00Co0000oooooooooooo00006Oooool01?l0003ooooo ooooool00007ooooo`Co00006_ooool01?l0003oooooooooool00008ooooo`?o00008Oooool00ol0 003oooooooooo`0mooooo`00>_ooool01?l0003oooooooooool00007ooooo`05o`000?oooooooooo ooooool000006Oooool01?l0003oooooooooool00008ooooo`03o`000?oooooo000001Wooooo00Co 0000oooooooooooo00001oooool00ol0003oooooooooo`0Kooooo`04o`000?ooooooooooo`0000Oo oooo00Go0000ooooooooooooooooo`00000Pooooo`03o`000?oooooooooo03gooooo000jooooo`04 o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`00000Iooooo`04o`000?oooooo ooooo`0000Wooooo0_l0000Iooooo`04o`000?ooooooooooo`0000Sooooo00?o0000ooooooooool0 6_ooool01?l0003oooooooooool00007ooooo`05o`000?ooooooooooooooool000007oooool2o`00 03oooooo000kooooo`;o00002Oooool3o`0001_ooooo0_l0000;ooooo`03o`000?oooooooooo01So oooo0_l0000:ooooo`;o00006oooool2o`0000Wooooo0ol0000Qooooo`03o`000?oooooooooo02Ko oooo00?o0000ooooooooool03?ooool00ol0003oooooooooo`05ooooo`006_ooool00ol0003ooooo ooooo`3Qooooo`Go00002Oooool00ol0003oooooooooo`0>ooooo`03o`000?oooooooooo00Cooooo 000Jooooo`03o`000?oooooooooo0=Gooooo1?l00005ooooo`03o`000?oooooooooo00Wooooo00Go 0000ooooooooooooooooo`000003ooooo`Go00001Oooool00ol0003oooooooooo`02ooooo`03o`00 0?oooooooooo00?ooooo000Jooooo`03o`000?oooooooooo0=Cooooo00Co0000oooooooooooo0000 1Oooool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool0 0oooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0 0oooool001Coooooeol00007ooooo`?o00001Oooool00ol0003oooooooooo`09ooooo`03o`000?oo oooooooo00;ooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`04ooooo`03o`000?oo oooooooo00?ooooo00?o0000ooooooooool00oooool001[ooooo00?o0000ooooooooool01oooool0 0ol0003oooooooooo`07ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool01oooool0 0ol0003oooooooooo`07ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool02?ooool0 0ol0003oooooooooo`07ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool01oooool0 0ol0003oooooooooo`07ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool02?ooool0 0ol0003oooooooooo`07ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool01oooool0 0ol0003oooooooooo`07ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool02?ooool0 0ol0003oooooooooo`05ooooo`03o`000?oooooo000000_ooooo00Co0000oooooooooooo00001?oo ool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool00ooo ool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool00ooo ool001[ooooo00?o0000ooooooooool09Oooool00ol0003oooooooooo`0Vooooo`03o`000?oooooo oooo02Gooooo00?o0000ooooooooool09_ooool00ol0003oooooooooo`0Rooooo`;o00000_ooool0 0ol0003oooooooooo`0:ooooo`;o00001Oooool00ol0003oooooooooo`09ooooo`03o`000?oooooo oooo00Cooooo00?o0000ooooooooool00ol00005ooooo`03o`000?oooooooooo00?ooooo00?o0000 ooooooooool01?ooool001[ooooo00?o0000ooooooooool0`_ooool2o`0001Oooooo00?o0000oooo ooooool02Oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo00?o0000oooo ooooool00oooool00ol0003oooooooooo`05ooooo`006_ooool00ol0003oooooooooo`31ooooo`03 o`000?oooooooooo01Oooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`0:ooooo`03 o`000?oooooooooo00;ooooo00?o0000ooooooooool02oooool001[ooooo00?o0000ooooooooool0 _oooool2o`0004Kooooo000Jooooo`03o`000?oooooooooo0;kooooo00?o0000ooooooooool0A_oo ool001[ooooo00?o0000ooooooooool0_?ooool2o`0004Wooooo000Jooooo`03o`000?oooooooooo 0;_ooooo00?o0000ooooooooool0BOooool001[ooooo00?o0000ooooooooool0^Oooool2o`0004co oooo000Jooooo`03o`000?oooooooooo0;Sooooo00?o0000ooooooooool0C?ooool001[ooooo00?o 0000ooooooooool0]_ooool2o`0004oooooo000Jooooo`03o`000?oooooooooo0;Gooooo00?o0000 ooooooooool0Coooool001[ooooo00?o0000ooooooooool0/oooool2o`0005;ooooo000Jooooo`03 o`000?oooooooooo0;7ooooo0_l0001Dooooo`006_ooool00ol0003oooooooooo`2`ooooo`03o`00 0?oooooooooo05Cooooo000Jooooo`03o`000?oooooooooo0:kooooo0_l0001Gooooo`006_ooool0 0ol0003oooooooooo`2/ooooo`;o0000FOooool001[ooooo00?o0000ooooooooool0Z_ooool2o`00 05_ooooo000Jooooo`03o`000?oooooooooo0:Wooooo00?o0000ooooooooool0Foooool001[ooooo 00?o0000ooooooooool0Yoooool2o`0005kooooo000Jooooo`03o`000?oooooooooo0:Gooooo0_l0 001Pooooo`006_ooool00ol0003oooooooooo`2Tooooo`03o`000?oooooooooo063ooooo0007oooo o`;o00001?ooool01?l0003oooooooooooooool5o`0000Cooooo00?o0000ooooooooool0X_ooool2 o`0006?ooooo0006ooooo`04o`000?ooooooooooo`0000Sooooo00Co0000oooooooooooo00001?oo ool00ol0003oooooooooo`2Qooooo`03o`000?oooooooooo06?ooooo0006ooooo`04o`000?oooooo ooooo`0000Wooooo00?o0000ooooooooool01?ooool2o`000:3ooooo0_l0001Vooooo`001_ooool0 1?l0003oooooooooool0000:ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0W_oo ool00ol0003oooooooooo`1Vooooo`001_ooool01?l0003oooooooooool00007ooooo`05o`000?oo ooooooooooooool000001?ooool00ol0003oooooooooo`2Looooo`;o0000JOooool000Kooooo00Co 0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo000000Cooooo00?o0000oooooooo ool0Voooool00ol0003oooooooooo`1Yooooo`001oooool2o`0000Wooooo0ol00005ooooo`03o`00 0?oooooooooo09Wooooo0_l0001/ooooo`006_ooool00ol0003oooooooooo`2Gooooo`;o0000K_oo ool001[ooooo00?o0000ooooooooool0U_ooool00ol0003oooooooooo`1^ooooo`006_ooool00ol0 003oooooooooo`2Dooooo`;o0000LOooool001[ooooo00?o0000ooooooooool0T_ooool2o`0007?o oooo000Jooooo`03o`000?oooooooooo093ooooo0_l0001eooooo`006_ooool00ol0003ooooooooo o`2?ooooo`03o`000?oooooooooo07Gooooo000Jooooo`03o`000?oooooooooo08gooooo0_l0001h ooooo`006_ooool00ol0003oooooooooo`2;ooooo`;o0000N_ooool001[ooooo00?o0000oooooooo ool0R_ooool00ol0003oooooooooo`1jooooo`006_ooool00ol0003oooooooooo`28ooooo`;o0000 OOooool001[ooooo00?o0000ooooooooool0Q_ooool2o`0007oooooo000Jooooo`03o`000?oooooo oooo08Gooooo00?o0000ooooooooool0Ooooool001[ooooo00?o0000ooooooooool0Poooool2o`00 08;ooooo000Jooooo`03o`000?oooooooooo08;ooooo00?o0000ooooooooool0P_ooool001[ooooo 00?o0000ooooooooool0P?ooool2o`0008Gooooo000Jooooo`03o`000?oooooooooo07kooooo0_l0 0027ooooo`006_ooool00ol0003oooooooooo`1mooooo`03o`000?oooooooooo08Oooooo000Joooo o`03o`000?oooooooooo07_ooooo0_l0002:ooooo`001oooool2o`0000Cooooo00?o0000oooooooo ool00oooool3o`0000Cooooo00?o0000ooooooooool0N_ooool00ol0003oooooooooo`2:ooooo`00 1_ooool01?l0003oooooooooool0000:ooooo`03o`000?oooooooooo00?ooooo00?o0000oooooooo ool0N?ooool2o`0008gooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo1Ol00004ooooo`03 o`000?oooooooooo07Oooooo00?o0000ooooooooool0SOooool000Kooooo00Co0000oooooooooooo 00001oooool01?l0003oooooooooool00005ooooo`;o0000M_ooool2o`00093ooooo0006ooooo`04 o`000?ooooooooooo`0000Sooooo00?o0000ooooool000001Oooool00ol0003oooooooooo`1doooo o`03o`000?oooooooooo093ooooo0006ooooo`04o`000?ooooooooooo`0000Wooooo0_l00005oooo o`03o`000?oooooooooo07;ooooo0_l0002Cooooo`001oooool2o`0000_ooooo00?o0000oooooooo ool00oooool00ol0003oooooooooo`1aooooo`03o`000?oooooooooo09?ooooo000Jooooo`03o`00 0?oooooooooo06oooooo0_l0002Fooooo`006_ooool00ol0003oooooooooo`1]ooooo`;o0000V?oo ool001[ooooo00?o0000ooooooooool0K?ooool00ol0003oooooooooo`2Hooooo`006_ooool00ol0 003oooooooooo`1Zooooo`;o0000Voooool001[ooooo00?o0000ooooooooool0J?ooool2o`0009go oooo000Jooooo`03o`000?oooooooooo06Kooooo0_l0002Oooooo`006_ooool00ol0003ooooooooo o`1Uooooo`03o`000?oooooooooo09oooooo000Jooooo`03o`000?oooooooooo06?ooooo0_l0002R ooooo`006_ooool00ol0003oooooooooo`1Qooooo`;o0000Y?ooool001[ooooo00?o0000oooooooo ool0H?ooool00ol0003oooooooooo`2Tooooo`006_ooool00ol0003oooooooooo`1Nooooo`;o0000 Yoooool001[ooooo00?o0000ooooooooool0G?ooool2o`000:Wooooo000Jooooo`03o`000?oooooo oooo05_ooooo00?o0000ooooooooool0ZOooool001[ooooo00?o0000ooooooooool0FOooool2o`00 0:cooooo000Jooooo`03o`000?oooooooooo05Sooooo00?o0000ooooooooool0[?ooool001[ooooo 00?o0000ooooooooool0E_ooool2o`000:oooooo000Jooooo`03o`000?oooooooooo05Cooooo0_l0 002aooooo`006_ooool00ol0003oooooooooo`1Cooooo`03o`000?oooooooooo0;7ooooo0007oooo o`;o00001?ooool00ol0003oooooooooo`02ooooo`?o00001Oooool00ol0003oooooooooo`1Aoooo o`;o0000]?ooool000Kooooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo 