Scale-invariant model of marine population dynamics

Jose A. Capitan, Gustav W. Delius

Research output: Contribution to journalArticlepeer-review

Abstract

A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence that the population dynamics in the ocean is approximately scale-invariant. We use this invariance in the construction and solution of a size-structured dynamical population model. Starting from a Markov model encoding the basic processes of predation, reproduction, maintenance respiration, and intrinsic mortality, we derive a partial integro-differential equation describing the dependence of abundance on weight and time. Our model represents an extension of the jump-growth model and hence also of earlier models based on the McKendrick-von Foerster equation. The model is scale-invariant provided the rate functions of the stochastic processes have certain scaling properties. We determine the steady-state power-law solution, whose exponent is determined by the relative scaling between the rates of the density-dependent processes (predation) and the rates of the density-independent processes (reproduction, maintenance, and mortality). We study the stability of the steady-state against small perturbations and find that inclusion of maintenance respiration and reproduction in the model has a strong stabilizing effect. Furthermore, the steady state is unstable against a change in the overall population density unless the reproduction rate exceeds a certain threshold.

Original languageEnglish
Article number061901
Pages (from-to)1-15
Number of pages15
JournalPhysical Review E
Volume81
Issue number6
DOIs
Publication statusPublished - 1 Jun 2010

Keywords

  • STRUCTURED FOOD WEBS
  • BIOMASS-SIZE SPECTRA
  • BODY-SIZE
  • PELAGIC ECOSYSTEM
  • FISH
  • ABUNDANCE
  • TEMPERATURE
  • PREDATION
  • MASS

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