Abstract
Almost every process related to animal ecology, including foraging, predator avoidance, mate encounter, invasion, dispersal and migration, is intimately related to animal movements. In recent years, improvements in tracking and observation technologies have led to an explosion of movement data on all manner of organisms. Movement processes are, however, difficult to model mathematically. They are the result of extremely complex interactions between an organism's internal state, behavioral tendencies and environmental cues. The data are multi-dimensional and almost always non-independent, and there is no consensus on the appropriate statistical summaries or underlying models. This dissertation aims to address several issues in quantitative movement ecology beginning with rigorous mathematical descriptions of individual movement and culminating in models of mass movements and dispersal. Part I, containing Chapters 2 and 3, is devoted to theoretical and mathematical considerations related to parameterizations of movement process. In Chapter 2, the correlated random walk model (CRW) is discussed in detail. Generalizations of the CRW for arbitrarily sampled data are presented, as well as methods to obtain the essential summaries of homogeneous movements: characteristic length scales and time-scales of independence. In Chapter 3, a continuous, autocorrelated stochastic model of movement and its parameterization is discussed, along with algorithms for estimating the associated parameters. The second part covers several applications and extensions of the basic movement models on an ecological scale. In Chapter 4, theoretical relationships between the fundamental time and length scales of movement and encounter rates are derived and applied to survival of migrating salmon. Chapter 5 presents a statistically robust and informative method for identifying multiple behavioral modes in irregularly sampled individual animal track data. In Chapter 6, migratory and dispersing mass movements are considered in terms of population level heterogeneity in the movement parameters. Methods of separating intrinsic randomness of movement from differences within and between populations from dispersal and travel-time distributions are derived. The models and methods throughout this work are applied to a wide range of aquatic organisms: microscopic algae in a laboratory, migrating salmonids and dispersing cyprinids in freshwater environments, dugongs in subtropical Australian waters and northern fur seals in the northwestern Pacific Ocean.