This repository derives analytical conditions for strategy evolution in populations using methods based on coalescent theory and/or pair approximation.
We use the sympy module in Python to derive famous results in classic papers. All detailed descriptions are provided in the Jupyter notebooks.
The three papers involved are:
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Fu F, Nowak MA, Christakis NA, Fowler JH. The evolution of homophily. Scientific reports. 2012 Nov 13;2(1):845.
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Antal T, Traulsen A, Ohtsuki H, Tarnita CE, Nowak MA. Mutation-selection equilibrium in games with multiple strategies. Journal of theoretical biology. 2009 Jun 21;258(4):614-22.
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Ohtsuki H, Hauert C, Lieberman E, Nowak MA. A simple rule for the evolution of cooperation on graphs and social networks. Nature. 2006 May 25;441(7092):502-5.