A stochastic model of evolutionary dynamics with deterministic large-population asymptotics.
An evolutionary birth-death process is proposed as a model of evolutionary dynamics. Agents residing in a continuous spatial environment X, play a game G, with a continuous strategy set S, against other agents in the environment. The agents' positions and strategies continuously change in response to other agents and to random effects. Agents spawn asexually at rates that depend on their current fitness, and agents die at rates that depend on their local population density. Agents' individual evolutionary trajectories in X and S are governed by a system of stochastic ODEs. When the number of agents is large and distributed in a smooth density on (X,S), the collective dynamics of the entire population is governed by a certain (deterministic) PDE, which we call a fitness-diffusion equation.
Simon
Burton
B
Department of Mathematical Sciences, University of Colorado Denver, Campus Box 170, P.O. Box 173364, Denver, CO 80217-3364, USA. Burt.Simon@cudenver.edu
D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D005716:Game Theory; D008954:Models, Biological; D015233:Models, Statistical; D011156:Population Density; D011157:Population Dynamics