Parameter dependence, size and survivability
The goal of this paper is to use the available mathematical theory for discrete size-structured models to provide an alternative perspective from which to consider some issues arising from the study of interactions among size-structured species, namely the Size-Efficiency Hypothesis of \textit{J. L. Brooks} and \textit{S. I. Dodson} [Science 150, 28-35 (1965)], and some types of life-history strategies and trade-offs. The Size-Efficiency Hypothesis, which was formulated based upon observations of planktivore-plankton systems, states in part that, ``\dots when predation is of low intensity the small planktonic herbivores will be competitively eliminated by large forms \dots'' This hypothesis has been tested on a variety of ecological systems, with varying results. In cases in which the hypothesis failed, many factors, such as the presence of a top predator, asymmetric competition, etc., have been pointed to as contributing to this failure. For the model presented here, we show conditions under which the Size-Efficiency Hypothesis holds and fails and discuss the dependence of these results upon the individual physiological parameters of the model. We then turn to the study of life-history strategies and use the size- structured model given here to study some aspects of life-history strategies and trade-offs for a population with density-dependent growth.
scientific article; zbMATH DE number 796941