Stochastic and deterministic models for age-structured populations with genetically variable traits

Regis Ferriere (1) , Viet Chi Tran (2)

1 EEB - Ecology and Evolutionary Biology [Tucson]
2 LPP - Laboratoire Paul Painlevé - UMR 8524

This work is a proceeding of the CANUM 2008 conference. Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. In a large population limit, the random process converges to the solution of a Gurtin-McCamy type PDE. We show that the random model has a long time behavior that differs from its deterministic limit. However, the results on the limiting PDE and large deviation techniques \textit{à la} Freidlin-Wentzell provide estimates of the extinction time and a better understanding of the long time behavior of the stochastic process. This has applications in the theory of Adaptive Dynamics. In a last section, we present on simulations three biological issues dealing with the consequences of size plasticity when taking growth into account, with growth-reproduction trade-offs and with periodic behavior.

Mots clés: Population dynamics; age-structure; individual-centered model; large population scaling; extinction; reproduction-growth trade-off

Domaines: Probabilités [math.PR]; Ecologie, Environnement; Biodiversité et Ecologie

Regis Ferriere, Viet Chi Tran. Stochastic and deterministic models for age-structured populations with genetically variable traits. 2008. ⟨hal-00323683v1⟩