Non-Markovian maximum likelihood estimation of autocorrelated movement processes

By viewing animal movement paths as realizations of a continuous stochastic process, we introduce a rigorous likelihood method for estimating the statistical parameters of movement processes. This method makes no assumption of a hidden Markov property, places no special emphasis on the sampling rate, is insensitive to irregular sampling and data gaps, can produce reasonable estimates with limited sample sizes and can be used to assign AIC values to a vast array of qualitatively different models of animal movement at the individual and population levels. To develop our approach, we consider the likelihood of the first two cumulants of stochastic processes, the mean and autocorrelation functions. Together, these measures provide a considerable degree of information regarding searching, foraging, migration and other aspects of animal movement. As a specific example, we develop the likelihood analyses necessary to contrast performance of animal movement models based on Brownian motion, the Ornstein-Uhlenbeck process and a generalization of the Ornstein-Uhlenbeck process that includes ballistic bouts. We then show how our framework also provides a new and more accurate approach to home-range estimation when compared to estimators that neglect autocorrelation in the movement path. We apply our methods to a data set on Mongolian gazelles (Procapra gutturosa) to identify the movement behaviours and their associated time and length scales that characterize the movement of each individual. Additionally, we show that gazelle annual ranges are vastly larger than those of other non-migratory ungulates.