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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/13607 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/13607 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/13607 archive 351 disk0/00/01/02/20 2016-01-15 08:48:00 2021-08-27 17:22:56 2016-01-15 08:48:00 monograph show 3 Metz J.A.J. 7506 Tran V.C. pub iis_ecl prog_eep 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 in- teraction 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 descrining the IBM can be approximated by the delay equation featured in (Diekmann et al., loc. cit.). 2012 published IR-12-055 IR-12-055 206 public interim_report IIASA, Laxenburg, Austria 18 FALSE info:eu-repo/semantics/book