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Daphnias: from the individual based model to the large population equation.
MedLine Citation:
PMID:  23143391     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
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 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.).
Authors:
J A J Metz; Viet Chi Tran
Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2012-11-11
Journal Detail:
Title:  Journal of mathematical biology     Volume:  -     ISSN:  1432-1416     ISO Abbreviation:  J Math Biol     Publication Date:  2012 Nov 
Date Detail:
Created Date:  2012-11-12     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Affiliation:
EEP, IIASA, Laxenburg, Austria, j.a.j.metz@biology.leidenuniv.nl.
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