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| HAL: hal-00495397, version 5 |
| arXiv: 1006.5136 |
| DOI: 10.1016/j.spa.2011.08.007 |
| Detailed view |  Export this paper |
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| Stochastic Processes and their Applications 122, 1 (2012) 250-276 |
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| Available versions: | v1 (2010-06-26) | v2 (2010-08-03) | v3 (2011-06-30) | v4 (2011-08-13) | v5 (2011-08-19) |
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| Slow and fast scales for superprocess limits of age-structured populations |
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Sylvie Méléard 1Viet Chi Tran 1, 2 |
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| (2012-01) |
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| A superprocess limit for an interacting birth-death particle system modelling 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. |
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| 1: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| 2: | Laboratoire Paul Painlevé (LPP) |
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CNRS : UMR8524 – Université Lille I - Sciences et technologies |
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| Subject | : | Mathematics/Probability Environmental Sciences/Biodiversity and Ecology |
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| Interacting particle system – age-structure – superprocess – slow and fast scales – trait-structured density-dependent population |
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| hal-00495397, version 5 | |
| http://hal.archives-ouvertes.fr/hal-00495397 | |
| oai:hal.archives-ouvertes.fr:hal-00495397 | |
| From: Viet Chi Tran | |
| Submitted on: Thursday, 18 August 2011 16:31:38 | |
| Updated on: Saturday, 26 November 2011 13:03:03 | |
