## MAP-PDMA

**Filipe Martins**

*CMUP - University of Porto*

**Abstract ::** In this talk I will consider evolutionary game theoretic versions of a general class of matrix models frequently used in population dynamics. The evolutionary components model the dynamics of a vector of mean phenotypic traits subject to natural selection [1]. One fundamental question in population and mathematical biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of other non-extinction equilibria. I will discuss this question through the prism of dynamic bifurcations. When the model parameters, more precisely, the inherent population growth rate, dynamic bifurcations occur, opening possibility for population persistence and recurrence, or to possible extinction. The results present a complete answer to a general class of evolutionary matrix models often used in mathematical biology, the mathematical assumption being that the matrix is primitive. I will present an application of the general theoretical results to an evolutionary version of a classic Ricker model. This application illustrates the theoretical results and, in addition, several other interesting dynamic phenomena.

Most part of the results and conclusions that I will talk about in this seminar are presented in [2] (joint work with Jim M. Cushing, Alberto Pinto and Amy Veprauskas).

[1] Joel S. Brown and Thomas L. Vincent, Evolutionary Game Theory, Natural Selection and Darwinian Dynamics, Cambridge University Press, 2005. [2] “A bifurcation theorem for evolutionary matrix models with multiple traits”, Journal of Mathematical Biology, Vol. 75, Issue 2, pp. 491–520, 2017.

Seminar Room of DMat-UMinho (3.08), and via zoom at

https://videoconf-colibri.zoom.us/j/94769148463?pwd=YWRVYjEzMkk2bmtMY2Q2OEhFM0hUdz09

Seminar for the Doctoral Program in Applied Mathematics (MAP-PDMA Seminar)