Theoretical Ecology,
L577, Spring 2011 COURSE WEBPAGE
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Instructor: Spencer Hall, Department of Biology Contact: email: sprhall@indiana.edu Phone: Office (812-85)5-6009,
cell 812-679-8858 Office: Meeting Time: Monday and Wednesdays, 1:30 - 2:45 pm and Location Jordan
Hall 248 (Cleland Room) Office hours: By
appointment OR just stop in (usually 9:30 am – 5 pm M-F) Course: www.indiana.edu/~halllab/courses/L577.htm webpage Posted
on this webpage: (1) lecture note templates (print and bring to
class) (2) topic assignments assignments,
and (3) code (Mathematica and Matlab);
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i. Preliminary stuff
Logistics and syllabus –
first day handout (PDF)
Helpful math stuff (Index
from Case 2000) (PDF)
Introduction to Matlab (see below)
List of
books from which readings are chosen and other books I consult for the
course.
Topic 1 Introduction
to models and stability analysis (
(Lecture
notes) (Assignment) (Mathematica Tutorial right-click notebook, save, then open)
(PPT
slides for LSA) (LSA
example: logistic)
More advanced intro to models: (Kooijman’s guide)
Local stability analysis (Case,
very readable) (Gurney
and Nisbet)
(Murdoch
et al.)
Yikes – calculus! Helpful math stuff (Appendix
from Case 2000)
More calculus primers: a more bare-bones one
(1
PDF); two with more packaging (2
PDF) (3
PDF)
‘Big fancy models’ forum on complex vs.
simple models in Ecology
Topic 2 Population
growth (exponential growth, density dependence in continuous and
discrete time, oscillations
and chaos)
(Lecture
notes) (Assignment) (Zip file of
Code) (Matlab Tutorial)
(Cobwebbing slide)
Reading: (Case
chapter 5) (Turchin Ch 3)
If you’re interest: (May
1974 Science) (May
and Oster 1976 AmNat) (Wikipedia article on
logistic map)
Topic 3 Harvest
models and introduction to more bifurcations (yield; transcritical
and fold
[saddle-node]
bifurcations, saddles, alternative stable states)
(Lecture
notes) (Assignment) (Zip file of
Code) (PPT
of harvest optimization) (Bifurcations
slides)
Reading: (Kot chapter 2) (Case on
Ludwig model)
If you’re interested: (Scheffer and Rinaldi 2000
Ecosystems) (Ludwig
et al. 1978 J Anim Ecol)
(Scheffer and Carpenter 2003 TREE) (Dakos
et al. 2008 PNAS)
Topic 4
the Jacobian matrix; competitive displacement, coexistence,
alternative stable
states; invasibility; nullclines)
(Lecture
notes) (Assignment) (Zip file of
code and tutorials)
Support: (Dynamicists Toolkit) (Derivation
of Interior LV-Comp Equilibrium)
If you’re interested: (Scheffer et al. 2003 PNAS)
Topic 5 Interspecific interactions II. Predator-prey
dynamics (functional responses,
neutral stability,
complex numbers and sinusoidal functions, eigenvalues;
generation of
predator-prey cycles; stable limit cycles; Hopf bifurcations)
(Lecture
notes) (Assignment)
(Zip file
of code)
For more info:
- Rootfinders, etc.
(Wikipedia on rootfinders) (Euler’s formula on
Wikipedia)
- Complex eigenvalues
to oscillations,
SRH’s attempt)
- Numerical integration from Numerical
Recipes – Runge Kutta and adaptive-step
RK
- If you’re interested: Crossing the Hopf in a live system
(Fussman et al. 2000 Science)
Topic 6 Interspecific interactions III. Multi-species
and disease models (global
bifurcations, homoclinic bifurcations; relative non-linearities
and Jensen’s
Inequality; chaotic attractors in 3D systems;
quasi-periodicity)
(Lecture
notes) (Assignment) (Matlab code zip file)
(Matlab tutorial, if needed) (Example
figure for 2B)
- Type IV functional responses and homoclinic bifurcations (Kot Chap 9) (Scheffer and Rinaldi 2000
Ecosystems)
- Cycles and coexistence: (Armstrong
and McGehee Am Nat 1980)
- Jensen’s inequality: (Ruel and Ayers TREE) (Chesson 2000 AREES)
- Floquet’s
multipliers: (Klausmeier 2008 Theoretical Ecology)
- Chaotic attractors: teacup: (Abrams
and Roth 1994 Ecology)
- Intro to host-parasitoid models: (Murdoch
et al. H-P models) More on
quasi-periodicity (Rohani et al.)
