### Abstract

Language | English |
---|---|

Pages | 861-885 |

Number of pages | 24 |

Journal | Bulletin of Mathematical Biology |

Volume | 69 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 |

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### Keywords

- size-at-age variation
- growth rate variability
- statistics
- biology
- mathematics

### Cite this

*Bulletin of Mathematical Biology*,

*69*(3), 861-885. https://doi.org/10.1007/s11538-006-9167-8

}

*Bulletin of Mathematical Biology*, vol. 69, no. 3, pp. 861-885. https://doi.org/10.1007/s11538-006-9167-8

**The dynamics of size at age variability.** / Gurney, W.S.C.; Veitch, R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The dynamics of size at age variability

AU - Gurney, W.S.C.

AU - Veitch, R.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - size-at-age variation

KW - growth rate variability

KW - statistics

KW - biology

KW - mathematics

UR - http://dx.doi.org/10.1007/s11538-006-9167-8

U2 - 10.1007/s11538-006-9167-8

DO - 10.1007/s11538-006-9167-8

M3 - Article

VL - 69

SP - 861

EP - 885

JO - Bulletin of Mathematical Biology

T2 - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 3

ER -