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| HAL : hal-00697716, version 1 |
| arXiv : 1205.4919 |
| DOI : 10.1007/s00285-012-0619-5 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Mathematical Biology 66, 4-5 (2013) 915--933 |
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| Daphnias: from the individual based model to the large population equation |
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| J.A.J. Metz 1Viet Chi Tran 2, 3 |
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| (2013) |
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| The class of deterministic 'Daphnia' models treated by Diekmann et~al. (J Math Biol 61: 277--318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114--135, 1983) and Diekmann et~al. (Nieuw Archief voor Wiskunde 4: 82--109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et~al., l.c.). |
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| 1 : | Mathematical institute |
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Leiden University |
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| 2 : | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| 3 : | Laboratoire Paul Painlevé (LPP) |
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CNRS : UMR8524 – Université Lille I - Sciences et technologies |
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| Domaine | : | Mathématiques/Probabilités Sciences de l'environnement/Biodiversité et Ecologie |
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| Birth and death process – age and size-structured populations – stochastic interacting particle systems – piecewise deterministic motion – large population limits |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00697716, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00697716 | |
| oai:hal.archives-ouvertes.fr:hal-00697716 | |
| Contributeur : Viet Chi Tran | |
| Soumis le : Mardi 22 Mai 2012, 10:18:06 | |
| Dernière modification le : Mardi 19 Février 2013, 14:18:59 | |
