Optimal Body Size and Resource Density

Abstract

A qualitative theory of the evolution of body size in relation to resource density is developed. Two characteristics of an organism are identified as being size limiting. The first is foraging capacity and the second the ingestion and food-processing capacity. A condition is derived showing that optimal body size always decreases with decreasing food availability when the digestive capacity scales to body size with a higher exponent than that of encounter rate. When the opposite is the case optimal body size may increase with decreasing food availability within a small resource density interval. If the cost for activities enhancing fitness is scaled to body size allometrically, an optimum can be found provided that the metabolic exponent is larger than the search capacity exponent and the food-processing exponent. Body size increases with reduced food availability (above a certain threshold food concentration) under one condition: when the exponent scaling the cost of activities enhancing fitness to body size is less than the exponent scaling food-processing capacity, which in turn is less than the exponent scaling search capacity. A reanalysis of a specific optimum body size model for planktivorous fish gave similar results to that derived by the general model. Optimal body models may be a useful tool to explore body size in relation to environmental conditions and increase the generality of mechanistic population models.