There is great interest in ecology to understand how wild animals are affected by anthropogenic disturbances, such as sounds. Behavioural response studies are an important approach to quantify the impact of naval activity on marine mammals. Controlled exposure experiments are undertaken where the behaviour of animals is quantified before, during, and after exposure to a controlled sound source, often using telemetry tags (e.g., accelerometers, or satellite trackers). Statistical modelling is required to formally compare patterns before and after exposure, to quantify deviations from baseline behaviour. We propose varying-coefficient stochastic differential equations (SDEs) as a flexible framework to model such data, with two components: (1) time-varying baseline dynamics, modelled with non-parametric or random effects of time-varying covariates, and (2) a non-parametric response model, which captures deviations from baseline. SDEs are specified in continuous time, which makes it straightforward to analyse data collected at irregular time intervals, a common situation for animal tracking studies. We describe how the model can be embedded into a state-space modelling framework to account for measurement error. We present inferential methods for model fitting, model checking, and uncertainty quantification (including on the response model). We apply this approach to two behavioural response study data sets on beaked whales: a satellite track, and high-resolution depth data. Our results suggest that the whales' horizontal movement and vertical diving behaviour changed after exposure to the sound source, and future work should evaluate the severity and possible consequences of these responses. These two very different examples showcase the versatility of varying-coefficient SDEs to measure changes in behaviour, and we discuss implications of disturbances for the whales' energetic balance.
The conditionally autoregressive hidden Markov model (CarHMM): Inferring behavioural states from animal tracking data exhibiting conditional autocorrelation
Detecting disease progression from animal movement using hidden Markov models
University of Minnesota（明尼苏达大学）；Harvard University（哈佛大学）；Dalhousie University（达尔豪斯大学）；Smithsonian’s National Zoo & Conservation Biology Institute（史密森国家动物园与保护生物学研究所）
Leibniz Institute for Zoo and Wildlife Research（莱布尼茨动物园与野生动物研究所）；Technische Universität Berlin（柏林工业大学）；University of Regensburg（雷根斯堡大学）；University of Goettingen（哥廷根大学）
