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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?
\
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NOW DEFINE THE VARIABLE, V, AS THE RATIO OF EGGS IN THE POPULATION TO SPERM \
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\
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TOTAL FITNESS OF THE INDIVIDUAL IS THE SUM OF FITNESS THROUGH FEMALE + MALE \
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\
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NOW CALCULATE THE FIRST DERIVATIVE OF INDIVIDUAL FITNESS WITH RESPECT TO  \
ALLOCATION TO MALE FUNCTION.
\
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CALCULATE THE SECOND DERIVATIVE OF INDIVIDUAL FITNESS AS A FUNCTION OF ITS \
ALLOCATION TO MALE FUNCTION.  Remember, local stability requires a negative \
second derivative
\
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SIMPLIFY THE SECOND DERIVATIVE. \
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SET THE FIRST DERIVATIVE EQUAL TO ZERO AND SOLVE FOR a.  
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a = (k - 1)/(2*k -1)\
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The ESS can be found for two mates by simplifying the population allocation, \
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Right!  Linear increase in fitness with increasing allocation to female \
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Bueno, Now let's plot the relationship between total fitness and the \
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Right!  Linear increase in fitness with increasing allocation to female \
function.  (This is a consequence of our assumtion that female function is \
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from right to left; it's equal to 1 - ai.  


Finally, let's plot the relationship between total fitness and the allocation \
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