Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

The dynamics of size at age variability

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

Full text not available in this repository. (Request a copy from the Strathclyde author)

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.