| Genetic drift |
Barbara Drossel, "Biological evolution and statistical physics," arXiv 0101409 e-print (2001) pp. 27--30
Carlo C. Maley at the Wistar Institute observes genetic diversity in Barrett's esophagus that progresses in ways that do not fit the picture of the rare and rapid fixation of a one mutant at a time in a population. Instead a variety of mutants can appear in quick succession before the initial mutant strain has enough time to dominate the population.
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Wright-Fisher reproduction simulation MatLab scripts for isolated populations and metapopulations
Using sets and pseudo-random number generators in MatLab to implement probabilistic models
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| Fitness landscapes and quasi-species |
Drossel, ibid, (2001), pp. 21--24
Brumer, Michor, Shakhnovich, "Genetic instability and the quasispecies model," J. Theor. Biol., 241: 216--222 (2006). Available online at Michor Lab web page.
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1-d fitness "landscape" Excel worksheet
Calculation of error threshold in a quasi-species model with a sharp-peak fitness landscape
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| Evolutionary game theory |
J. McKenzie Alexander, "Evolutionary game theory," Stanford Encyclopedia of Philosophy, 2002--2009 online. Sections 1 and 2.
Current uses of game theory involve complications, such as players that do not always breed true. See for instance the non-technical discussion by Casey Jones, "Game theory shows evolution follows most successful member," Ars Technica 2010 January 19 (Available online).
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2x2 evolutionary game with replicator dynamics Excel worksheet
Working with difference and differential equations using MatLab
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| Spatially-resolved models |
Alexander, ibid (2002--2009), Figures 4, 5, and 6.
Nowak and May, "Evolutionary games and spatial chaos," Nature 359: 826--829 (1992).
Benjamin C. Kirkup and Margaret A. Riley, "Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo," Nature 428, 412--414 (2004).
Benjamin Kerr, Margaret A. Riley, Marcus W. Feldman, and Brendan J. M. Bohannan, "Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors," Nature 418, 171--174 (2002).
Modern spatially-resolved models sometimes explicitly describe diffusion of chemicals that influence cell growth so some cellular interactions occur indirectly. Irregular lattices can be used instead of rectangular lattices. J. L. Gevertz and S. Torquato, "Modeling the effects of vasculature evolution on early brain tumor growth," J. Theor. Biol. 243: 517 (2006). Available online from Sal Torquato's publications page.
C. Athena Aktipis, Arizona State University, has prepared a guide to agent-based modeling including links to free graphical-user-interface-based software for modeling agents in spatially-resolved environments.
See erratum re: Nowak and May description in dissertation and tutorial.
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Spatially-resolved simulation MatLab scripts
Using arrays to represent local processes in spatially-distributed systems in MatLab: Using the convolution theorem for efficient computation.
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