2. Overview of models of dispersing animals
2.1. Introduction

Models of animal dispersal date back to the early part of this century. Pearson and Blakeman (1908) and Brownlee (1911) are credited with developing the first models of animal dispersal, using random walk models to describe movement patterns. Two landmark works of the middle of the century are Dobzhansky and Wright's (1943), which modeled the dispersal of fruit flies, and Skellam's (1951), which modeled the range expansion of small mammals. Also during this period, Patlak (1953a; 1953b) developed a fairly complex random walk based model of dispersal that was overlooked at the time but has received attention lately. In 1969, two papers marked the beginning of the computer era for dispersal models: Rohlf and Davenport (1969) simulated random walk models to mimic various dispersal behaviors, and Siniff and Jensen (1969) conducted simulations of the movements of foxes and hares in their home ranges. The past two decades have seen many refinements in the models and in methods of applying the models to data.

Models based on the movements of individuals are referred to as "microscopic" models (Aronson, 1985). For these models, the spatial and temporal scales are relatively fine, and more detail can be included in the model. Models based on group dynamics are labeled "macroscopic" models. These models are usually concerned with gross patterns on broader temporal and spatial scales. It is interesting to note that each microscopic model has a corresponding macroscopic model, and vice versa. Also, it is not always clear whether a model should be classified as microscopic or macroscopic since there is a gradation between the two.