
A JumpGrowth Model for Predator–Prey Dynamics: Derivation and Application to Marine Ecosystems
Title  A JumpGrowth Model for Predator–Prey Dynamics: Derivation and Application to Marine Ecosystems 
Publication Type  Journal Article 
Year of Publication  2010 
Authors  Datta S, Delius GW, Law R 
Journal  Bulletin of Mathematical Biology 
Abstract  This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jumpgrowth equation, and a linear FokkerPlanck equation for the stochastic fluctuations. The McKendrickvon Foerster equation, used in previous studies, is shown to be a firstorder approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a powerlaw steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jumpgrowth equation and the McKendrickvon Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.

URL  http://arxiv.org/abs/0812.4968 
DOI  10.1007/s1153800994965 
Eprint number  arXiv:0812.4968

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Edited 22 Jun 2011  14:40 by gwd2
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