The Approximately Ideal, More or Less Free Distribution

Abstract

We present the minimum set of requirements necessary and sufficient to represent the foraging behaviour of an animal, and its utilisation of food, in order to explore the emergent properties of behaviour that allow animals to reduce their hunger. We present an individual-based model of foraging that provides a simple quantification of the requirements, which is sufficiently simple to yield some analytical results. Complex interactions beyond the scope of analysis have been explored through simulating animals foraging in regenerating patchy environments. In most cases the populations pass into equilibrium distributions which appear to be stable. The equilibria always approximate closely to the ideal free distribution, although typically with a small degree of undermatching. (Undermatching is the term applied to the departure from the ideal free distribution caused by a smaller proportion of the population than expected occupying areas with a higher than average regeneration rate). The model therefore implies that the distribution, hitherto accounted for in terms of ESSs may, in fact, be simply an effect of the animal's utilization of the food it collects to reduce its hunger. The model defines a specific feeling rate, v, the rate at which an animal can feed on a unit of food. This is a function of three parameters, v1, the specific feeding rate when alone, v∞, the rate, possibly zero, at which it can feed in the presence of an indefinitely large number of conspecifics, and n1/2, the number of conspecifics that cause v to take the value (v1+v∞)/2. Exploitation competition in the absence of interference is represented by setting v1=v∞. Differences in competitive ability in exploitation have been represented by simulating animals with a range of values of v1, those with the larger values, feeding more rapidly, being the more effective competitors, and those with the lower values being the less effective. Interference competition is represented by setting v1>v∞ and social facilitation by v1<v∞. Individual differences in the strength of interaction are represented by different values of n1/2. In competition, the animals with the larger values of n1/2 are the more effective competitors: in facilitation, they are the less effective facilitators. The addition of physiological and behavioural detail makes very little alteration to the emergent equilibria, always close to the ideal free distribution, almost always showing undermatching.