Identifying latent behavioral states in animal movement with non-parametric Bayesian methods

Understanding animal movement often relies upon telemetry and biologging devices. These data are frequently used to estimate latent behavioral states to help understand why animals move across the landscape (or seascape). While there are a variety of methods that make behavioral inference from biotelemetry data, some features of these methods (e.g., analysis of a single data stream, use of parametric distributions) may result in the misclassification of behavioral states. We address some of the limitations of segmentation and state-space models (SSMs) in our non-parametric Bayesian framework, available within the open-source R package bayesmove. This framework can analyze multiple data streams, which may capture complex behaviors more successfully than a single data stream. Additionally, parametric distributions are not used in our framework since they may poorly characterize the underlying true distributions. We tested our Bayesian framework using simulated trajectories and compared model performance against a representative segmentation method (behavioral change point analysis; BCPA) and one type of SSM, a hidden Markov model (HMM). We also illustrated this Bayesian framework using movements of juvenile snail kites (Rostrhamus sociabilis) in Florida, USA. The Bayesian framework estimated breakpoints more accurately than BCPA for tracks of different lengths, albeit at a slower computational speed. Likewise, the Bayesian framework provided more accurate estimates of behavior than the HMM when simulations were generated from atypical distributions. This framework also performed up to three times faster than the HMM when run in a similar fashion. Three behavioral states were estimated from snail kite movements, which were labeled as ‘encamped’, ‘area-restricted search’, and ‘transit’. Changes in these behaviors over time were associated with known dispersal events from the nest site, as well as movements to and from possible breeding locations. Our framework estimated behavioral states with comparable or superior accuracy compared to BCPA and HMM when step lengths and turning angles of simulations were generated from atypical distributions. Since empirical data can be complex and do not necessarily conform to parametric distributions, methods (such as our Bayesian framework) that can flexibly classify latent behavioral states will become increasingly important to address questions in movement ecology.

We assessed the performance of our model compared to other methods via simulations.

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We first evaluated the ability of our track segmentation method to detect true breakpoints and 2 2 9 compared its results to those obtained by a representative segmentation method (behavioral  We generated multiple three-state trajectories from a correlated random walk at regular (2) slow and tortuous movement ('area-restricted search' or ARS), as well as (3)  were not identical to those used to generate the data. Step lengths and turning angles were the data streams used to make inference on latent 2 5 9 behavioral states.
Step lengths were separated into five bins using the 25 th , 50 th , 75 th , 90 th , and 2 6 0 100 th quantiles as upper limits. These quantiles were used to discretize step lengths since this ) since the distribution of this variable was relatively balanced. Selecting the number of bins and the binning method is relatively subjective and 2 6 5 therefore it is important that prior biological reasoning be used to inform these decisions. In distribution and there should be biologically meaningful differences in the movement pattern represented by the different bins. These assumptions during the discretization process are not 2 6 9 unlike assumptions made for HMMs when selecting probability distributions to fit data streams, 2 7 0 but require practitioners to make more decisions up front. were selected to account for minor deviations of the model estimates from the true breakpoints. The use of other thresholds resulted in the same relative pattern of accuracy measures when 2 7 9 comparing among simulations of different lengths (JA Cullen, unpublished data). were tuned to provide a close approximation of the true number and location of simulated 3 0 3 breakpoints with window size set to 80, sensitivity set to 2, and clusterwidth set to 30.

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A discrete-time HMM was also fitted to each of the simulated trajectories using the R Step lengths were modeled using 3 0 6 a gamma distribution and turning angles were assumed to arise from a wrapped Cauchy Michelot 2018). The optimal number of states was selected using a combination of AIC and BIC, where the model with the lowest value was considered to be optimal. However, if the difference shapes. Accuracy was measured by RMSE across bins of all states and data streams per As part of a larger investigation on the effects of wetland management on wildlife, solar- comparable step lengths and turning angles, we filtered our data to the most common time in 26 individuals retained for all subsequent analyses.

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Step lengths and turning angles were used to estimate latent behavioral states. As was 3 4 1 performed on the simulated tracks, step lengths were discretized into five bins using the 25 th , Step lengths and turning angles for each of the 26 snail kites were segmented by the iterations with a burn-in of 500 iterations and vague priors were used with hyperparameters set at The Bayesian segmentation model successfully recovered breakpoints from the run (2 to 120 min) compared to the BCPA model (0.25 to 21 min) (Fig. 4a). The Bayesian model tracks of increasing length (Fig. 4b). Additionally, BCPA missed 3× more of the 2034 true breakpoints than the Bayesian model. The distribution shapes of step lengths and turning angles were also more accurate in the estimated by the HMM regardless of simulated track length (Fig. 6) approximately 25 min to run and it estimated 1 to 51 breakpoints for these individuals.

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Breakpoints were then used to define 439 track segments from all 26 individuals (Fig. 7a). These comprised 94.1% of all behavior assignments on average (Fig. 7b). To ensure that these three 4 2 5 states were biologically interpretable, distributions of step lengths and turning angles were also 4 2 6 evaluated ( Fig. 7c). The distributions showed: 1) a slow and tortuous behavior; 2) a tortuous We demonstrated that our Bayesian framework (available within the bayesmove R Bayesian framework. Although the BCPA was notably faster at track segmentation than the Bayesian method, 4 6 6 accuracy of the estimated breakpoints was much higher with the latter. More specifically, BCPA 4 6 7 estimated a greater number of breakpoints than there were true breakpoints for all but the longest from natal sites could be due to a variety of factors, such as hatching date, body condition, and the characterization of activity budgets over ontogeny, future research could also explore the 5 1 8 primary drivers of snail kite movement and habitat use within each behavioral state through the 5 1 9 inclusion of environmental covariates. Although the Bayesian framework effectively classified behavioral states from both number and width of bins during the discretization of data streams is a subjective choice that states. Additionally, our model does not currently take location error into account, implicitly 5 2 7 assuming that location error is negligible or requiring that it be accounted for via another 5 2 8 method. Although our model can analyze data streams from regular or irregular time intervals, 5 2 9 this will also depend on the inherent properties of the data streams themselves. Since step lengths 5 3 0 and turning angles are calculated from multiple successive observations, these values will not be 5 3 1 comparable once the data are not close to a regular time interval. However, variables such as net This Bayesian framework can be extended to analyze other types of data streams and can turning angles were analyzed for the simulated and empirical tracks, additional ancillary data coming from the sensor (e.g., elevation, salinity, temperature, or accelerometer data) can be used 5 3 8 to make behavioral inference. These data streams can come from all types of distributions (i.e., 5 3 9 continuous, discrete, bounded between 0 and 1). It is also relatively straightforward to deal with 5 4 0 zero-inflated data by including all zeroes in a single bin. Additionally, our segmentation model can be implemented in a semi-supervised fashion, by which practitioners pre-specify breakpoints 5 4 2