HMMs are commonly used to model animal movement data and infer aspects of animal behavior. Their ability to connect an observation process to an underlying state process, generally serving as a proxy for a finite set of animal behaviors of interest, matches the intuition that the observed movements stem from an underlying (unobserved) behavioral process. We can further extend the HMM framework to consist of multiple state processes to reflect that different behaviors are identified by different compositions of the observed movement processes. We refer to this extension as a multi-scale HMM whereby one state process is connected to the underlying behaviors that generate the movements at the temporal scale at which the data are processed and another is connected to a larger-scale behavioral process, defined as a composition of fine-scale behavioral states. We present two formulations of the multi-scale HMM. We illustrate the application of multi-scale HMMs in four real-data examples, vertical movements of harbor porpoises observed in the field, and garter snake movement data collected as part of an experimental design, in chapter 2 and under two different formulations applied to tiger shark data in chapter 3.

HMMs again play a feature role in chapter 4, where we aim to connect movement and physiology dynamics and their evolution and interaction over time. A long-sought goal in ecology is to connect movement with population dynamics. For many species and especially for ungulates, there is a known link between condition (e.g. fat reserves) and the probability of survival and reproduction. Assuming a particular genetic makeup and physiology, condition reflects the history of behavioral decisions, including movement and habitat use. However, the condition of an animal can also have a direct implication on the types of movements that it performs and the habitats that it visits. Movement data for ungulates are typically collected at a fine temporal scale, e.g. a position recorded by a GPS device every five or ten minutes. However, fat reserves cannot be measured remotely and must be done manually. This in turn creates a mismatch in the temporal scale at which the two data streams are observed, i.e. every five minutes for movement vs approximately once a month for condition. Further, the temporal mismatch leads to various challenges when jointly modeling the two processes. For the movement model, we use discrete-time, finite-state HMMs with the positional data of the sheep serving as the observation process and the underlying state process serving as a proxy for behaviors of interest. To incorporate condition as a potential covariate affecting the movement, and thus behavioral, process, we make use of the physiological equations that describe the evolution of body fat in Merino sheep in order to predict daily values of the condition process. The physiological equations are expressed as a function of the states inferred by HMM, as well as the distance that the sheep travels.