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Pré-Publication, Document De Travail Année : 2010

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

Résumé

A superprocess limit for an interacting birth-death particle system modelling a population with trait and 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 dynamics, on another time scale, averages to an equilibrium that depends 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.
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Dates et versions

hal-00495397 , version 1 (25-06-2010)
hal-00495397 , version 2 (03-08-2010)
hal-00495397 , version 3 (29-06-2011)
hal-00495397 , version 4 (12-08-2011)
hal-00495397 , version 5 (18-08-2011)

Identifiants

Citer

Sylvie Méléard, Viet Chi Tran. Slow and fast scales for superprocess limits of age-structured populations. 2010. ⟨hal-00495397v1⟩
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