Non-Markovianmaximum likelihood estimation of autocorrelatedmovement processes

1 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 hiddenMarkov 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 assignAIC values to a vast array of qualitatively differentmodels of animalmovement at the individual and population levels. 2 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 movementmodels based on Brownian motion, the Ornstein–Uhlenbeck process and a generalization of the Ornstein–Uhlenbeck process that includes ballistic bouts. 3 We then show how our framework also provides a new and more accurate approach to home-range estimationwhen compared to estimators that neglect autocorrelation in themovement path. 4 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.