000000Cooooo00?o0000ooooooooool0D?ooool00ol0003oooooooooo`2dooooo`001_ooool01?l0 003oooooooooool00007ooooo`05o`000?ooooooooooooooool000001?ooool00ol0003ooooooooo o`1>ooooo`;o0000]oooool000Kooooo00Co0000oooooooooooo00001oooool4o`0000Gooooo0_l0 001>ooooo`03o`000?oooooooooo0;Oooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo00?o 0000ooooooooool01_ooool00ol0003oooooooooo`1;ooooo`;o0000^_ooool000Kooooo00Co0000 oooooooooooo00002?ooool00ol0003oooooooooo`05ooooo`03o`000?oooooooooo04[ooooo00?o 0000ooooooooool0^_ooool000Oooooo0_l0000:ooooo`;o00001Oooool00ol0003oooooooooo`18 ooooo`;o0000_Oooool001[ooooo00?o0000ooooooooool0Aoooool00ol0003oooooooooo`2moooo o`006_ooool00ol0003oooooooooo`15ooooo`;o0000`?ooool001[ooooo00?o0000ooooooooool0 @oooool2o`000<;ooooo000Jooooo`03o`000?oooooooooo04;ooooo00?o0000ooooooooool0`_oo ool001[ooooo00?o0000ooooooooool0@?ooool2o`000oooool00ol0003oooooooooo`39ooooo`006_ooool00ol0003ooooooooo o`0iooooo`;o0000c?ooool001[ooooo00?o0000ooooooooool0=oooool2o`000?ooooo0006ooooo`04o`000?ooooooooooo`0000Oooooo00Go0000oooo ooooooooooooo`000004ooooo`03o`000?oooooooooo027ooooo00?o0000ooooooooool0hoooool0 00Oooooo0_l00009ooooo`?o00001Oooool00ol0003oooooooooo`0Oooooo`;o0000i_ooool001[o oooo00?o0000ooooooooool07Oooool2o`000>Sooooo000Jooooo`03o`000?oooooooooo01cooooo 00?o0000ooooooooool0j?ooool001[ooooo00?o0000ooooooooool06_ooool2o`000>_ooooo000J ooooo`03o`000?oooooooooo01Sooooo0_l0003]ooooo`006_ooool00ol0003oooooooooo`0Goooo o`03o`000?oooooooooo0>gooooo000Jooooo`03o`000?oooooooooo01Gooooo0_l0003`ooooo`00 6_ooool00ol0003oooooooooo`0Dooooo`03o`000?oooooooooo0?3ooooo000Jooooo`03o`000?oo oooooooo01;ooooo0_l0003cooooo`006_ooool00ol0003oooooooooo`0@ooooo`;o0000mOooool0 01[ooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`3eooooo`006_ooool00ol0003o ooooooooo`0=ooooo`;o0000n?ooool001[ooooo00?o0000ooooooooool03?ooool00ol0003ooooo ooooo`3hooooo`006_ooool00ol0003oooooooooo`0:ooooo`;o0000noooool001[ooooo00?o0000 ooooooooool02Oooool00ol0003oooooooooo`3kooooo`006_ooool00ol0003oooooooooo`07oooo o`;o0000o_ooool001[ooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`3nooooo`00 6_ooool00ol0003oooooooooo`04ooooo`;o0000ooooool2ooooo`006_ooool00ol0003ooooooooo o`03ooooo`03o`000?oooooooooo0?oooooo0_ooool001;ooooo0ol00005ooooo`04o`000?oooooo ooooooooo`;o0000ooooool5ooooo`004oooool00ol0003oooooooooo`04ooooo`04o`000?oooooo 0000o`000?oooooo1oooool001?ooooo00?o0000ooooooooool01?ooool2o`000?oooooo2Oooool0 01?ooooo00?o0000ooooooooool01?ooool2o`000?oooooo2Oooool001?ooooo00?o0000oooooooo ool01?ooool00ol0003oooooooooo`3oooooo`Sooooo000Booooo`;o00001_ooool00ol0003ooooo ooooo`3oooooo`Sooooo000Cooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool0oooo ool8ooooo`00oooooolUooooo`00oooooolUooooo`00oooooolUooooo`00oooooolUooooo`00oooo oolUooooo`00oooooolUooooo`007_ooool00ol0003oooooooooo`0ooooo`03o`000?oooooooooo0??o oooo0003ooooo`03o`000?oooooo000000Kooooo00?o0000ooooooooool02Oooool01Ol0003ooooo oooooooooooo000000?ooooo1Ol00005ooooo`03o`000?oooooooooo00;ooooo00?o0000oooooooo ool0l_ooool000?ooooo00?o0000ooooool000001Oooool00ol0003oooooooooo`09ooooo`03o`00 0?oooooooooo00;ooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`04ooooo`03o`00 0?oooooooooo00?ooooo00?o0000ooooooooool0l_ooool000?ooooo00?o0000ooooool000001Ooo ool00ol0003oooooooooo`09ooooo`03o`000?oooooooooo00;ooooo00?o0000ooooooooool00ooo ool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0l_oo ool000;ooooo00Go0000ooooool0003oooooo`000003ooooo`03o`000?oooooooooo00Wooooo00?o 0000ooooooooool00oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo00?ooooo00?o 0000ooooooooool01?ooool00ol0003oooooooooo`3booooo`000_ooool01Ol0003oooooo`000?oo oooo000000?ooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`04ooooo`04o`000?oo ooooooooooooo`Co00000oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo0??ooooo 0002ooooo`05o`000?oooooo0000ooooool000000_ooool00ol0003oooooooooo`09ooooo`03o`00 0?oooooooooo00Kooooo00Go0000ooooooooooooooooo`000004ooooo`03o`000?oooooooooo00?o oooo00?o0000ooooooooool0m?ooool000;ooooo1_l000000ooooooo0000ooooo`0:ooooo`03o`00 0?oooooooooo00_ooooo0_l00002ooooo`03o`000?oooooooooo0?[ooooo003oooooobGooooo003o ooooobGooooo003oooooobGooooo003oooooobGooooo003oooooobGooooo003oooooobGooooo003o ooooobGooooo003oooooobGooooo003oooooobGooooo003oooooobGooooo003oooooobGooooo003o ooooobGooooo003oooooobGooooo0000\ \>"], ImageRangeCache->{{{0, 291.625}, {179.875, 0}} -> {-0.127952, -0.181058, \ 0.00492105, 0.00796243}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[ "\nRight! Linear increase in fitness with increasing allocation to female \ function. (This is a consequence of our assumtion that female function is \ limited only by resources.) REMEMBER: allocation to female fitness increases \ from right to left; it's equal to 1 - ai. \n\n\nFinally, let's plot the \ relationship between total fitness and the allocation by the ith individual \ to male function.\n"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ StyleBox["(", FontFamily->"Helvetica", FontColor->RGBColor[0, 0, 1]], StyleBox[ "Put the cursor anywhere in the bracket below and press \"SHIFT-RETURN.\")", FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wi}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 -117.118 117.132 [ [.21429 .00221 -9 -9 ] [.21429 .00221 9 0 ] [.40476 .00221 -9 -9 ] [.40476 .00221 9 0 ] [.59524 .00221 -9 -9 ] [.59524 .00221 9 0 ] [.78571 .00221 -9 -9 ] [.78571 .00221 9 0 ] [.97619 .00221 -3 -9 ] [.97619 .00221 3 0 ] [1.025 .01471 0 -6 ] [1.025 .01471 52 6 ] [.01131 .13185 -30 -4.5 ] [.01131 .13185 0 4.5 ] [.01131 .24898 -30 -4.5 ] [.01131 .24898 0 4.5 ] [.01131 .36611 -30 -4.5 ] [.01131 .36611 0 4.5 ] [.01131 .48324 -30 -4.5 ] [.01131 .48324 0 4.5 ] [.01131 .60038 -30 -4.5 ] [.01131 .60038 0 4.5 ] [.02381 .64303 -26 0 ] [.02381 .64303 26 12 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01471 m .21429 .02096 L s [(0.2)] .21429 .00221 0 1 Mshowa .40476 .01471 m .40476 .02096 L s [(0.4)] .40476 .00221 0 1 Mshowa .59524 .01471 m .59524 .02096 L s [(0.6)] .59524 .00221 0 1 Mshowa .78571 .01471 m .78571 .02096 L s [(0.8)] .78571 .00221 0 1 Mshowa .97619 .01471 m .97619 .02096 L s [(1)] .97619 .00221 0 1 Mshowa .125 Mabswid .07143 .01471 m .07143 .01846 L s .11905 .01471 m .11905 .01846 L s .16667 .01471 m .16667 .01846 L s .2619 .01471 m .2619 .01846 L s .30952 .01471 m .30952 .01846 L s .35714 .01471 m .35714 .01846 L s .45238 .01471 m .45238 .01846 L s .5 .01471 m .5 .01846 L s .54762 .01471 m .54762 .01846 L s .64286 .01471 m .64286 .01846 L s .69048 .01471 m .69048 .01846 L s .7381 .01471 m .7381 .01846 L s .83333 .01471 m .83333 .01846 L s .88095 .01471 m .88095 .01846 L s .92857 .01471 m .92857 .01846 L s .25 Mabswid 0 .01471 m 1 .01471 L s gsave 1.025 .01471 -61 -10 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (a) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .13185 m .03006 .13185 L s [(1.001)] .01131 .13185 1 0 Mshowa .02381 .24898 m .03006 .24898 L s [(1.002)] .01131 .24898 1 0 Mshowa .02381 .36611 m .03006 .36611 L s [(1.003)] .01131 .36611 1 0 Mshowa .02381 .48324 m .03006 .48324 L s [(1.004)] .01131 .48324 1 0 Mshowa .02381 .60038 m .03006 .60038 L s [(1.005)] .01131 .60038 1 0 Mshowa .125 Mabswid .02381 .03814 m .02756 .03814 L s .02381 .06157 m .02756 .06157 L s .02381 .08499 m .02756 .08499 L s .02381 .10842 m .02756 .10842 L s .02381 .15527 m .02756 .15527 L s .02381 .1787 m .02756 .1787 L s .02381 .20213 m .02756 .20213 L s .02381 .22555 m .02756 .22555 L s .02381 .27241 m .02756 .27241 L s .02381 .29583 m .02756 .29583 L s .02381 .31926 m .02756 .31926 L s .02381 .34269 m .02756 .34269 L s .02381 .38954 m .02756 .38954 L s .02381 .41296 m .02756 .41296 L s .02381 .43639 m .02756 .43639 L s .02381 .45982 m .02756 .45982 L s .02381 .50667 m .02756 .50667 L s .02381 .5301 m .02756 .5301 L s .02381 .55352 m .02756 .55352 L s .02381 .57695 m .02756 .57695 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 69.