Continuous-time modelling of behavioural responses in animal movement
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There is great interest in ecology to understand how wild animals are affected by anthropogenic disturbances, such as sounds. For example, 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 nonparametric 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.
Michelot , T , Glennie , R , Thomas , L , Quick , N J & Harris , C M 2023 , ' Continuous-time modelling of behavioural responses in animal movement ' , Annals of Applied Statistics , vol. 17 , no. 4 , pp. 3570-3588 . https://doi.org/10.1214/23-AOAS1776
Annals of Applied Statistics
Copyright © 2023 Institute of Mathematical Statistics. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at https://doi.org/10.1214/23-AOAS1776.
DescriptionFunding: TM, RG, CH, and LT were funded by the US office of Naval Research, Grant N000141812807. This work was supported by the US Fleet Forces Command through the Naval Facilities Engineering Command Atlantic under Contract No. N62470-15-D-8006, Task Order 50, Issued to HDR, Inc.
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