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DY: Fachverband Dynamik und Statistische Physik

DY 9: Poster I: Statistical Physics in Biological Systems (joint with BP)

DY 9.17: Poster

Montag, 11. März 2013, 17:30–19:30, Poster B2

Mutation and Migration in Structured Populations — •Matthias Lechner, Jonas Cremer, Anna Melbinger, and Erwin Frey — Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München

Despite the risk of exploitation, altruistic individuals are a common phenomenon in nature. The solution to this so called Dilemma of Cooperation is the purpose of many models in the field of evolutionary dynamics. A recent approach to explain this dilemma is to combine population dynamics with evolutionary game theory in a stochastic description, which shows a transient initial increase of cooperation [1]. This model was then extended by a group-structured population that is subject to repetitive regrouping events, giving rise to a long-term maintenance of cooperation under certain initial conditions [2].

Here, we study the consequences of introducing mutation and migration to this model. With the use of numerical simulations we show that both have similar effects on the system's dynamics. The evolution of purely cooperative groups turns out to be pivotal in the explanation of these changes. For mutation, we support this claim by an analytical approximation, which reproduces our numerical results. In summary, we find that although mutation and migration eventually inhibit cooperation in this model, cooperative behavior is still maintained for a wide range of parameters.

[1] A. Melbinger et al., PRL 105, 178101 (2010)

[2] J. Cremer et al., Scientific Reports, 2, 281 (2012)