A mathematical framework for movement ecology that can be used to generate and analyze movement data

We present a framework for generating the paths of individuals in a diverse population (accounting for species, gender, age, etc.) as they move over a common landscape, as well as for analyzing large sets of movement data, particularly with respect to identifying modes of behavior responsible for different types of movement. The underlying concept is that an individual has μ distinguishable behavioral modes influencing movement, with mixing of modes permitted. At any time t, the state of an individual is given by its position in space and values in a mode-weighting vector. Also associated with an individual are μ canonical distributions that are used to construct likelihoods that an individual will move from its current to some neighboring point. These distributions are independent of landscape information, the latter taken into account in a separate computation. From an updatable GIS landscape map that reflects the current landscape state (e.g. resources, locations of individuals) a set of mode-specific, landscape-value maps are constructed for each individual (these maps are discretized and generated using GIS software). These maps reflect what an individual can see and remember about its environment, as well as a value based on the resource and occupancy state of cells (e.g. a particular cell may have a low forage-mode value but a high safety-mode value). Procedures for computing movement distributions and updating information are presented.