Gurney, W.S.C. and Veitch, R. (2007) *The dynamics of size at age variability.* Bulletin of Mathematical Biology, 69 (3). pp. 861-885. ISSN 0092-8240

## Abstract

In this paper, we propose a theoretical framework within which a unified treatment of the key sources of size-at-age variability - size dependence of growth rate, stochastic growth rate variations and individual-to-individual variability in growth performance - is possible. We use this framework to develop a general criterion for growth depensation in cohorts, which we define as the increase of the coefficient of variation of size-at-age, with increasing age. We use this criterion to show that size dependence of growth rate, acting alone, is depensatory only if the growth rate increases faster than linearly with size (that is, if growth is faster than exponential), while stochastic growth rate variation is invariably depensatory. Many species exhibit growth rates that scale less than linearly with size; indeed the commonly used von Bertalanffy model shows growth rates which actually decrease with size. In such a species, the size dependence of growth rate acts compensatorily, while stochastic growth rate variability is depensatory. We show that the tension between these two mechanisms leads to quasi-stationary size-at-age variability, which we can calculate analytically in some special cases and obtain by a simple numerical procedure where analysis is impractical.

Item type: | Article |
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ID code: | 4610 |

Keywords: | size-at-age variation, growth rate variability, statistics, biology, mathematics, Probabilities. Mathematical statistics, Biology, Agricultural and Biological Sciences(all), Neuroscience(all), Biochemistry, Genetics and Molecular Biology(all), Environmental Science(all), Immunology, Computational Theory and Mathematics, Mathematics(all), Pharmacology |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics Science > Natural history > Biology |

Department: | Faculty of Science > Mathematics and Statistics Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science |

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Depositing user: | Strathprints Administrator |

Date Deposited: | 06 Nov 2007 |

Last modified: | 04 Sep 2014 17:41 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4610 |

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