## Math Biology Seminar: Joe Yuichiro Wakano

- Date: 03/06/2014
- Time: 15:00

*Meji Institute for Advanced Study of Mathematical Sciences*

University of British Columbia

Evolutionary branching in deme-structured populations

Adaptive dynamics demonstrates that a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called "evolutionary branching." Evolutionary branching in spatial models such as island or meta-population models is still not completely understood. One summary statistics representing the effect of population structure on selection is relatedness. It is thus expected that the branching condition can be described in terms of relatedness coefficients in combination with disruptive selection intensity. Here, by constructing a model of the trait variance dynamics in the population, we obtain such an analytic prediction for the criteria of evolutionary branching in a deme-structured population. As an application of our theory, we evaluate the threshold migration rate below which evolutionary branching cannot occur in a pairwise interaction game. This agrees very well with the individual-based simulation results.

Location: ESB 2012