Mathematical methods for exploring the cognitive drivers of animal movement

The spatial distributions of animals have fascinated scientists for centuries. Understanding where animals go and why helps ecologists conserve their populations. Technological advances during the 21st century have allowed scientists to record the spatial location of animals over time, motivating the development of models that explain these patterns. Animals use external factors, such as qualities of their environments, and internal processes, such as memory, when deciding where to move. Interest in models that relate these internal processes to movement has increased in the last decade. In this thesis, I expand on existing work to model how perception, memory, and learning affects the way animals move. The methods described here incorporate different mathematical perspectives with a collective goal of identifying how moving animals account for temporal variation in their environments, predictable or unpredictable. Temporal environmental variation results from many biological processes. When this variation is directly caused by animals themselves (e.g., through resource depletion), these animals navigate away from patches they visited (and depleted) recently. Resources may also vary independently from the animal, and when this variation is predictable, animals may benefit from learning schedules of resource availability. Chapter 2 describes a model that uses animal tracking data to identify patch revisitation patterns. The model’s ability to quantify these patterns was verified on simulated data before being fit to brown bear (Ursus arctos) data from the Canadian Arctic. These bears live in an environment where food resources vary seasonally, and the model suggested that they use spatiotemporal memory to leverage these predictable patterns. Using advanced model-fitting techniques to obtain maximum likelihood estimates and confidence intervals, the model suggested that brown bears wait approximately one year before navigating to resource-rich patches they visited previously. When temporal variation in an animal’s environment is not so predictable, animals must learn and adjust their foraging behaviour to survive. Psychologists and ecologists have theorized that animal learning resembles Bayesian inference, suggesting that animals refine their prior knowledge by incorporating the outcome of subsequent experiences (data). Chapter 4 incorporates this theory into a mechanistic model that simulates how animals learn, using Bayesian Markov chain Monte Carlo sampling to model how animals optimize a task with a quantifiable outcome. Using a mechanistic model that simulates the movement of spatially informed foragers within a home range, we apply this framework to predict how animals may learn to adjust to rapid and unpredictable changes in their environments. At larger spatial scales, predictable temporal variation in the environment may give rise to migratory behaviour. Chapter 5 presents a model that can statistically identify the beginning and end of migration from animal tracking data. This model can be used to partition animal location data into biologically reasonable behavioural segments for further analysis. Movement ecologists have used statistical models to identify important biological patterns from data, and mechanistic models can incorporate causal links to make important predictions about how animals may move in the future. The work presented in this thesis advances movement ecology by introducing statistical and mechanistic tools that describe how cognitive processes inform animal foraging patterns.

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