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica1Mono %%IncludeFont: Mathematica1Mono /Mathematica1Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (_) show 81.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (H) show 93.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (i) show 99.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\\\) show %%IncludeResource: font Mathematica2Mono %%IncludeFont: Mathematica2Mono /Mathematica2Mono findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (L) show 111.000 13.000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .1072 L .10458 .19899 L .14415 .27659 L .18221 .34337 L .22272 .40602 L .26171 .45815 L .30316 .50476 L .34309 .54114 L .3815 .56824 L .40095 .57902 L .42237 .5886 L .43215 .59218 L .44268 .59548 L .45255 .59805 L .46172 .59997 L .47182 .60159 L .47716 .60223 L .47989 .6025 L .48285 .60275 L .48568 .60295 L .48828 .60309 L .49076 .6032 L .49201 .60324 L .49339 .60327 L .49463 .6033 L .49577 .60331 L .49708 .60332 L .49833 .60332 L .49948 .60331 L .50054 .6033 L .5017 .60328 L .50294 .60325 L .50532 .60317 L .50783 .60305 L .51231 .60276 L .51713 .60233 L .52241 .60172 L .53188 .60027 L .54069 .59851 L .56115 .59285 L .57974 .58584 L .61972 .56471 L .65818 .53661 L .6991 .49837 L .73851 .45344 L .77639 .40275 L .81673 .34073 L .85556 .27322 L .89683 .19305 L Mistroke .9366 .10767 L .97484 .01801 L .97619 .01472 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{283.812, 175.438}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgooooo`03o`000?oooooooooo00Cooooo000Pooooo`03o`000?oooooooooo0ooooo`03o`000?oo oooooooo09Wooooo00?o0000ooooooooool0C?ooool0023ooooo00?o0000ooooooooool03_ooool0 0ol0003oooooooooo`2Hooooo`03o`000?oooooooooo04cooooo000Pooooo`03o`000?oooooooooo 00kooooo00?o0000ooooooooool0Uoooool00ol0003oooooooooo`1=ooooo`008?ooool00ol0003o ooooooooo`0?ooooo`03o`000?oooooooooo09Kooooo00?o0000ooooooooool0COooool0023ooooo 00?o0000ooooooooool03oooool00ol0003oooooooooo`2Eooooo`03o`000?oooooooooo04kooooo 000Pooooo`;o00004Oooool00ol0003oooooooooo`2Dooooo`03o`000?oooooooooo04kooooo000P ooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0Toooool00ol0003oooooooooo`1? ooooo`0000Coooooo`000?l0003o00001?ooool00ol0003oooooooooo`03ooooo`;o00001?ooool2 o`0000;ooooo1Ol00003ooooo`03o`000?oooooooooo017ooooo00?o0000ooooooooool0T_ooool0 0ol0003oooooooooo`1?ooooo`000_ooool00ol0003oooooooooo`08ooooo`04o`000?oooooooooo o`0000;ooooo00Co0000oooooooooooo00000_ooool01?l0003oooooooooool00003ooooo`03o`00 0?oooooooooo017ooooo00?o0000ooooooooool0TOooool00ol0003oooooooooo`1@ooooo`000_oo ool00ol0003oooooooooo`08ooooo`04o`000?ooooooooooo`0000;ooooo00Co0000oooooooooooo 00000oooool00ol0003oooooooooo`03ooooo`;o00004oooool00ol0003oooooooooo`2@ooooo`03 o`000?oooooooooo053ooooo0002ooooo`03o`000?oooooooooo00Sooooo00Co0000oooooooooooo 00000_ooool01?l0003oooooooooool00004ooooo`03o`000?oooooooooo00;ooooo00?o0000oooo ooooool04_ooool00ol0003oooooooooo`2?ooooo`03o`000?oooooooooo057ooooo0002ooooo`03 o`000?oooooooooo00Sooooo00Co0000oooooooooooo00000_ooool01_l0003oooooooooool0003o ooooo`0000?ooooo00Go0000ooooooooooooooooo`00000Eooooo`03o`000?oooooooooo08kooooo 00?o0000ooooooooool0DOooool00003ooooool0003o000000[ooooo00Co0000oooooooooooo0000 0_ooool01_l0003oooooooooool0003oooooo`0000?ooooo00Go0000ooooooooooooooooo`00000E ooooo`03o`000?oooooooooo08gooooo00?o0000ooooooooool0D_ooool000;ooooo00?o0000oooo ooooool02Oooool2o`0000Cooooo0_l00003ooooo`?o00001?ooool00ol0003oooooooooo`0Doooo o`03o`000?oooooooooo08cooooo00?o0000ooooooooool0D_ooool0023ooooo0_l0000Eooooo`03 o`000?oooooooooo08_ooooo00?o0000ooooooooool0Doooool0023ooooo00?o0000ooooooooool0 5Oooool00ol0003oooooooooo`2:ooooo`03o`000?oooooooooo05?ooooo000Pooooo`03o`000?oo oooooooo01Gooooo00?o0000ooooooooool0ROooool00ol0003oooooooooo`1Dooooo`008?ooool0 0ol0003oooooooooo`0Fooooo`03o`000?oooooooooo08Oooooo00?o0000ooooooooool0EOooool0 023ooooo0_l0000Gooooo`03o`000?oooooooooo08Oooooo00?o0000ooooooooool0EOooool0023o oooo00?o0000ooooooooool05oooool00ol0003oooooooooo`25ooooo`03o`000?oooooooooo05Ko oooo000Pooooo`03o`000?oooooooooo01Oooooo00?o0000ooooooooool0QOooool00ol0003ooooo ooooo`1Fooooo`008?ooool00ol0003oooooooooo`0Hooooo`03o`000?oooooooooo08?ooooo00?o 0000ooooooooool0Eoooool0023ooooo00?o0000ooooooooool06Oooool00ol0003oooooooooo`21 ooooo`03o`000?oooooooooo05Sooooo000Pooooo`;o00006_ooool00ol0003oooooooooo`21oooo o`03o`000?oooooooooo05Sooooo000Pooooo`03o`000?oooooooooo01[ooooo00?o0000oooooooo ool0Ooooool00ol0003oooooooooo`1Iooooo`008?ooool00ol0003oooooooooo`0Jooooo`03o`00 0?oooooooooo07oooooo00?o0000ooooooooool0FOooool0023ooooo00?o0000ooooooooool06ooo ool00ol0003oooooooooo`1mooooo`03o`000?oooooooooo05[ooooo000Pooooo`03o`000?oooooo oooo01_ooooo00?o0000ooooooooool0O?ooool00ol0003oooooooooo`1Kooooo`008?ooool2o`00 01gooooo00?o0000ooooooooool0Noooool00ol0003oooooooooo`1Kooooo`008?ooool00ol0003o ooooooooo`0Looooo`03o`000?oooooooooo07[ooooo00?o0000ooooooooool0G?ooool00004oooo ool0003o0000o`0000Cooooo00?o0000ooooooooool00oooool2o`0000Cooooo0_l00003ooooo`?o 00001?ooool00ol0003oooooooooo`0Mooooo`03o`000?oooooooooo07Sooooo00?o0000oooooooo ool0GOooool000;ooooo00?o0000ooooooooool02?ooool01?l0003oooooooooool00002ooooo`06 o`000?ooooooooooo`000?oooooo00000oooool01Ol0003ooooooooooooooooo0000023ooooo00?o 0000ooooooooool0Moooool00ol0003oooooooooo`1Mooooo`000_ooool00ol0003oooooooooo`08 ooooo`04o`000?ooooooooooo`0000;ooooo00Co0000oooooooooooo00001Oooool01?l0003ooooo ooooooooool2o`0001oooooo00?o0000ooooooooool0M_ooool00ol0003oooooooooo`1Nooooo`00 0_ooool00ol0003oooooooooo`08ooooo`04o`000?ooooooooooo`0000;ooooo00Co0000oooooooo oooo00000oooool2o`0000Cooooo00?o0000ooooooooool07oooool00ol0003oooooooooo`1eoooo o`03o`000?oooooooooo05kooooo0002ooooo`03o`000?oooooooooo00Sooooo00Co0000oooooooo oooo00000_ooool01?l0003oooooooooool00005ooooo`05o`000?ooooooooooooooool000008_oo ool00ol0003oooooooooo`1cooooo`03o`000?oooooooooo05oooooo00000ooooooo0000o`00000: ooooo`04o`000?ooooooooooo`0000;ooooo00Ko0000oooooooooooo0000ooooool00003ooooo`05 o`000?ooooooooooooooool000008_ooool00ol0003oooooooooo`1booooo`03o`000?oooooooooo 063ooooo0002ooooo`03o`000?oooooooooo00Wooooo0_l00004ooooo`;o00000oooool3o`0000Co oooo00?o0000ooooooooool08Oooool00ol0003oooooooooo`1aooooo`03o`000?oooooooooo063o oooo000Pooooo`;o00008oooool00ol0003oooooooooo`1_ooooo`03o`000?oooooooooo067ooooo 000Pooooo`03o`000?oooooooooo02;ooooo00?o0000ooooooooool0Koooool00ol0003ooooooooo o`1Qooooo`008?ooool00ol0003oooooooooo`0Sooooo`03o`000?oooooooooo06gooooo00?o0000 ooooooooool0H_ooool0023ooooo00?o0000ooooooooool09?ooool00ol0003oooooooooo`1[oooo o`03o`000?oooooooooo06?ooooo000Pooooo`03o`000?oooooooooo02Cooooo00?o0000oooooooo ool0Joooool00ol0003oooooooooo`1Sooooo`008?ooool2o`0002Kooooo00?o0000ooooooooool0 JOooool00ol0003oooooooooo`1Tooooo`008?ooool00ol0003oooooooooo`0Vooooo`03o`000?oo oooooooo06Oooooo00?o0000ooooooooool0IOooool0023ooooo00?o0000ooooooooool09oooool0 0ol0003oooooooooo`1Vooooo`03o`000?oooooooooo06Gooooo000Pooooo`03o`000?oooooooooo 02Oooooo00?o0000ooooooooool0IOooool00ol0003oooooooooo`1Vooooo`008?ooool2o`0002Wo oooo00?o0000ooooooooool0Hoooool00ol0003oooooooooo`1Wooooo`008?ooool00ol0003ooooo ooooo`0Yooooo`03o`000?oooooooooo067ooooo00?o0000ooooooooool0J?ooool0023ooooo00?o 0000ooooooooool0:Oooool00ol0003oooooooooo`1Qooooo`03o`000?oooooooooo06Sooooo000P ooooo`03o`000?oooooooooo02[ooooo00?o0000ooooooooool0Goooool00ol0003oooooooooo`1Y ooooo`008?ooool00ol0003oooooooooo`0[ooooo`03o`000?oooooooooo05gooooo00?o0000oooo