Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 5: Statistical physics in biological systems (joint session DY/BP)

DY 5.5: Vortrag

Montag, 25. Februar 2008, 15:30–15:45, MA 001

Drift reversal in asymmetric coevolutionary conflicts: Influence of the microscopic processes and the population size — •Jens Christian Claussen — Theoret. Phys. & Astrophys., Univ. Kiel

Coevolutionary dynamics in finite populations is investigated in chemical catalysis, biological evolution, social and economic systems; often formulated within the unifying framework of evolutionary game theory. From a payoff matrix characterizing the elementary interactions, traditionally evolutionary game theory proeceeds with the (deterministic) replicator equation ansatz tacitly assuming an infinite population size, In contrary, in finite populations the dynamics is inherently stochastic which can lead to new effects. In asymmetric conflicts between two populations with a cyclic dominance, a finite-size dependent drift reversal recently was demonstrated, depending on underlying microscopic process of the evolutionary update. Cyclic dynamics appears widely in biological coevolution, be it within a homogeneous population, or be it between disjunct populations (asymmetric conflicts) as female and male. Here the average drift is calculated analytically for the frequency-dependent Moran process and for different pairwise comparison processes. It is explicitely shown that the drift reversal cannot occur if the process relies on payoff differences between pairs of individuals. Further, also a linear comparison with the average payoff does not lead to a drift towards the internal fixed point. Hence the nonlinear comparison function of the frequency-dependent Moran process, together with its usage of nonlocal information via the average payoff, is essential for the (meta)stability of the internal fixed point.