Title :

Daphnias: from the individual based model to the large population equation

Author(s) :

Metz, J.A.J. [Auteur]
Mathematical institute
Tran, Chi [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Mathematical Biology

Pages :

915--933

Publisher :

Springer

Publication date :

2013

ISSN :

0303-6812

English keyword(s) :

Birth and death process
age and size-structured populations
stochastic interacting particle systems
piecewise deterministic motion
large population limits

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Sciences de l'environnement/Biodiversité et Ecologie

English abstract : [en]

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 ...
Show more >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.).Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL