The Equilibrium Distribution of Optimal Search and Sampling Effort of Foraging Animals in Patchy Environments

Abstract

The optimal allocation of time and effort by foraging animals for searching, sampling and learning the distribution of food in patches is modelled. The optimal effort maximises the net gain, which is the difference between the benefit and the cost of searching. The optimal search effort increases as a function of the variance of quality between the patches, and the turnover of new patches. It decreases as a function of the cost of searching, e.g. the movement cost between the patches.The variance of quality in the patches decreases as a function of the total search effort by all the foragers. A joint stable equilibrium of search effort and patch variance is reached when the variance reaches the level which is generated by the search effort which is optimal for all the foragers. The joint equilibrium search effort is a decreasing function of the population density, and of the search cost. It is an increasing function of the inherent variance in patch quality, and of the patch renewal rate. The equilibrium variance in patch quality is a decreasing function of the populaton density of the foragers, and of the search cost.A rare type with a different optimal search as a function of the variance, behaves according to the variance equilibrium with the common type. The optimal search effort of rare types diverges from that of the common type more than it would if they were on their own. In heterogeneous populations with several different types, the equilibrium search effort of each type is the optimal search effort at the variance generated by the total search effort of all the types.Coexistence is possible between species with high information gathering and high energy reqirements, which utilise the richer newly discovered food sources, and species with low information gathering and low energy demands, which utilise poorer depleted food sources.A small average number of foraging visits per patch generates a stochastic distribution of patch quality even in inherently uniform patches. In such cases, the equilibrium search effort and patch variance may be high, and may be determined entirely by this stochastic generation of variance.KeywordsSearch CostSearch EffortOptimal SearchFood PatchPatch QualityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.