Stochastic von Bertalanffy models, with applications to fish recruitment

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We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalatiffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed. (c) 2006 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)640-655
Number of pages16
JournalJournal of Theoretical Biology
Issue number4
Publication statusPublished - 21 Feb 2007


  • individual-based models
  • stochastic differential equations
  • first hitting time density

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