Slow and fast scales for superprocess limits of age-structured populations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Meleard, Sylvie²  Viet Chi Tran^1,2 

[1] Univ Sci & Technol Lille 1, Lab Paul Paineve, CNRS, UMR 8524, F-59655 Villeneuve Dascq, France

[2] Ecole Polytech, CNRS, Ctr Math Appl, UMR 7641, F-91128 Palaiseau, France

关键词: Interacting particle system;    Age-structure;    Superprocess;    Slow and fast scales;    Trait-structured density-dependent population;   

DOI  :  10.1016/j.spa.2011.08.007

来源: Elsevier

【 摘 要 】

A superprocess limit for an interacting birth-death particle system modeling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while ages are set to zero. Because of interactions between individuals, standard approaches based on the Laplace transform do not hold. We use a martingale problem approach and a separation of the slow (trait) and fast (age) scales. While the trait marginals converge in a pathwise sense to a superprocess, the age distributions, on another time scale, average to equilibria that depend on traits. The convergence of the whole process depending on trait and age, only holds for finite-dimensional time-marginals. We apply our results to the study of examples illustrating different cases of trade-off between competition and senescence. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free