- Parasites and predators (Lafferty
and Kuris 2002 TREE)
Topic 7 Interspecific interactions IV. Niche models (Mechanistic competition models;
R*
again; the famous Resource Ratio model; rock-scissors-paper game,
heteroclinic
orbits, and fractal basins of attraction; assembly rules in food webs)
(Lecture
notes) (Assignment) (MBC Appendix) (Huisman slides)
Resource competition and resource ratio (RR):
(Grover 1997: Chap 2
) Resource-dependent food webs (Chap 6)
Mechanistic niche concept: (Leibold 1995 Ecology)
RR and disease (Smith 1993, Smith
and Holt 1996, Smith
2007)
Critique of RR: (Miller
et al. 2005 AmNat) (Wilson
et al reply) (Miller
et al’s response)
Multiple-species competition: (Huisman&Weissing ’01 Ecology) (Huisman&Weissing ’01 Am Nat)
Heteroclinic
cycles: Vandermeer chapter (here,
pg 136-139) Online
encyclopedias: (1) (2)
Permanence theory: (Hutson
and Law 1985)
Topic 8 Environmental
variation (stochasticity, time series analysis
basics, noise color;
synchrony and the
Moran effect; autoregressive processes; noise-excited
oscillations;
noise-induced chaos)
(Lecture notes: Part A Part B) (Slides: Part A Part B)
(Assignment) (Zipped Matlab code)
Time series basics: (Ranta et al., Ch 2) (Turchin Ch 7)
Exponential growth and white noise (Case,
Chap 2) (Wikipedia on averages)
Synchronicity: (Ranta et al., Ch 5) (Liebhold et al. 2004)
(Heino 1998) (Earn
et al. 1998)
Pink noise: (Halley 1995) Noisy population dynamics (Kaitala
et al. 1997)
Extinction and noise: (Ripa and Heino 1999)
Sinusoidally-forced
consumer resource: gleaner-opportunitist (Grover
1990), storage specialist (Grover
1991)
More seasonally-forced consumer-resource (Scheffer et al. 1997) (King 1999) (related: entrainment Vandemeer 1993)
Noise transmission in food webs: (Ripa et al. 1998 Am Nat)
Wavelets, disease, synchrony, traveling
waves: (Grenfell
et al. 2001 Nature)
(Wavelets,
Wikipedia)
Noise-induced chaos: (Rand
and Wilson 1991) (Dwyer
et al. 2004)
Books: Chatfield 1999 (time series) Nisbet
and Gurney 1982 (modeling fluctuating populations)
Turchin
2003 (overview of methods to tackle time series)
Case, Ted. 2000.
Theoretical ecology: an illustrated guide
Grover, Jim. 1997.
Resource competition. Chapman and Hall.
Gurney,
Bill, and Roger Nisbet. 1998. Ecological dynamics.
Hastings, Alan. 1997.
Population biology: concepts and models.
Springer
Kot, Mark. 2001.
Elements of mathematical ecology.
Murdoch et al. 2003.
Consumer-resource dynamics
Turchin, Peter.
2003. Complex population
dynamics: a theoretical/empirical synthesis.
LINKS:
Graeme Chandler’s
Introduction to Matlab (HTML)
– great place to start
Stephen Ellner
and John Guckenheimer’s Matlab
guide for Biologial Modeling (PDF)
SVC’s Tutorial (HTML)
David Griffith’s great PDF
tutorial (PDF)
Kristian Sandberb’s tutorial (HTML)
A page at IUPUI (HTML)
(B). Matlab
packages for analysis of models and statistics:
GRIND – a toolkit for analysis of ODEs, difference equations, etc.
FATHOM
– a toolkit for multivariate statistics
CL_MatCont –
continuation software for numerical characterization of bifurcations
TSA – a toolkit for time
series analysis
Different wavelets packages: