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 is increasingly gathered at very high frequencies, e.g. ≥1Hz, 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 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 step-time, 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.


Introduction
Understanding the factors that drive animal movement is a cornerstone of movement ecology (Nathan et al., 2008).
Step selection analysis (SSA) is a powerful and well-used tool for providing such understanding, by identifying the habitat selection decisions that shape an animal's movement patterns (Fortin et al., 2005;Rhodes et al., 2005). Recently, integrated Step Selec-tion Analysis (iSSA) (Avgar et al., 2016) was introduced to generalise SSA. This provides a solid mathematical foundation for step selection analysis studies and enables inference of how landscape features influence both the movement and habitat selection of animals.
So far, the principal use of SSA (and iSSA) has been on data gathered at a sufficiently low frequency that it is reasonable to suppose an animal makes a distinct choice to move between successive location measurements, with GPS data being the prime example. Recently, however, tracking technology has begun to allow scientists to gather data at sufficiently high frequencies that the resulting data is essentially continuous, since the distance between successive location fixes of an animal is typically less than its body length. Data from magnetometers and accelerometers have allowed path reconstruction at sub-second frequencies, often over long periods of time, such as weeks or months (Wilson et al., , 2013aStreet et al., 2018). Alongside this, accelero-magnetometer data can be used to understand energy expenditure (Wilson et al., 2020), classify behaviours (Yoda et al., 1999;Moreau et al., 2009;Nathan et al., 2012), and gain insight into an animal's internal state (Wilson et al., 2014;Downey et al., 2017;Kröschel et al., 2017). These insights have the potential to be combined with location data to uncover details of what drives animal movement decisions in greater detail than ever before (Williams et al., 2019).
In comparison, GPS data, typically gathered at much lower resolutions, may not give a good indication of an animal's behavioural decisions over short temporal scales (Hebblewhite and Haydon, 2010). Although some GPS data can now reach high frequencies (1Hz) (Ryan et al., 2004), the battery lifespan is greatly reduced, since GPS-based systems are power hungry.
This leads to either a decrease in the duration of the study or an increase in battery size and therefore tag weight, which is limited to a recommended < 3% of the animal's body weight (Kenward, 2000) so as not to have too great an effect on the animal's behaviour (Rasiulis et al., 2014). Transmission telemetry is limited by the environment whereas biologging systems (such as accelero-magnetometers) are not, which means that biologgers can be applied across a wide range of taxa from marine (Tanaka et al., 2001;Noda et al., 2014) to aerial Williams et al., 2015) to terrestrial (Bidder et al., 2012;Street et al., 2018).
However, it is not always simple to adapt existing statistical techniques for use with highfrequency biologging data, since such techniques were often developed with lower frequency data in mind. For example, it does not make sense to apply SSA to "steps" between successive measurements which may be less than a second apart, as is often the case with acceleromagnetometer data, since such steps cannot reasonably be viewed as representing distinct behavioural decisions of an animal. Instead, over the majority of such "steps", an animal will most likely just continue to follow an already chosen path.
As a first stage towards resolving these issues, Potts et al. (2018) proposed an algorithm (referred to here as the Turning-Points Algorithm) which identifies the key turning-points in an animal's path. Using this, we can consider the movement from one turning-point to the next as a "step". These likely corresponds to an actual movement decision made by the animal: since turns are energetically costly (Wilson et al., 2013b), they would only be made if there were a benefit sufficient to outweigh the costs of turning. However, unlike applications of SSA to successive, regularly-gathered GPS locations, steps between turning-points are not evenly spaced in time.
In principle, it is possible to ignore time and just use the SSA (or iSSA) method on the steps between successive turning-points. However, there are disadvantages to this approach. One is that certain movement covariates may depend upon step-time; for example, animals may tend to have a longer time between turns in open environments compared to those that are more difficult to cross. Failure to incorporate the effect of covariates on step-times could potentially lead to inaccurate inference of behaviour. In addition, the resulting movement kernel would not describe a model that explicitly incorporates time, so it could not be propagated forwards in time to make predictions of long-term space-use patterns (e.g. home ranges; Börger et al. (2008)). Yet prediction of broad-scale space use is one of the key aims of many recent studies in step selection analysis (Potts et al., 2014a,b;Avgar et al., 2016;Merkle et al., 2017;Signer et al., 2017;Potts and Schlägel, 2020). Ideally, the SSA procedure should be adapted to accommodate explicitly for the non-constant step-times inherent in paths described by the actual turns of the animals. The principle technical advance of this work is to enhance iSSA so it can be used on data with such non-constant step-times. We call this method time-varying iSSA (tiSSA).
To demonstrate the efficacy of tiSSA, we apply it to 1Hz dead-reckoned data (1 location per second) from a group of free-ranging goats (Capra aegagrus hircus) during the summer and living in a narrow valley surrounded by steep slopes in the French Alps. They spend most of their time (roughly 40% of the study duration) in a relatively small region (radius approximately 70m) around a central area, which encompasses a goat pen and nearby salt-licks. As a basic demonstration of our method, we make three simple hypotheses about goat movement: that they will have a tendency to (i) display a preference to move toward the central area, where the strength of attraction is greater the further they are away from it, (ii) choose smaller-angled turns than larger, since turning is energetically expensive (Wilson et al., 2013b) and (iii) avoid steep-sided terrain, since this requires more energy expenditure to traverse (Minetti et al., 2002;Ardigò et al., 2003). Whilst these hypotheses are intended principally as a proof of concept for the tiSSA algorithm, it is worth noting that the third hypothesis has a plausible alternative: that goats may indeed prefer steep sided terrain to reach areas of high elevation where they can take refuge from predators. Our analysis for (iii) can thus be viewed as testing between these competing hypotheses.
In addition to these habitat-and movement-selection covariates, we also demonstrate the use of tiSSA for inferring environmental drivers of the duration of time between successive turns, termed step-times. Visual observations suggest that the goats have more directed paths when moving back toward the central area. Furthermore, when the temperature is high, they tend to restrict their area of movement to the shaded regions near the pen and other nearby buildings. We also noticed the goats seem to find it more difficult to move in rocky terrain, so make more turns. Inspired by these observations, we give a simple demonstration of the utility of incorporating time-dependent covariates with three further hypotheses: (a) that step-times are longer when the goats are moving toward the central point, (b) that step-times are shorter when the temperature is higher, and (c) that step-times are shorter when the goats are moving through rocky terrain.
We further demonstrate the value of tiSSA by comparing it with the traditional use of SSA (or iSSA) (Fortin et al., 2005;Rhodes et al., 2005;Avgar et al., 2016), whereby the step-time between successive location fixes is constant. For this, we subsample our paths at a variety of constant step-times and compare the inference using these subsampled paths with that from the paths defined by the Turning-Points Algorithm. We investigate how the accuracy and precision of inference varies as the subsampling interval is changed, thus demonstrating how step selection with constant subsampling of a movement path (as is typical in many SSA or iSSA studies) may give rise to misleading results. In summary, our study both (a) shows the great value in gathering high frequency data to understand the drivers of animal movement, and (b) gives a usable method for making behavioural inferences with such data, where the inference is now drawn from movements between behaviourally meaningful points: the points where the animal has actually made a decision to turn.

Data
Data on goat (Capra aegagrus hircus) movement were collected at the Bauges Mountain (Massif des Bauges, 45.61 o N, 6.19 o E) of the French Alps, using triaxial accelerometers and magnetometers (Wildbytes Technologies http://www.wildbyte-technologies.com) contained in Daily Diary tags , combined with Gipsy5 GPS tags (TechnoSmArtTracking Systems http://www.technosmart.eu) inside custom-built 3D printed ABS plastic housings attached to commercial nylon collars (Fearing Lifestyles, Durham, UK). Accelerometer data were collected at a frequency of 20 Hz, magnetometer at 8 Hz, and temperature at 2 Hz. GPS locations were collected every 15 minutes. The data were dead-reckoned at 1 Hz (Bidder et al., 2015) with the Framework4 software  to reconstruct paths of locations over time. Overall, seven week-long trajectories were reconstructed from the data.
The goats tended to spend most of their time in a central area (radius ∼ 70m) which contains a pen and nearby salt licks. We define the centre of this area as the central point for the purposes of this manuscript. As well as locational data, we also use data on the terrain and elevation. The terrain consisted of areas of scree biotope (Devillers et al., 1991), which we term rocky terrain, as well as woodland and grassland. Elevation recordings were found using Google's Elevation API (https://developers.google.com/maps/documentation/javascript/elevation) at a resolution of 1m.

Time-varying integrated step selection analysis (tiSSA)
The central aim of this work is to demonstrate the benefit of using high frequency data for SSA.
Usually, SSA is used to analyse the movement choices between successive recorded locations.
However, for data collected at very high frequencies (e.g. ≥ 1Hz), the distances between successive locations are so short that we cannot expect to infer useful behavioural information by applying SSA to every possible step in the path. Instead, we use a pre-processing method to find those locations on each path where the animal appears to have made a distinct decision to turn, which are more interesting from a behavioural viewpoint than regularly (in time) sampled locations, before applying the SSA procedure.
Specifically, we use the method of Potts et al. (2018) to identify these turning points, thus simplifying an animal's path into a series of turning-points and straight line segments joining these points ( Fig. 1a-b). These straight line segments will then be the "steps" in our subsequent analysis. Each step has both a step-length and a step-time. Different from the way SSA and iSSA have usually be used in previous work, the step-times will not all be the same. Thus we need to modify the iSSA method to incorporate this.
The tiSSA method, which we now introduce, is designed to make this required extension to iSSA (Avgar et al., 2016). We start by defining the movement kernel, which is the probability density function (pdf) of the animal making its next turn at location x after a time τ has elapsed, given that it is currently making a turn at location y and arrived at y on a bearing of α y . This has the following functional form (1) Here, ∝ means 'proportional to', and the associated constant of proportionality is defined so that f (x, τ |y, α y ) integrates to 1 over all possible values for x and τ (i.e. f is a probability density function). The function φ is a kernel of available step-lengths and times, which we refer to here as the sampling kernel, whilst W is called the weighting function.
In iSSA (or SSA) the step-times are constant, so the sampling kernel, φ, is a distribution of step-lengths and turning angles. Here, however, since the step-times are non-constant, we also need to incorporate a distribution of step-times into φ. We thus define the sampling kernel as where l = |x − y| is the step-length, ψ = H(x, y) is the heading from y to x, h(ψ) is the distribution of headings, g 1 (τ ) is the distribution of step-times, and g 2 (l|τ ) is the distribution of step-lengths given a particular step-time. Avgar et al. (2016) suggest using a gamma distribution for the step-lengths, due to its generality (e.g. the exponential and χ 2 distributions are special cases). Similarly, we use gamma distributions for both g 1 (τ ) and g 2 (l|τ ).
The pdf of a gamma distribution can be written in exponential form as follows where k and θ are the shape and scale parameters, respectively, and σ represents either the step-time, τ , or step-length, l. This particular way of writing the gamma distribution is useful during the inference procedure, below. When performing step selection analysis with nonconstant step-times, we sample randomly from the kernel given by Equation (2). This gives control locations for each start position, which can be compared with the measured case location using conditional logistic regression, following the procedure given in, for example, Avgar et al. (2016). Mathematical justification for using this conditional logistic regression procedure to parametrise Equation (1) is given in Supplementary Appendix S1.
The weighting function has the following form where Z = [Z 1 (x, y, α y , τ ), Z 2 (x, y, α y , τ ), . . . , Z n (x, y, α y , τ )] is a vector of covariates and B = [β 1 , β 2 , . . . β n ] is a vector of coefficients representing the effect of each covariate on movement decisions (Avgar et al., 2016). Here, β n+1 and β n+3 correct for the step-time, whilst β n+2 and β n+4 correct for the step-speed. Notice now the reason for writing the gamma distribution in the form of Equation (3): β n+1 and β n+2 correct the scale parameter of the time and speed respectively, whilst β n+3 and β n+4 correct the shape parameter of the time and speed respectively. Including these correcting factors is important to avoid potentially biased results (Forester et al., 2009;Avgar et al., 2016).
The covariates, Z i , may depend on the end of the step, x, the start of the step, y, along the step (between x and y), the direction the animal is moving in when it arrives at y and/or the time it takes to move from y to x, given by τ . Consequently the Z i are functions of x, y, α y and τ . Each Z i (x, y, α y , τ ) represents a statement about what drives the animal's decision to move.

Application to empirical data
We use tiSSA on paths reconstructed from the goat movement data using the Turning-Points Algorithm (Potts et al., 2018). To compare our method with the traditional use of iSSA, which uses data sampled regularly at a relatively low resolution (e.g. every few minutes or hours), we subsample each of our paths at regular time-intervals, referred to as regular subsampling. For this, we use step-times (i.e. subsampling resolutions) ranging from 5 seconds to 420 minutes.
Each of these step-times leads to a slightly different rarefied path. By considering the β ivalues inferred using the paths from the Turning-Points Algorithm as indicative of the 'real' movement tendencies (denoted β i .

Non-constant step-times
To apply tiSSA to the paths inferred using the Turning-Points algorithm, we use a uniform distribution for the headings and gamma distributions for the step-times and step-lengths. In other words, we define where k 1 and θ 1 are, respectively, the shape and scale parameters of the gamma distribution fitted to the step-times, and k 2 and θ 2 are the best fit shape and scale parameters (respectively) for the probability density function g 2 (l|τ ). (We also show that the same k 2 and θ 2 are the best fit shape and scale parameters for a gamma distribution of step-speeds in Supplementary Appendix S2, which can ease inference of these parameters). We use the superscript (r) to represent functions and coefficients used for non-constant step-time data.
Substituting Equation (5) into Equation (2) gives the following To build our weighting function, W (r) (x, τ, y, α y ), we test various hypotheses, namely that goats tend to Notice that A1 and A2 should not be tested within the same weighting function, as they conflate with one another (hence the labelling). Each of these hypotheses has a corresponding covariate. These covariates have the following functional forms Here, elev(x) is the elevation at x (found using Google's Elevation API), Temp(x) is the temperature recorded from the collar when the goat was at x, Temp is the average temperature across all recordings, I(x) is an indicator function equaling 1 when x is in rocky terrain (as defined in Section 2.1) and 0 otherwise and x cp is the location of the central point. We note that there maybe a non-linear relationship between temperature and step-time, but here we assume that the relationship is linear for simplicity.
The point x cp is defined to be the centre of the single site of interest found using the method The functional forms of the movement kernels under the other models are given in Supplementary Appendix S4.

Constant step-times
To perform iSSA on the regularly subsampled paths, and thus compare it with tiSSA plus the Turning-Points Algorithm, we define the sampling kernel as follows (Avgar et al., 2016) where k 3 and θ 3 are the shape and scale parameters from the gamma distribution fitted to the step-lengths. Note the difference between Equations (6) and (8): in the latter, no step-time distribution is required. The superscript (c) refers to any function or coefficient used with constant step-time data.
We use the same covariates as the Base Model above, but instead of correcting for the step-time (β (r) 6 ) and step-speed (β ). This leads to the following weighting function Note that in some goat paths and for certain step-times (namely path 4 for step times of less than 5 minutes; paths 6 and 7 for step-times of less than one minute), there are steps of length zero, so in these cases we cannot correct for the natural logarithm of the step-length. In these cases, we omit β The movement kernel is then In all of our step selection analyses, both for constant and non-constant step-time data, we drew 100 control steps from the sampling kernel (φ (r) or φ (c) for non-constant or constant steptimes, respectively) for each case step. For the non-constant step-time paths, drawing from the sampling kernel, φ (r) , is a two-step procedure, involving first drawing a step-time before a step-length. We use conditional logistic regression to find the β i -values, using the clogit function from the R package, survival.

Results
Selection for moving down slopes is insignificant, both for the constant step-time paths and the paths created using the Turning-Points Algorithm, which may be due to the fact that the goats sometimes use areas of high altitude as refuges. Thus we removed the corresponding covariate (Z 3 ) from all of our weighting functions for the subsequent analysis. Figure 2. Results of step selection analysis on an example path, Goat Path 1. Panels (a) and (b) relate to the β 1 and β 2 values, respectively. Recall that β 1 corresponds to the goat's tendency to move toward the central point and β 2 corresponds to the goat's directional persistence. Results from regular subsampling are presented in blue and the Turning-Points Algorithm results in red. The horizontal location of the latter corresponds to the average step-time. Vertical bars represent 95% confidence intervals. Fig. 2 shows results of analysing the Base Model with iSSA applied to constant subsampling (blue dots), compared with tiSSA applied to the paths rarefied by the Turning-Points Algorithm (red dot), for an example path (see Supplementary Figures S2-7 for the other paths). For β 1 , which represents a tendency to move toward the central point, Fig. 2a shows that the inference from iSSA is highly dependent upon the frequency of the subsampling. The accuracy of inference (i.e. how close each blue dot is to the red dot in Fig. 2a) decreases as the frequency of subsampling moves away from the frequency of turns (as inferred by the Turning-Points Algorithm).
Indeed, when the subsampling frequency is very high, the inferred β 1 -values actually become negative for some of the goat paths, which might naïvely be interpreted as goats having a tendency to move away from the central point. However, since this contradicts the results both from tiSSA and lower-frequency subsamping, there must be an alternative explanation.
Revisiting the data suggests that goats move more quickly back towards the central point than when moving away, meaning that if sampled at a high frequency, we will see less steps that move towards the central point than those moving away. This could lead to negative β 1 -values at overly-high-frequency subsampling. Thus, we see how using overly-small step-times could give rise to misleading results. On the other hand, when using low frequency subsampling, as well as poor accuracy of inference, the precision (i.e. the size of the 95% confidence intervals) is low.
Across nearly all regularly subsampled paths we see that the inferred β 2 -values, representing the degree of directional persistence, are inaccurate when compared to the inferred values from the non-constant step-time paths (Fig. 2b), whereas for small constant step-times (those to the left of the red dot), β 2 -values increase rapidly with the subsampling frequency. However, all this means is that goats move in straight lines over very short time-periods, and as such it does not represent anything biologically meaningful about the tendency to choose short turns over longer ones. As the step-time increases, on the other hand, the confidence intervals around the inferred value of β 2 increase so that β 2 eventually becomes insignificant for high step-times.
When testing the time-dependent covariates (Z 1 , Z 4 and Z 5 ), the strength of directional persistence and tendency to orient turns towards the central point are both significantly higher than zero for all paths (Figure 3a,c). Figure 3b shows that theβ 1 -value, representing the tendency for the goats to move toward the central point with longer step-times, is significantly different from zero for four of the seven paths. All goats tend to have shorter step-times when the temperature is higher (Figure 3d), likely caused by the goats restricting their movements within shaded areas caused by the goat pen and other nearby buildings. Finally, all goat paths showed a tendency to have shorter step-times when moving through the rocky terrain (Fig.  3e). This is likely to be because it is more difficult to cross rocky terrain in a straight line than when crossing grassland or woodland, so the animals make more turns. Figure 3. Coefficient values for β 1 (a),β 1 (b), β 2 (c), β 4 (d) and β 5 (e) with 95% confidence intervals, where β 1 represents the tendency of the goats to move toward the central point with greater strength the further they are from the central point,β 1 also represents the tendency to move toward the central point, with greater strength when further away from the central point and also greater step-times, β 2 represents the tendency to move in the same general direction, β 4 represents the tendency for the goats to have shorter step-times when the temperature is higher and β 5 represents the tendency for the goats to have shorter step-times when moving in rocky terrain.
We have presented a method for step selection analysis with high resolution data, to help identify what drives animals to change their direction of movement. The method first finds the points at which an animal has made a turn, using the Turning-Points Algorithm from Potts et al. (2018), then uses these points as locations in a modified version of iSSA, called time-varying iSSA (tiSSA). This generalises iSSA to allow for locations separated by differing time intervals, as arise in the output of the Turning-Points Algorithm. We compare the tiSSA method on high frequency data to the usual use of iSSA, whereby decisions are inferred based on successive locations in low frequency data, showing that the latter can lead to both inaccurate and imprecise inference. From our analysis of the movement of free-ranging goats, regularly subsampled paths at low frequencies tend to give both imprecise and inaccurate results compared to those using tiSSA, whereas those at high frequencies tend to give precise but inaccurate results.
Being a direct generalisation of iSSA, and therefore SSA, our method can, in principle, be used to examine any of the behavioural processes affecting movement that have been demonstrated in the existing literature on step selection. These include attraction to areas of higher quality food (Merkle et al., 2016), avoidance of or attraction to linear features (Dickie et al., 2019), avoidance of prey (Latombe et al., 2014) or competitors (Vanak et al., 2013), territorial interactions (Potts et al., 2014a), effects of anthropogenic disturbances (Ladle et al., 2019), memory processes (Merkle et al., 2014), and much more (Thurfjell et al., 2014). However, tiSSA applied to ultra-high-resolution data comes with the particular advantage that it is inferring movements that happen at points in space and time where the animal is known to have changed direction. Such changes cost energy (Wilson et al., 2013b) and so are likely to indicate distinct decisions by the animal (Potts et al., 2018). Therefore, the inference from tiSSA is likely to be more behaviourally meaningful than using SSA or iSSA on locations sampled at regular time-intervals.
The output of tiSSA also has the advantage of parametrising a model of animal movement, given by the movement kernel (Equation 1). This is also a feature of iSSA (and some predecessors, e.g. Potts et al. (2014b)), and is increasingly important for various applications, including finding mechanistic underpinnings of utilisation distributions (Signer et al., 2017), predicting aggregation and segregation phenomena (Potts and Schlägel, 2020), demarcating spatial scales of habitat selection (Bastille-Rousseau et al., 2015), predicting disease transmission rates (Merkle et al., 2018), and determining the energetic benefits of foraging strategies (Merkle et al., 2017). Our new technique thus opens up the possibility for such application based on the sort of high resolution data that is becoming increasingly prevalent in movement ecology Williams et al. (2019).
As well as enabling such data to be used to answer questions already examined using iSSA with lower-resolution data, our tiSSA technique can also uncover processes that can cause animals to take turns more or less frequently. We have shown here that the goats in our study turn more frequently when the temperature is higher and the ground is rocky. In many behavioural changepoint studies, changes in turning frequency are viewed as changes in behavioural state (Patterson et al., 2008;Edelhoff et al., 2016). Whilst this may well be true, we have demonstrated that environmental conditions can also have an effect on turning frequency. This suggests it is important to account for such environmental effects in studies that seek to infer behavioural state from animal movement paths.
Alongside application to high frequency data, via the Turning-Points Algorithm, tiSSA can in principle be used for any data where the steps are unevenly spaced in time. For example, many passerines tend to travel from tree to tree whilst foraging (Ellison et al., 2020). If one records the times and locations of a bird each time it switches tree then this would result in a sequence of locations, unevenly spaced in time, but where each 'step' from one location to the next represents a distinct decision by the animal. It would make sense to use tiSSA to understand the features of the trees that correlate to the decisions to leave one and move to another.
Many data sets also have measurements irregularly spaced in time due to limitations of tagging technology. However, unless there is reason to believe that the locations are gathered at behaviourally-meaningful points in time, we would recommend using continuous-time techniques instead of tiSSA (Wang et al., 2019), as continuous-time methods are capable of incorporating situations where decisions are made away from the measured locations (Blackwell et al., 2016). Even if the locations are gathered at behaviourally meaningful points in time, these continuous-time methods do not assume that these points are behaviourally significant, so do not make best use of the data. Another disadvantage of such techniques is that inference can often be prohibitively slow. However, there is evidence that this limitation is being overcome, thanks to improved statistical techniques, such as template model builder (Auger-Méthé et al., 2017;Jonsen et al., 2019).
In summary, our study provides the requisite methodological advance for meaningful use of step selection analysis with high frequency data, such as is becoming increasingly prevalent due to technological advances in both tagging hardware and software for post processing (Williams et al., 2019). Our study also demonstrates why this technique is advantageous in terms of producing accurate and precise results compared to using regularly subsampled, lower frequency data. As such, it opens the way for better inference for uncovering what drives animals to make movement decisions.