A Competition Model for Size-Structured Species

Abstract

The asymptotic dynamics of a system of ordinary differential equations describing the dynamics of nsize-structured species competing for a single (unstructured) resource are studied. The system is based on a single species growth model for a size-structured species due to Diekmann, Metz, Kooijman, and Heijmans in which physiological parameters at the level of the individual are incorporated. It is shown that all trajectories asymptotically approach a lower-dimensional positive cone where the dynamics are governed by an easily determined lower-dimensional competition system of a type commonly studied in the literature for unstructured populations. It is also shown that, regardless of the asymptotic dynamics or the outcome of the competitive interaction, the average size of individuals for every species asymptotically equilibrates to a positive value. These results permit a study of competitive exclusion in terms of the physiological parameters and average size of individuals of the species. Illustrative applications are made to competing species in a chemostat and to species competing for a renewable resource. The relationship between competitive success and species size and other physiological parameters is discussed and related to the Size Efficiency Hypothesis (SEH) for zooplankton communities.