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International Conference on Mathematical Biology and

Annual Meeting of The Society for Mathematical Biology,

July 27-30, 2009

University of British Columbia, Vancouver

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Program

CTH4e
Jenny Burrow
University of York
Title Linking plankton dynamics and stochastic fish recruitment models
Abstract Fish larvae live in an extremely variable environment. They are small relative to the spatial scales of prey heterogeneity and to the turbulent fluid flow at these spatial scales; they have only a local knowledge of their immediate environment, limited by a visual perceptive distance of around one body length; and they are subject to massive mortality, with a newly hatched individual’s probability of survival to metamorphosis being O(1%) or less, driven by typical mortality rates of 10% per day in the larval stage. Because the key natural phenomena are inherently stochastic, deterministic models are likely to be inappropriate for quantifying recruitment. However, the usual stochastic modelling approach, which assumes that individual-based variability can be captured at the population level by a diffusion equation, may not be universally suitable. In particular, diffusion-based models cannot necessarily capture sudden jumps in growth caused by rare encounters with favourable patches of prey, or turbulent effects. Lévy process based models provide the necessary mathematical extensions to capture these jumps. Initial work has extended simple diffusion-based models of larval growth to Lévy jump-diffusion models, and has examined the consequences for recruitment probabilities [1]. Here we develop an explicit coupled stochastic model of larval-zooplankton-phytoplankton interactions, with the aim of exploring the roles of temporal matching of spawning and prey abundance, and prey heterogeneity and foraging strategies on the relationship between stock and recruitment. [1] J. F. Burrow, P.D. Baxter and J.W. Pitchford (2008): Lévy processes, saltatory foraging, and superdiffusion. Math. Mod. Nat. Phenom., 3(3):115-130.
CoauthorsJon Pitchford, Paul Baxter, Alex James, Mike Plank, Joe Horwood
LocationWoodward 4