The Maximum Entropy Principle to predict foragerspatial distributions: an alternate perspective formovement ecology

The Maximum Entropy Principle (MaxEnt) is a powerful inference principle that allows to determine the distribution that describes a system on the basis of the information available, usually in the form of averages of observables (random variables) of interest for the system, and the assumption of maximal ignorance (maximum entropy) beyond the stated prior information.In this work we focus on the use of MaxEnt in the context of spatial ecology for building theory to predict equilibrium foraging distributions. This represents a new application of MaxEnt and a novel approach to compute spatial foraging distributions, which is able to incorporate mechanisms such as resource-depletion, optimallity of the foraging strategy, travel costs, information uncertanity, and inter-specific and intra-specific competition into the statistical inference. Our results show how our model predictions can resemble both, the predictions of optimal and random foraging, and give a simple quantitative way to connect these two extreme foraging behaviours. In addition, our work show the capability of modelling using energy and entropy arguments to relax most of the basic assumptions of the Ideal Free Distribution of ecology to expand its range of applicability.Overall, we show the power of MaxEnt to build theory and to relate existing models in spatial ecology by use of a universal principle. We further discuss the potential applicability of MaxEnt to build theory in other contexts of ecology, such as to formulate population dynamics models, and the potential use of the dynamic form of MaxEnt, i.e. the Maximum Caliber Principle, to develop further theory on dynamical systems in spatial ecology.