ooooool0J_ooool0023ooooo0_l0000]ooooo`03o`000?oooooooooo05cooooo00?o0000oooooooo ool0J_ooool0023ooooo00?o0000ooooooooool0;?ooool00ol0003oooooooooo`1Kooooo`03o`00 0?oooooooooo06_ooooo00001?oooooo0000o`000?l00004ooooo`03o`000?oooooooooo00?ooooo 0_l00004ooooo`;o00001?ooool3o`0000?ooooo00?o0000ooooooooool0;Oooool00ol0003ooooo ooooo`1Iooooo`03o`000?oooooooooo06cooooo0002ooooo`03o`000?oooooooooo00Sooooo00Co 0000oooooooooooo00000_ooool01?l0003oooooooooool00004ooooo`03o`000?oooooooooo00;o oooo00?o0000ooooooooool0;_ooool00ol0003oooooooooo`1Gooooo`03o`000?oooooooooo06go oooo0002ooooo`03o`000?oooooooooo00Sooooo00Co0000oooooooooooo00000_ooool01Ol0003o ooooooooool0003ooooo00Go00000oooool00ol0003oooooooooo`0_ooooo`03o`000?oooooooooo 05Gooooo00?o0000ooooooooool0K_ooool000;ooooo00?o0000ooooooooool02?ooool01?l0003o ooooooooool00002ooooo`06o`000?ooooooooooo`000?oooooo00000_ooool00ol0003ooooooooo o`02ooooo`;o0000Oooool00ol0003oooooooooo`11ooooo`03o`000?oooooooooo07Sooooo 000Pooooo`;o0000>oooool00ol0003oooooooooo`0oooooo`03o`000?oooooooooo07Wooooo000P ooooo`03o`000?oooooooooo03_ooooo00?o0000ooooooooool0??ooool2o`0007cooooo000Poooo o`03o`000?oooooooooo03cooooo0_l0000kooooo`03o`000?oooooooooo07cooooo000Pooooo`03 o`000?oooooooooo03kooooo00?o0000ooooooooool0=oooool00ol0003oooooooooo`1mooooo`00 8?ooool00ol0003oooooooooo`0oooooo`;o0000=Oooool2o`00083ooooo000Pooooo`;o0000@_oo ool2o`0003;ooooo00?o0000ooooooooool0P?ooool0023ooooo00?o0000ooooooooool0@oooool0 0ol0003oooooooooo`0^ooooo`03o`000?oooooooooo087ooooo000Pooooo`03o`000?oooooooooo 04Cooooo0_l0000/ooooo`;o0000Q?ooool0023ooooo00?o0000ooooooooool0A_ooool00ol0003o ooooooooo`0Wooooo`;o0000Q_ooool0023ooooo0_l00018ooooo`03o`000?oooooooooo02Cooooo 0_l00028ooooo`008?ooool00ol0003oooooooooo`18ooooo`?o00008Oooool2o`0008[ooooo0000 1?oooooo0000o`000?l00004ooooo`03o`000?oooooooooo00?ooooo0_l00004ooooo`;o00000ooo ool3o`0000Cooooo00?o0000ooooooooool0Boooool3o`0001_ooooo0ol0002?ooooo0009ooooo`03o`000?oooooo000000Gooooo00?o 0000ooooooooool02Oooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo00?ooooo00?o 0000ooooooooool01?ooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo0>?ooooo0009 ooooo`03o`000?oooooo000000Gooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`02 ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`03 ooooo`03o`000?oooooooooo0>?ooooo0008ooooo`05o`000?oooooo0000ooooool000000oooool0 0ol0003oooooooooo`09ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool00oooool0 0ol0003oooooooooo`03ooooo`03o`000?oooooooooo00Cooooo00?o0000ooooooooool0hoooool0 00Sooooo00Go0000ooooool0003oooooo`000003ooooo`03o`000?oooooooooo00Wooooo00?o0000 ooooooooool01?ooool00ol0003oooooooooo`03o`0000Gooooo00?o0000ooooooooool00oooool0 0ol0003oooooooooo`3Tooooo`002?ooool01Ol0003oooooo`000?oooooo000000;ooooo00?o0000 ooooooooool02Oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo00Kooooo00?o0000 ooooooooool00oooool00ol0003oooooooooo`3Uooooo`002?ooool6o`000003ooooool0003ooooo 00[ooooo00?o0000ooooooooool02_ooool00ol0003oooooooooo`02ooooo`03o`000?oooooooooo 0>_ooooo003ooooooacooooo003ooooooacooooo003ooooooacooooo003ooooooacooooo003ooooo oacooooo003ooooooacooooo003ooooooacooooo003ooooooacooooo003ooooooacooooo003ooooo oacooooo003ooooooacooooo003ooooooacooooo003ooooooacooooo003ooooooacooooo003ooooo oacooooo0000\ \>"], ImageRangeCache->{{{0, 282.812}, {174.438, 0}} -> {-0.172142, 0.998941, \ 0.00530039, 4.30966*^-5}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "Note that individual fitness, W", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], ", is maximal when a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], " = a = 0.50. \n\nIf you are wondering why the surface is humped shaped, \ good for you! But notice the y axis. Compared to the previous hump for k = \ 2, this hump is virtually flat." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[StyleBox[ "Now, set k to whatever you want and run through the same steps. Simply type \ in a number after the \"k=\" sign. You can then return to this point, change \ k to a new value and go again. Have fun.", FontColor->RGBColor[1, 0, 0]]], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["k = 50", "Input", AspectRatioFixed->True], Cell[BoxData[ \(50\)], "Output"] }, Open ]], Cell[TextData[ "The new ESS for k mates is found by simplifying the parameter, a."], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell["Simplify [a]", "Input", AspectRatioFixed->True], Cell[BoxData[ \(49\/99\)], "Output"] }, Open ]], Cell[TextData[{ "\n\nPlot the relationship between fitness through ", StyleBox["male", FontVariations->{"Underline"->True}], " function and the allocation by the ith individual to male function." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wm}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["m", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 0.588604 [ [.21429 .00222 -9 -9 ] [.21429 .00222 9 0 ] [.40476 .00222 -9 -9 ] [.40476 .00222 9 0 ] [.59524 .00222 -9 -9 ] [.59524 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [1.025 .01472 0 -7 ] [1.025 .01472 52 7 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [.02381 .64303 -26 0 ] [.02381 .64303 26 14 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(0.2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(0.4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(0.6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(0.8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(1)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (a) show 69.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (_) show 81.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 93.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (i) show 99.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (L) show 111.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (W) show 69.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (_) show 81.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 93.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (m) show 99.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (L) show 111.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .03954 L .10458 .06651 L .14415 .09176 L .18221 .11595 L .22272 .14162 L .26171 .16625 L .30316 .19233 L .34309 .21737 L .3815 .24138 L .42237 .26684 L .46172 .29127 L .49955 .31468 L .53984 .33953 L .57861 .36336 L .61984 .38862 L .65954 .41286 L .69774 .4361 L .73838 .46076 L .77751 .48441 L .81909 .50946 L .85916 .53352 L .89771 .55658 L .93871 .58104 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{311, 311}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo003oOolh Ool00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00 ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolh Ool00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00 ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolh Ool00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00 ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolh Ool00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00 ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolh Ool00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00 ogoo>7oo003oOolhOol00?moocQoo`00?goo0P0017oo0P000goo10007Goo0P0017oo0P0017oo0`00 7Goo0P0017oo0P0017oo0P007Woo0P0017oo0P0017oo0P008goo0`00@7oo000nOol01000Oomoo`00 0goo0P0017oo00<007ooOol077oo00@007ooOol000=oo`8000Eoo`03001oogoo01]oo`04001oogoo 0003Ool20003Ool01000Oomoo`0077oo00@007ooOol000=oo`8000=oo`04001oogoo000SOol00`00 Oomoo`0oOol003ioo`04001oogoo000:Ool00`00Oomoo`0KOol01000Oomoo`0027oo100077oo00@0 07ooOol000Qoo`04001oogoo000LOol01000Oomoo`0027oo00@007ooOol002=oo`03001oogoo03mo o`00?Woo00@007ooOol000]oo`03001oogoo01Yoo`04001oogoo0008Ool00`00Ool0000MOol01000 