Back to Search Start Over

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

Authors :
Metz, J.
Tran, Viet
Source :
Journal of Mathematical Biology. Mar2013, Vol. 66 Issue 4/5, p915-933. 19p.
Publication Year :
2013

Abstract

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61:277-318, ) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23:114-135, ) and Diekmann et al. (Nieuw Archief voor Wiskunde 4:82-109, ). 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 through 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., loc. cit.). [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
03036812
Volume :
66
Issue :
4/5
Database :
Academic Search Index
Journal :
Journal of Mathematical Biology
Publication Type :
Academic Journal
Accession number :
85597285
Full Text :
https://doi.org/10.1007/s00285-012-0619-5