Regensburg 2010 – scientific programme

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BP: Fachverband Biologische Physik

BP 35: Posters: Statistical Physics, Evolution, and Networks

BP 35.12: Poster

Thursday, March 25, 2010, 17:15–20:00, Poster B2

Fixation time in zero-sum and non zero-sum cyclic coevolution — •Markus Schütt and Jens Christian Claussen — Inst. für Neuro- und Bioinformatik, Universität zu Lübeck

In the territorial and mating behavior of Uta stanburiana, as well as in the colicin secretion and resistance, cyclic coevolutionary dynamics is observed. The coevolutionary payoff matrix has the structure of the rock-paper-scissors (RPS) game, which typically is zero-sum: what one player loses, equals the gain of the winning opponent. In biology, payoffs are difficult to measure, but in general the game can deviate from the zero-sum condition, and the examples mentioned above represent the positive and negative sum cases. In previous work, we have shown that a positive-sum game can stabilize the coexistence (and therefore preserve biodiversity) for a population size below a critical value [1], similar as for the Moran process in cyclic bimatrix games [2]. Here [3], we investigate the scaling of the fixation time and show that the crossover from polynomial to exponential scaling is consistent with the drift reversal as demonstrated in [1].

[1] JC Claussen and A Traulsen, Phys. Rev. Lett (2008)

[2] JC Claussen, Eur. Phys. J. (2007)

[3] M Schütt and JC Claussen (in preparation)