Oomoo`0027oo0`007Goo00@007ooOol000Uoo`8002Aoo`03001oogoo03moo`00?Woo00@007ooOol0 00Qoo`04001oogoo000LOol01000Oomoo`0027oo00<007oo00007Goo00@007ooOol000Qoo`03001o ogoo01eoo`04001oogoo0008Ool01000Oomoo`008goo00<007ooOol0?goo000oOol2000:Ool2000N Ool2000:Ool2000NOol2000:Ool3000MOol2000:Ool2000SOol2000ZOol00`00Oomoo`0Qoo`D000Aoo`03001oogoo00Uoo`05001o ogooOol00004Ool50004Ool00`00Oomoo`02Ool00`00Oomoo`03Ool001Yoo`03001oogoo0>Qoo`04 001oogoo0004Ool00`00Oomoo`09Ool00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`03Ool0 0`00Oomoo`03Ool00`00Oomoo`03Ool001Yoo`03001oogoo0>Qoo`@000Aoo`03001oogoo00Uoo`03 001oogoo009oo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo00=oo`00 57ooj@002goo00D007ooOomoo`0000]oo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo009o o`03001oogoo00Aoo`03001oogoo00=oo`006Woo00<007oo000027oo00<007ooOol027oo00<007oo Ool027oo00<007ooOol027oo00<007ooOol027oo00<007ooOol027oo00<007ooOol027oo00<007oo Ool027oo00<007ooOol027oo00<007ooOol027oo00<007ooOol027oo00<007ooOol027oo00<007oo Ool027oo00<007ooOol027oo00<007ooOol027oo00<007ooOol027oo00<007ooOol027oo00<007oo Ool027oo00<007ooOol027oo00<007ooOol027oo00<007ooOol03Goo0`000goo00<007ooOol02Goo 00<007ooOol017oo00<007ooOol00Woo0P0017oo00<007ooOol00goo00<007ooOol017oo000JOol0 0`00Oomoo`02003/Ool00`00Oomoo`09Ool00`00Oomoo`06Ool00`00Oomoo`06Ool00`00Oomoo`03 Ool00`00Oomoo`05Ool001Yoo`03001oogoo009oo`800>Yoo`03001oogoo00Uoo`03001oogoo00]o o`05001oogooOol0000=Ool001Yoo`03001oogoo00Aoo`03001oogoo0?mooaAoo`006Woo00<007oo Ool01Goo0P00ogoo57oo000JOol00`00Oomoo`07Ool00`00Oomoo`3oOolAOol001Yoo`03001oogoo 00Qoo`800?mooa5oo`006Woo00<007ooOol02Woo00<007ooOol0ogoo3Woo000JOol00`00Oomoo`0; Ool00`00Oomoo`3oOol=Ool001Yoo`03001oogoo00aoo`800?moo`eoo`006Woo00<007ooOol03Woo 00<007ooOol0ogoo2Woo000JOol00`00Oomoo`0?Ool2003oOol:Ool001Yoo`03001oogoo015oo`03 001oogoo0?moo`Moo`006Woo00<007ooOol04Woo0P00ogoo1goo000JOol00`00Oomoo`0DOol00`00 Oomoo`3oOol4Ool001Yoo`03001oogoo01Eoo`800?moo`Aoo`006Woo00<007ooOol05goo00<007oo Ool0ogoo0Goo000JOol00`00Oomoo`0HOol2003oOol1Ool001Yoo`03001oogoo01Yoo`800?ioo`00 6Woo00<007ooOol077oo0P00o7oo000JOol00`00Oomoo`0NOol00`00Oomoo`3iOol001Yoo`03001o ogoo01moo`800?Uoo`006Woo00<007ooOol08Goo0P00mgoo000JOol00`00Oomoo`0SOol2003eOol0 00Moo`8000Aoo`8000=oo`@000Aoo`03001oogoo02Eoo`03001oogoo0?9oo`001Woo00@007ooOol0 00=oo`8000Aoo`03001oogoo00Aoo`03001oogoo02Ioo`800?9oo`001Woo00@007ooOol000Yoo`03 001oogoo00=oo`8002Uoo`800?1oo`001Woo00@007ooOol000]oo`03001oogoo009oo`03001oogoo 02Yoo`03001oogoo0>eoo`001Woo00@007ooOol000Qoo`04001oogoo0004Ool00`00Oomoo`0[Ool2 003]Ool000Moo`8000Yoo`8000Eoo`03001oogoo02eoo`03001oogoo0>Yoo`006Woo00<007ooOol0 ;Woo0P00jWoo000JOol00`00Oomoo`0`Ool00`00Oomoo`3WOol001Yoo`03001oogoo035oo`800>Mo o`006Woo00<007ooOol05oo`006Woo00<007ooOol0=goo0P00hGoo000JOol00`00Oomoo`0i Ool00`00Oomoo`3NOol001Yoo`03001oogoo03Yoo`800=ioo`006Woo00<007ooOol0?7oo00<007oo Ool0fgoo000JOol00`00Oomoo`0mOol2003KOol001Yoo`03001oogoo03moo`03001oogoo0=Qoo`00 6Woo00<007ooOol0@7oo0P00f7oo000JOol00`00Oomoo`12Ool00`00Oomoo`3EOol001Yoo`03001o ogoo04=oo`800=Eoo`006Woo00<007ooOol0AGoo00<007ooOol0dWoo000JOol00`00Oomoo`16Ool2 003BOol001Yoo`03001oogoo04Qoo`800=1oo`006Woo00<007ooOol0BWoo0P00cWoo000JOol00`00 Oomoo`1Ool0 01Yoo`03001oogoo08Yoo`8008ioo`006Woo00<007ooOol0S7oo00<007ooOol0Rgoo000JOol00`00 Oomoo`2=Ool2002;Ool001Yoo`03001oogoo08moo`03001oogoo08Qoo`006Woo00<007ooOol0T7oo 0P00R7oo000JOol00`00Oomoo`2BOol20026Ool001Yoo`03001oogoo09Aoo`8008Aoo`006Woo00<0 07ooOol0UWoo00<007ooOol0PGoo000JOol00`00Oomoo`2GOol20021Ool001Yoo`03001oogoo09Uo o`8007moo`006Woo00<007ooOol0Vgoo00<007ooOol0O7oo000JOol00`00Oomoo`2LOol2001lOol0 01Yoo`03001oogoo09ioo`03001oogoo07Uoo`006Woo00<007ooOol0Wgoo0P00NGoo000JOol00`00 Oomoo`2QOol00`00Oomoo`1fOol001Yoo`03001oogoo0:9oo`8007Ioo`006Woo00<007ooOol0Y7oo 0P00M7oo000JOol00`00Oomoo`2VOol2001bOol001Yoo`03001oogoo0:Qoo`03001oogoo06moo`00 1goo0P0017oo0P0017oo0P001Goo00<007ooOol0ZGoo0P00Kgoo0006Ool01000Oomoo`000goo0P00 0goo00@007ooOol000Aoo`03001oogoo0:]oo`8006eoo`001Woo00@007ooOol000Qoo`04001oogoo 0004Ool2002^Ool2001[Ool000Ioo`04001oogoo0009Ool20005Ool00`00Oomoo`2_Ool00`00Oomo o`1XOol000Ioo`04001oogoo0008Ool01000Oomoo`0017oo00<007ooOol0/7oo0P00J7oo0007Ool2 000:Ool20005Ool00`00Oomoo`2bOol2001VOol001Yoo`03001oogoo0;Aoo`03001oogoo06=oo`00 6Woo00<007ooOol0]Goo0P00Hgoo000JOol00`00Oomoo`2gOol00`00Oomoo`1POol001Yoo`03001o ogoo0;Qoo`80061oo`006Woo00<007ooOol0^Woo00<007ooOol0GGoo000JOol00`00Oomoo`2kOol2 001MOol001Yoo`03001oogoo0;eoo`03001oogoo05Yoo`006Woo00<007ooOol0_Woo0P00FWoo000J Ool00`00Oomoo`30Ool2001HOol001Yoo`03001oogoo0<9oo`8005Ioo`006Woo00<007ooOol0a7oo 00<007ooOol0Dgoo000JOol00`00Oomoo`35Ool2001COol001Yoo`03001oogoo07oo003oOolhOol0 0?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`007Woo00<007ooOol037oo00<007ooOol0ogoo 27oo000Ool00?moocQoo`00ogoo>7oo 003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?mo ocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo 003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?mo ocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo 003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?mo ocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo 003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?mo ocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo 003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00ogoo>7oo003oOolhOol00?mo ocQoo`00ogoo>7oo003oOolhOol00?moocQoo`00\ \>"], ImageRangeCache->{{{0, 310}, {310, 0}} -> {-0.117818, -0.594978, 0.00453129, 0.00733178}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "\n\nNow, plot the relationship between fitness through ", StyleBox["female", FontVariations->{"Underline"->True}], " function and the allocation by the ith indiviudal to male function." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wf}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["f", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 0.588604 [ [.21429 .00222 -9 -9 ] [.21429 .00222 9 0 ] [.40476 .00222 -9 -9 ] [.40476 .00222 9 0 ] [.59524 .00222 -9 -9 ] [.59524 .00222 9 0 ] [.78571 .00222 -9 -9 ] [.78571 .00222 9 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [1.025 .01472 0 -7 ] [1.025 .01472 52 7 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [.02381 .64303 -26 0 ] [.02381 .64303 26 14 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(0.2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(0.4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(0.6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(0.8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(1)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (a) show 69.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (_) show 81.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 93.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (i) show 99.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (L) show 111.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (W) show 69.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (_) show 81.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 93.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (f) show 99.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (L) show 111.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .57944 L .10458 .5534 L .14415 .52894 L .18221 .50542 L .22272 .48039 L .26171 .45629 L .30316 .43067 L .34309 .406 L .3815 .38225 L .42237 .357 L .46172 .33268 L .49955 .30929 L .53984 .2844 L .57861 .26043 L .61984 .23495 L .65954 .21041 L .69774 .18681 L .73838 .16169 L .77751 .13751 L .81909 .11181 L .85916 .08704 L .89771 .06322 L .93871 .03788 L .97619 .01472 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{262, 262}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol001Yoo`03001oogoo09Qoo`03 001oogoo04ioo`006Woo00<007ooOol0UWoo0P00DGoo000JOol00`00Oomoo`2DOol2001COol001Yo o`03001oogoo09=oo`03001oogoo05=oo`006Woo00<007ooOol0TGoo0P00EWoo000JOol00`00Oomo o`2@Ool00`00Oomoo`1FOol001Yoo`03001oogoo08moo`03001oogoo05Moo`006Woo00<007ooOol0 SGoo0P00FWoo000JOol00`00Oomoo`2Woo0P00[Goo000J Ool00`00Oomoo`0iOol00`00Oomoo`2]Ool001Yoo`03001oogoo03Qoo`03001oogoo0:ioo`006Woo 00<007ooOol0=Woo0P00/Goo000JOol00`00Oomoo`0dOol2002cOol001Yoo`03001oogoo03=oo`03 001oogoo0;=oo`006Woo00<007ooOol09o o`006Woo00<007ooOol00goo0P00i7oo000JOol00`00Oomoo`02Ool00`00Oomoo`3TOol001Yoo`03 001oogoo00800>Moo`004Woo0`001Goo00<007oo0000jGoo000COol00`00Oomoo`04Ool2003ZOol0 01=oo`03001oogoo00Aoo`800>Yoo`004goo00<007ooOol017oo00<007ooOol0jGoo000COol00`00 Oomoo`04Ool00`00Oomoo`3YOol0019oo`800?9oo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo 1goo003oOol7Ool001ioo`03001oogoo00aoo`03001oogoo0=Ioo`0037oo00<007ooOol01@0017oo 00<007ooOol00Woo00<007ooOol02Woo00D007ooOomoo`000=Moo`000goo00@007ooOol000Eoo`03 001oogoo00Uoo`05001oogooOol00004Ool40005Ool00`00Oomoo`02Ool00`00Oomoo`3DOol000=o o`04001oogoo0004Ool00`00Oomoo`09Ool00`00Oomoo`02Ool00`00Oomoo`03Ool00`00Oomoo`04 Ool00`00Oomoo`03Ool00`00Oomoo`3DOol000=oo`@000Aoo`03001oogoo00Uoo`03001oogoo009o o`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo0=Aoo`000goo00@007oo 000000=oo`03001oogoo00Uoo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo00=oo`03001o ogoo00Aoo`03001oogoo0=Aoo`000goo00@007ooOol000=oo`03001oogoo00Uoo`03001oogoo00Ao o`04001oogooOol40003Ool00`00Oomoo`03Ool00`00Oomoo`3EOol0009oo`80009oo`800003Ool0 07oo00Yoo`03001oogoo00Ioo`05001oogooOol00004Ool00`00Oomoo`03Ool00`00Oomoo`3FOol0 00Uoo`03001oogoo00Uoo`03001oogoo00Yoo`<0009oo`03001oogoo0=aoo`00ogoo1goo003oOol7 Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00 ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7 Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00 ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7 Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00 ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7 Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00 ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7Ool00?moo`Moo`00ogoo1goo003oOol7 Ool00?moo`Moo`00ogoo1goo0000\ \>"], ImageRangeCache->{{{0, 261}, {261, 0}} -> {-0.149364, -0.666633, 0.00574459, 0.00929494}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[ "\n\n\nFinally, plot the relationship between total fitness and the \ allocation by the ith individual to male function.\n"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[TextData[{ "Plot [{Wi}, {ai, 0, 1}, \nAxesLabel->{\"a", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\",\"W", StyleBox["i", FontVariations->{"CompatibilityType"->"Subscript"}], "\"}]" }], "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 -58.2571 58.2718 [ [.21429 .00221 -9 -9 ] [.21429 .00221 9 0 ] [.40476 .00221 -9 -9 ] [.40476 .00221 9 0 ] [.59524 .00221 -9 -9 ] [.59524 .00221 9 0 ] [.78571 .00221 -9 -9 ] [.78571 .00221 9 0 ] [.97619 .00221 -3 -9 ] [.97619 .00221 3 0 ] [1.025 .01471 0 -7 ] [1.025 .01471 52 7 ] [.01131 .13126 -30 -4.5 ] [.01131 .13126 0 4.5 ] [.01131 .2478 -30 -4.5 ] [.01131 .2478 0 4.5 ] [.01131 .36435 -30 -4.5 ] [.01131 .36435 0 4.5 ] [.01131 .48089 -30 -4.5 ] [.01131 .48089 0 4.5 ] [.01131 .59743 -24 -4.5 ] [.01131 .59743 0 4.5 ] [.02381 .64303 -26 0 ] [.02381 .64303 26 14 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01471 m .21429 .02096 L s [(0.2)] .21429 .00221 0 1 Mshowa .40476 .01471 m .40476 .02096 L s [(0.4)] .40476 .00221 0 1 Mshowa .59524 .01471 m .59524 .02096 L s [(0.6)] .59524 .00221 0 1 Mshowa .78571 .01471 m .78571 .02096 L s [(0.8)] .78571 .00221 0 1 Mshowa .97619 .01471 m .97619 .02096 L s [(1)] .97619 .00221 0 1 Mshowa .125 Mabswid .07143 .01471 m .07143 .01846 L s .11905 .01471 m .11905 .01846 L s .16667 .01471 m .16667 .01846 L s .2619 .01471 m .2619 .01846 L s .30952 .01471 m .30952 .01846 L s .35714 .01471 m .35714 .01846 L s .45238 .01471 m .45238 .01846 L s .5 .01471 m .5 .01846 L s .54762 .01471 m .54762 .01846 L s .64286 .01471 m .64286 .01846 L s .69048 .01471 m .69048 .01846 L s .7381 .01471 m .7381 .01846 L s .83333 .01471 m .83333 .01846 L s .88095 .01471 m .88095 .01846 L s .92857 .01471 m .92857 .01846 L s .25 Mabswid 0 .01471 m 1 .01471 L s gsave 1.025 .01471 -61 -11 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (a) show 69.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (_) show 81.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 93.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (i) show 99.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (L) show 111.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore .02381 .13126 m .03006 .13126 L s [(1.002)] .01131 .13126 1 0 Mshowa .02381 .2478 m .03006 .2478 L s [(1.004)] .01131 .2478 1 0 Mshowa .02381 .36435 m .03006 .36435 L s [(1.006)] .01131 .36435 1 0 Mshowa .02381 .48089 m .03006 .48089 L s [(1.008)] .01131 .48089 1 0 Mshowa .02381 .59743 m .03006 .59743 L s [(1.01)] .01131 .59743 1 0 Mshowa .125 Mabswid .02381 .04385 m .02756 .04385 L s .02381 .07299 m .02756 .07299 L s .02381 .10212 m .02756 .10212 L s .02381 .16039 m .02756 .16039 L s .02381 .18953 m .02756 .18953 L s .02381 .21867 m .02756 .21867 L s .02381 .27694 m .02756 .27694 L s .02381 .30607 m .02756 .30607 L s .02381 .33521 m .02756 .33521 L s .02381 .39348 m .02756 .39348 L s .02381 .42262 m .02756 .42262 L s .02381 .45175 m .02756 .45175 L s .02381 .51003 m .02756 .51003 L s .02381 .53916 m .02756 .53916 L s .02381 .5683 m .02756 .5683 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -87 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 22 translate 1 -1 scale 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (W) show 69.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math1Mono %%IncludeFont: Math1Mono /Math1Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (_) show 81.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (H) show 93.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (i) show 99.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (\\\\) show %%IncludeResource: font Math2Mono %%IncludeFont: Math2Mono /Math2Mono findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor (L) show 111.000000 15.000000 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.000000 0.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth %%DocumentNeededResources: font Math1Mono %%+ font Math2Mono %%+ font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Math1Mono %%+ Math2Mono %%+ Courier %%DocumentSuppliedFonts: %%DocumentFonts: font Math1Mono %%+ font Math2Mono %%+ font Courier grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .10808 L .10458 .20055 L .14415 .27858 L .18221 .3456 L .22272 .40833 L .26171 .46039 L .30316 .5068 L .34309 .54287 L .3815 .5696 L .40134 .58036 L .42237 .58951 L .43178 .59285 L .4419 .59593 L .45139 .59833 L .4602 .60014 L .47031 .60171 L .47564 .60233 L .47838 .60258 L .48134 .60282 L .48416 .603 L .48676 .60313 L .48925 .60323 L .4905 .60326 L .4912 .60328 L .49187 .60329 L .49312 .60331 L .49426 .60332 L .49548 .60332 L .49617 .60332 L .49681 .60331 L .49788 .6033 L .49905 .60328 L .50027 .60325 L .50143 .60322 L .50386 .60312 L .50612 .60301 L .51126 .60265 L .51626 .60217 L .52161 .60151 L .5313 .59994 L .54011 .59809 L .5593 .59268 L .58009 .58467 L .62101 .56244 L .66042 .53294 L .6983 .49714 L .73864 .45103 L .77747 .39892 L .81874 .33523 L Mistroke .8585 .26585 L .89675 .19172 L .93745 .10491 L .97619 .01472 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{308, 308}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol0 