## Math Biology Seminar: Joe Yuichiro Wakano

- Date: 10/03/2018
- Time: 15:00

University of British Columbia

Derivation of replicator-mutator equation as a limit of individual-based simulations

We introduce a Markov chain model to study evolution of a continuous trait based on population genetics. It corresponds to individual-based model which includes frequency dependent selection caused by m-player game interactions and stochastic fluctuations due to random genetic drift and mutation. We prove that under a proper scaling limit as the population size increases the system converges to the solution of replicator-mutator equations. Our result establishes an affirmative mathematical base to the adaptive dynamics formulation employed in the theory of the mathematical biology.

Location: ESB 4127