Replicator dynamics as the large population limit of a discrete Moran process

Abstract: The replicator dynamics accomplishes the task of modelling the evolution of strategies in a population by subjecting the probability of reproduction to their fitness: The higher the fitness, the higher the chance of being selected to reproduce. Yet, the criterion followed by individual agents to select their strategies is latent in the replicator equation, which describes the continuous-time evolution of the proportions of strategies in an averaged fashion.

In this talk, we provide a mathematical framework to derive the replicator equation as a mean-field limit of a discrete stochastic process modelling this evolutionary mechanism from the point of view of individual agents and their pairwise interactions. In this context, the classical Moran process is a prototypical example of discrete stochastic process that models natural selection in finite populations with two strategies (alleles, in biology) competing for dominance. We study the mean-field limit of a generalised Moran process as the number of agents diverges and we show that, in the weak selection regime, it converges to the replicator dynamics.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)