021oo`03001oogoo00eoo`03001oogoo0;1oo`03001oogoo04ioo`0087oo0P003goo00<007ooOol0 [Woo00<007ooOol0Cgoo000POol00`00Oomoo`0>Ool00`00Oomoo`2^Ool00`00Oomoo`1?Ool0021o o`03001oogoo00moo`03001oogoo0:aoo`03001oogoo051oo`0087oo00<007ooOol03goo00<007oo Ool0[7oo00<007ooOol0D7oo000POol00`00Oomoo`0@Ool00`00Oomoo`2ZOol00`00Oomoo`1AOol0 021oo`03001oogoo011oo`03001oogoo0:Yoo`03001oogoo055oo`0087oo0P004Woo00<007ooOol0 Z7oo00<007ooOol0DWoo000POol00`00Oomoo`0AOol00`00Oomoo`2XOol00`00Oomoo`1BOol0021o o`03001oogoo019oo`03001oogoo0:Ioo`03001oogoo05=oo`0087oo00<007ooOol04Woo00<007oo Ool0YWoo00<007ooOol0Dgoo000POol00`00Oomoo`0COol00`00Oomoo`2UOol00`00Oomoo`1COol0 0004Ool000000004Ool20004Ool20004Ool20004Ool30003Ool00`00Oomoo`0COol00`00Oomoo`2T Ool00`00Oomoo`1DOol0009oo`03001oogoo00=oo`8000=oo`04001oogoo0002Ool01000Oomoo`00 17oo00<007ooOol00Woo00<007ooOol057oo00<007ooOol0Xgoo00<007ooOol0E7oo0002Ool00`00 Oomoo`08Ool01000Oomoo`000Woo00@007ooOol0009oo`@000=oo`<001Aoo`03001oogoo0:9oo`03 001oogoo05Eoo`000Woo00<007ooOol027oo00@007ooOol0009oo`04001oogoo0002Ool00`00Ool0 0004Ool00`00Oomoo`0EOol00`00Oomoo`2QOol00`00Oomoo`1EOol0009oo`03001oogoo00Qoo`04 001oogoo0002Ool01000Oomoo`000Woo00<007oo000017oo00<007ooOol05Goo00<007ooOol0X7oo 00<007ooOol0EWoo00000goo0000000;Ool20004Ool20004Ool20004Ool00`00Oomoo`0FOol00`00 Oomoo`2OOol00`00Oomoo`1FOol0021oo`03001oogoo01Ioo`03001oogoo09ioo`03001oogoo05Mo o`0087oo00<007ooOol05goo00<007ooOol0WGoo00<007ooOol0Egoo000POol2000HOol00`00Oomo o`2LOol00`00Oomoo`1HOol0021oo`03001oogoo01Qoo`03001oogoo09Yoo`03001oogoo05Uoo`00 87oo00<007ooOol067oo00<007ooOol0VWoo00<007ooOol0FGoo000POol00`00Oomoo`0IOol00`00 Oomoo`2HOol00`00Oomoo`1JOol0021oo`03001oogoo01Uoo`03001oogoo09Qoo`03001oogoo05Yo o`0087oo00<007ooOol06Woo00<007ooOol0UWoo00<007ooOol0Fgoo000POol00`00Oomoo`0JOol0 0`00Oomoo`2EOol00`00Oomoo`1LOol0021oo`8001aoo`03001oogoo09Aoo`03001oogoo05aoo`00 87oo00<007ooOol06goo00<007ooOol0Tgoo00<007ooOol0GGoo000POol00`00Oomoo`0LOol00`00 Oomoo`2BOol00`00Oomoo`1MOol0021oo`03001oogoo01eoo`03001oogoo091oo`03001oogoo05io o`0087oo00<007ooOol07Goo00<007ooOol0Sgoo00<007ooOol0Ggoo000POol00`00Oomoo`0NOol0 0`00Oomoo`2>Ool00`00Oomoo`1OOol0021oo`8001moo`03001oogoo08eoo`03001oogoo061oo`00 87oo00<007ooOol07goo00<007ooOol0S7oo00<007ooOol0H7oo000POol00`00Oomoo`0OOol00`00 Oomoo`2;Ool00`00Oomoo`1QOol0021oo`03001oogoo021oo`03001oogoo08Uoo`03001oogoo069o o`0087oo00<007ooOol087oo00<007ooOol0RGoo00<007ooOol0HWoo000017oo0000000017oo0P00 17oo0P0017oo0P0017oo0P0017oo00<007ooOol08Goo00<007ooOol0Qgoo00<007ooOol0Hgoo0002 Ool00`00Oomoo`03Ool20003Ool01000Oomoo`000Woo00@007ooOol0009oo`04001oogoo0003Ool0 0`00Oomoo`0ROol00`00Oomoo`25Ool00`00Oomoo`1TOol0009oo`03001oogoo00Qoo`04001oogoo 0002Ool01000Oomoo`000Woo00@007ooOol000=oo`<0029oo`03001oogoo08Eoo`03001oogoo06Ao o`000Woo00<007ooOol027oo00@007ooOol0009oo`04001oogoo0002Ool30004Ool00`00Oomoo`0S Ool00`00Oomoo`23Ool00`00Oomoo`1UOol0009oo`03001oogoo00Qoo`04001oogoo0002Ool01000 Oomoo`000Woo00<007ooOol017oo00<007ooOol097oo00<007ooOol0PWoo00<007ooOol0IGoo0000 0goo0000000;Ool20004Ool20004Ool30003Ool00`00Oomoo`0TOol00`00Oomoo`21Ool00`00Oomo o`1VOol0021oo`03001oogoo02Eoo`03001oogoo07moo`03001oogoo06Moo`0087oo00<007ooOol0 9Goo00<007ooOol0Ogoo00<007ooOol0Igoo000POol2000WOol00`00Oomoo`1mOol00`00Oomoo`1X Ool0021oo`03001oogoo02Moo`03001oogoo07]oo`03001oogoo06Uoo`0087oo00<007ooOol09goo 00<007ooOol0Ngoo00<007ooOol0JGoo000POol00`00Oomoo`0XOol00`00Oomoo`1iOol00`00Oomo o`1ZOol0021oo`03001oogoo02Uoo`03001oogoo07Moo`03001oogoo06]oo`0087oo00<007ooOol0 :Goo00<007ooOol0MWoo00<007ooOol0K7oo000POol00`00Oomoo`0ZOol00`00Oomoo`1eOol00`00 Oomoo`1/Ool0021oo`8002aoo`03001oogoo07=oo`03001oogoo06eoo`0087oo00<007ooOol0;7oo 00<007ooOol0LGoo00<007ooOol0KWoo000POol00`00Oomoo`0]Ool00`00Oomoo`1_Ool00`00Oomo o`1_Ool0021oo`03001oogoo02ioo`03001oogoo06ioo`03001oogoo06moo`0087oo00<007ooOol0 ;Woo00<007ooOol0KGoo00<007ooOol0L7oo000POol00`00Oomoo`0_Ool00`00Oomoo`1[Ool00`00 Oomoo`1aOol0021oo`80035oo`03001oogoo06Uoo`03001oogoo079oo`0087oo00<007ooOol0Goo00<007ooOol0Egoo00<007ooOol0Ngoo000POol00`00 Oomoo`0jOol00`00Oomoo`1EOol00`00Oomoo`1lOol0021oo`03001oogoo03]oo`8005Aoo`03001o ogoo07eoo`0087oo0P00?Woo00<007ooOol0D7oo00<007ooOol0OWoo000POol00`00Oomoo`0nOol0 0`00Oomoo`1>Ool00`00Oomoo`1oOol0021oo`03001oogoo03moo`03001oogoo04aoo`03001oogoo 081oo`0087oo00<007ooOol0@7oo00<007ooOol0BWoo00<007ooOol0PGoo000POol00`00Oomoo`11 Ool00`00Oomoo`18Ool00`00Oomoo`22Ool0021oo`03001oogoo049oo`03001oogoo04Eoo`8008Eo o`0087oo00<007ooOol0@goo00<007ooOol0@goo00<007ooOol0QGoo000POol20015Ool20012Ool0 0`00Oomoo`26Ool0021oo`03001oogoo04Ioo`03001oogoo03eoo`8008Uoo`0087oo00<007ooOol0 Agoo0P00?7oo00<007ooOol0RGoo000POol00`00Oomoo`19Ool00`00Oomoo`0hOol00`00Oomoo`2: Ool0021oo`03001oogoo04Yoo`8003Moo`03001oogoo08]oo`0087oo00<007ooOol0C7oo00<007oo Ool0Ool2000`Ool2002@Ool0021oo`03001oogoo04moo`03001oogoo 02]oo`80099oo`0087oo00<007ooOol0D7oo00<007ooOol0:Goo00<007ooOol0TWoo000POol00`00 Oomoo`1AOol2000WOol2002EOol000Moo`<000Aoo`8000Aoo`8000=oo`<000Aoo`03001oogoo05=o o`<0025oo`<009Moo`0027oo00<007ooOol00goo0P000goo00@007ooOol000=oo`03001oogoo00=o o`03001oogoo05Ioo`@001Uoo`@009Yoo`0027oo00<007ooOol027oo00@007ooOol000=oo`03001o ogoo00=oo`<005Yoo`8001Eoo`8009ioo`0027oo00<007ooOol027oo00@007ooOol000=oo`03001o ogoo00=oo`03001oogoo05aoo`H000Yoo`D00:1oo`0027oo00<007ooOol027oo00@007ooOol000=o o`03001oogoo00=oo`03001oogoo069oo`X00:Eoo`001goo0P002goo0P000goo0P001Goo00<007oo Ool0ogoo4Woo000POol00`00Oomoo`3oOolBOol0021oo`03001oogoo0?mooa9oo`00ogoo=Goo003o OoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo000TOol00`00Oomoo`0< Ool00`00Oomoo`3nOol0019oo`03001oogoo00D000Aoo`03001oogoo009oo`03001oogoo00Yoo`05 001oogooOol0003oOol000Uoo`04001oogoo0005Ool00`00Oomoo`09Ool01@00Oomoogoo000017oo 1@0017oo00<007ooOol00Woo00<007ooOol0o7oo0009Ool01000Oomoo`0017oo00<007ooOol02Goo 00<007ooOol00Woo00<007ooOol017oo00<007ooOol00goo00<007ooOol00goo00<007ooOol0o7oo 0009Ool40004Ool00`00Oomoo`09Ool00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`03Ool0 0`00Oomoo`03Ool00`00Oomoo`3lOol000Uoo`04001oo`000003Ool00`00Oomoo`09Ool00`00Oomo o`03Ool00`00Oomoo`04Ool00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`3lOol000Uoo`04 001oogoo0003Ool00`00Oomoo`09Ool00`00Oomoo`04Ool00`00Oomoo`02Ool20004Ool00`00Oomo o`03Ool00`00Oomoo`3mOol000Qoo`80009oo`800003Ool007oo00Yoo`03001oogoo00Ioo`03001o ogoo00Ioo`03001oogoo00=oo`03001oogoo0?ioo`003goo00<007ooOol02Goo00<007ooOol02goo 00D007ooOomoo`000?moo`Moo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol0 0?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo =Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol0 0?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo =Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol0 0?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo =Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol0 0?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo =Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol0 0?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo=Goo003oOoleOol00?moocEoo`00ogoo =Goo003oOoleOol00001\ \>"], ImageRangeCache->{{{0, 307}, {307, 0}} -> {-0.155048, 0.993609, 0.0047306, 7.73159*^-5}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData["\n\nIs the maximum fitness at the ESS?"], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[{ "\nGo back to the top of the Red text to run the program again.\n\n\n\n\ Please close the application ", StyleBox["Mathematica", FontSlant->"Italic"], " when you are finished. This will reset the variables for the next \ person." }], "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell["\<\ k=. a=. ai=. R=. V=.