Predicting Spatial Distribution of Foragers over Large Resource Landscapes: A Modeling Analysis of the Ideal Free Distribution

Abstract

Ideal Free Distributions (IFD) have successfully been used to describe the spatial distributions of animals in heterogeneous or patchy environments over relatively small areas. Ideal Free theory and the logic underlying it have recently been used to describe animal distributions over large landscapes and in doing so, these studies have not precisely met all of the assumptions of the IFD. Here, we use an individual-based simulation model of a population of generalized foragers to test the ability of the IFD to predict the equilibrium distribution of organisms in a large environment. Conditions of the model meet the assumptions of Ideal Free theory. Food abundance follows a fractal distribution spatially through the environment. Model foragers have a type II functional response and a marginal-value theorem type patch departure rule. Foragers may move through the environment without cost, and foraging does not affect food availability. In a simulation experiment, we manipulate the scale of heterogeneity in food distribution, the number of foragers in the population, the distance foragers move, and the scale of IFD predictions to determine the ability of the IFD to predict equilibrium spatial distribution of foragers. The experiment shows that correlations between IFD predictions and the distribution of simulated foragers were lower when food had a fractal distribution than when food resources had a random spatial distribution. IFD predictions best fit simulated forager distributions on fractal food landscapes when the scale at which distributions were measured was similar to the maximum movement distance of the foragers. Large differences between maximum movement distance and scale of measure resulted in low correlations between equilibrium distributions of simulated foragers and IFD predictions. These results indicate that the IFD is likely not a good predictor of animal distributions in large environments and that the extent of the area over which an IFD is used should be similar to the maximum daily movement of the animals under study.