A framework for generating and analyzing movement paths on ecological landscapes.

The movement paths of individuals over landscapes are basically represented by sequences of points (x(i), y(i)) occurring at times t(i). Theoretically, these points can be viewed as being generated by stochastic processes that in the simplest cases are Gaussian random walks on featureless landscapes. Generalizations have been made of walks that (i) take place on landscapes with features, (ii) have correlated distributions of velocity and direction of movement in each time interval, (iii) are Lévy processes in which distance or waiting-time (time-between steps) distributions have infinite moments, or (iv) have paths bounded in space and time. We begin by demonstrating that rather mild truncations of fat-tailed step-size distributions have a dramatic effect on dispersion of organisms, where such truncations naturally arise in real walks of organisms bounded by space and, more generally, influenced by the interactions of physiological, behavioral, and ecological factors with landscape features. These generalizations permit not only increased realism and hence greater accuracy in constructing movement pathways, but also provide a biogeographically detailed epistemological framework for interpreting movement patterns in all organisms, whether tossed in the wind or willfully driven. We illustrate the utility of our framework by demonstrating how fission-fusion herding behavior arises among individuals endeavoring to satisfy both nutritional and safety demands in heterogeneous environments. We conclude with a brief discussion of potential methods that can be used to solve the inverse problem of identifying putative causal factors driving movement behavior on known landscapes, leaving details to references in the literature.