\ \>", "Input", AspectRatioFixed->True] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{4, 1280}, {0, 832}}, WindowToolbars->{}, CellGrouping->Automatic, WindowSize->{943, 568}, WindowMargins->{{136, Automatic}, {76, Automatic}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, 128}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, CharacterEncoding->"MacintoshAutomaticEncoding", Magnification->2, StyleDefinitions -> "Classroom.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1754, 51, 523, 16, 260, "Text", Evaluatable->False], Cell[2280, 69, 1060, 27, 533, "Text", Evaluatable->False], Cell[3343, 98, 129, 5, 243, "Input"], Cell[3475, 105, 421, 15, 157, "Text", Evaluatable->False], Cell[3899, 122, 757, 27, 95, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[4681, 153, 58, 1, 117, "Input"], Cell[4742, 156, 49, 1, 119, "Output"] }, Open ]], Cell[4806, 160, 546, 19, 153, "Text", Evaluatable->False], Cell[5355, 181, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[5860, 203, 54, 1, 117, "Input"], Cell[5917, 206, 42, 1, 119, "Output"] }, Open ]], Cell[5974, 210, 382, 12, 184, "Text", Evaluatable->False], Cell[6359, 224, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[6864, 246, 75, 1, 117, "Input"], Cell[6942, 249, 82, 1, 151, "Output"] }, Open ]], Cell[7039, 253, 373, 12, 184, "Text", Evaluatable->False], Cell[7415, 267, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[7920, 289, 55, 1, 117, "Input"], Cell[7978, 292, 122, 3, 151, "Output"] }, Open ]], Cell[8115, 298, 390, 12, 184, "Text", Evaluatable->False], Cell[8508, 312, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[9013, 334, 63, 1, 117, "Input"], Cell[9079, 337, 159, 2, 151, "Output"] }, Open ]], Cell[9253, 342, 458, 13, 219, "Text", Evaluatable->False], Cell[9714, 357, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[10219, 379, 70, 1, 117, "Input"], Cell[10292, 382, 161, 2, 151, "Output"] }, Open ]], Cell[10468, 387, 315, 10, 102, "Text", Evaluatable->False], Cell[10786, 399, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[11291, 421, 63, 1, 117, "Input"], Cell[11357, 424, 121, 2, 151, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11515, 431, 63, 1, 119, "Input"], Cell[11581, 434, 289, 4, 222, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11907, 443, 46, 1, 119, "Input"], Cell[11956, 446, 191, 4, 151, "Output"] }, Open ]], Cell[12162, 453, 934, 23, 489, "Text", Evaluatable->False], Cell[13099, 478, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[13604, 500, 71, 4, 144, "Input"], Cell[13678, 506, 39, 1, 119, "Output"], Cell[13720, 509, 39, 1, 119, "Output"] }, Open ]], Cell[13774, 513, 343, 11, 149, "Text", Evaluatable->False], Cell[14120, 526, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[14625, 548, 71, 1, 117, "Input"], Cell[14699, 551, 85, 1, 146, "Output"] }, Open ]], Cell[14799, 555, 420, 14, 243, "Text", Evaluatable->False], Cell[15222, 571, 340, 10, 55, "Text", Evaluatable->False], Cell[15565, 583, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[16070, 605, 76, 4, 144, "Input"], Cell[16149, 611, 67, 1, 146, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[16253, 617, 52, 1, 119, "Input"], Cell[16308, 620, 80, 1, 151, "Output"] }, Open ]], Cell[16403, 624, 263, 6, 184, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[16691, 634, 46, 1, 119, "Input"], Cell[16740, 637, 97, 2, 155, "Output"] }, Open ]], Cell[16852, 642, 622, 11, 430, "Text", Evaluatable->False], Cell[17477, 655, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[17982, 677, 61, 4, 118, "Input"], Cell[18046, 683, 35, 1, 93, "Output"] }, Open ]], Cell[18096, 687, 236, 6, 149, "Text", Evaluatable->False], Cell[18335, 695, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[18840, 717, 46, 1, 91, "Input"], Cell[18889, 720, 35, 1, 93, "Output"] }, Open ]], Cell[18939, 724, 363, 12, 90, "Text", Evaluatable->False], Cell[19305, 738, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[19810, 760, 59, 1, 91, "Input"], Cell[19872, 763, 38, 1, 120, "Output"] }, Open ]], Cell[19925, 767, 512, 16, 184, "Text", Evaluatable->False], Cell[20440, 785, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[20945, 807, 268, 9, 134, "Input"], Cell[21216, 818, 24854, 623, 411, 8575, 418, "GraphicsData", "PostScript", \ "Graphics"], Cell[46073, 1443, 130, 3, 93, "Output"] }, Open ]], Cell[46218, 1449, 539, 16, 325, "Text", Evaluatable->False], Cell[46760, 1467, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[47265, 1489, 268, 9, 134, "Input"], Cell[47536, 1500, 22699, 597, 360, 8558, 418, "GraphicsData", "PostScript", \ "Graphics"], Cell[70238, 2099, 130, 3, 93, "Output"] }, Open ]], Cell[70383, 2105, 706, 21, 465, "Text", Evaluatable->False], Cell[71092, 2128, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[71597, 2150, 268, 9, 134, "Input"], Cell[71868, 2161, 24958, 686, 300, 9576, 492, "GraphicsData", "PostScript", \ "Graphics"], Cell[96829, 2849, 130, 3, 93, "Output"] }, Open ]], Cell[96974, 2855, 560, 16, 294, "Text", Evaluatable->False], Cell[97537, 2873, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[98042, 2895, 48, 1, 91, "Input"], Cell[98093, 2898, 37, 1, 93, "Output"] }, Open ]], Cell[98145, 2902, 351, 12, 55, "Text", Evaluatable->False], Cell[98499, 2916, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[99004, 2938, 55, 1, 91, "Input"], Cell[99062, 2941, 41, 1, 120, "Output"] }, Open ]], Cell[99118, 2945, 556, 16, 266, "Text", Evaluatable->False], Cell[99677, 2963, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[100182, 2985, 268, 9, 134, "Input"], Cell[100453, 2996, 24275, 616, 407, 8575, 418, "GraphicsData", "PostScript", \ "Graphics"], Cell[124731, 3614, 130, 3, 93, "Output"] }, Open ]], Cell[124876, 3620, 591, 17, 266, "Text", Evaluatable->False], Cell[125470, 3639, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[125975, 3661, 268, 9, 134, "Input"], Cell[126246, 3672, 23262, 604, 378, 8558, 418, "GraphicsData", "PostScript", \ "Graphics"], Cell[149511, 4278, 130, 3, 93, "Output"] }, Open ]], Cell[149656, 4284, 687, 16, 430, "Text", Evaluatable->False], Cell[150346, 4302, 480, 18, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[150851, 4324, 268, 9, 134, "Input"], Cell[151122, 4335, 28423, 704, 367, 9203, 462, "GraphicsData", "PostScript", \ "Graphics"], Cell[179548, 5041, 130, 3, 93, "Output"] }, Open ]], Cell[179693, 5047, 680, 20, 235, "Text", Evaluatable->False], Cell[180376, 5069, 491, 13, 125, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[180892, 5086, 50, 1, 91, "Input"], Cell[180945, 5089, 36, 1, 93, "Output"] }, Open ]], Cell[180996, 5093, 347, 11, 55, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[181368, 5108, 55, 1, 91, "Input"], Cell[181426, 5111, 40, 1, 120, "Output"] }, Open ]], Cell[181481, 5115, 472, 15, 184, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[181978, 5134, 268, 9, 134, "Input"], Cell[182249, 5145, 18474, 531, 638, 8070, 398, "GraphicsData", "PostScript", \ "Graphics"], Cell[200726, 5678, 130, 3, 93, "Output"] }, Open ]], Cell[200871, 5684, 479, 15, 184, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[201375, 5703, 268, 9, 134, "Input"], Cell[201646, 5714, 17080, 514, 540, 8065, 398, "GraphicsData", "PostScript", \ "Graphics"], Cell[218729, 6230, 130, 3, 93, "Output"] }, Open ]], Cell[218874, 6236, 403, 12, 278, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[219302, 6252, 268, 9, 134, "Input"], Cell[219573, 6263, 21927, 598, 632, 8547, 428, "GraphicsData", "PostScript", \ "Graphics"], Cell[241503, 6863, 130, 3, 93, "Output"] }, Open ]], Cell[241648, 6869, 319, 10, 149, "Text", Evaluatable->False], Cell[241970, 6881, 524, 17, 325, "Text", Evaluatable->False], Cell[242497, 6900, 71, 7, 199, "Input"] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)