Why did the animal turn? Time-varying step selection analysis for inference between observed turning-points in high frequency data

Step selection analysis (SSA) is a fundamental technique for uncovering the drivers of animal movement decisions. Its typical use has been to view an animal as 'selecting' each measured location, given its current (and possibly previous) locations. Although an animal is unlikely to make decisions precisely at the times its locations are measured, if data are gathered at a relatively low frequency (every few minutes or hours) this is often the best that can be done. Nowadays, though, tracking data are increasingly gathered at very high frequencies, often >= 1 Hz, so it may be possible to exploit these data to perform more behaviourally-meaningful step selection analysis. Here, we present a technique to do this. We first use an existing algorithm to determine the turning-points in an animal's movement path. We define a 'step' to be a straight-line movement between successive turning-points. We then construct a generalised version of integrated SSA (iSSA), called time-varying iSSA (tiSSA), which deals with the fact that turning-points are usually irregularly spaced in time. We demonstrate the efficacy of tiSSA by application to data on both simulated animals and free-ranging goats Capra aegagrus hircus, comparing our results to those of regular iSSA with locations that are separated by a constant time-interval. Using (regular) iSSA with constant time-steps can give results that are misleading compared to using tiSSA with the actual turns made by the animals. Furthermore, tiSSA can be used to infer covariates that are dependent on the time between turns, which is not possible with regular iSSA. As an example, we show that our study animals tend to spend less time between successive turns when the ground is rockier and/or the temperature is hotter. By constructing a step selection technique that works between observed turning-points of animals, we enable step selection to be used on high-frequency movement data, which are becoming increasingly prevalent in modern biologging studies. Furthermore, since turning-points can be viewed as decisions, our method places step selection analysis on a more behaviourally-meaningful footing compared to previous techniques.