Effects of Temporal Resolution on an Inferential Model of Animal Movement

<div><p>Recently, there has been much interest in describing the behaviour of animals by fitting various movement models to tracking data. Despite this interest, little is known about how the temporal ‘grain’ of movement trajectories affects the outputs of such models, and how behaviours classified at one timescale may differ from those classified at other scales. Here, we present a study in which random-walk state-space models were fit both to nightly geospatial lifelines of common brushtail possums (<i>Trichosurus vulpecula</i>) and synthetic trajectories parameterised from empirical observations. Observed trajectories recorded by GPS collars at 5-min intervals were sub-sampled at periods varying between 10 and 60 min, to approximate the effect of collecting data at lower sampling frequencies. Markov-Chain Monte-Carlo fitting techniques, using information about movement rates and turning angles between sequential fixes, were employed using a Bayesian framework to assign distinct behavioural states to individual location estimates. We found that in trajectories with higher temporal granularities behaviours could be clearly differentiated into ‘slow-area-restricted’ and ‘fast-transiting’ states, but for trajectories with longer inter-fix intervals this distinction was markedly less obvious. Specifically, turning-angle distributions varied from being highly peaked around either or at fine temporal scales, to being uniform across all angles at low sampling intervals. Our results highlight the difficulty of comparing model results amongst tracking-data sets that vary substantially in temporal grain, and demonstrate the importance of matching the observed temporal resolution of tracking devices to the timescales of behaviours of interest, otherwise inter-individual comparisons of inferred behaviours may be invalid, or important biological information may be obscured.</p> </div

Data from a single night's activity of possum #1882.

<p>Example of a nightly movement trajectory of possum #1882 at sub-sampling intervals of 5, 15, 30 and 60 min. Inferred behavioural states are shown for each location estimated by the two-state model. Panel (a) shows the original trajectory as recorded at 5-min intervals from a GPS collar. Panels (b–d) indicate sub-samples of the original trajectory at progressively larger intervals (15, 30, and 60 min, respectively). Piecharts show the proportions of the two behavioural modes (red is ‘slow-area-restricted’, green is ‘fast-directed’). In this example, it is obvious that as sub-sampling interval increases, the proportion of ‘slow-area-restricted’ behaviour correspondingly decreases (by 25%). The figure also demonstrates the considerable loss of information about behaviour at larger sampling intervals.</p

Synthetic data, at original frequency.

<p>Inferred behavioural states from the MCMC fitting are shown for each location (red is ‘slow-area-restricted’, green is ‘fast-directed’), and the colour scale indicates the posterior probability of each data point being in State 1.</p

Movement-rate and turning-angle distributions for MCMC output from synthetic data.

<p>Each sub-figure shows, for each state in the two-state model, movement-rate (top) and turning-angle (bottom) distributions, at subsampling frequencies of (a) 1, (b) 3, (c) 6 and (d) 12 units, where the original data are ‘observed’ every unit. Solid lines are posterior Weibull and wrapped Cauchy distributions, with one (two) posterior standard deviations shown in dark (light) grey. Histograms are observed frequencies, with division of data into states using output from MCMC computations. Histogram bars are coloured according to the mean probability of observations in that bar being in State 1 or 2, as given in the colour bar in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057640#pone-0057640-g001" target="_blank">Fig. 1</a>, that is, red bars are more likely to be in State 1 and green bars more likely to be in State 2. Yellow bars are close to being undetermined - that is, they have an approximately equal probability of being in either state.</p

Posterior means of movement-rate distributions with respect to the temporal resolution of modelled trajectories.

<p>The figures show the posterior means of the Weibull distributions for movement rates (in m/s), with error bars of one posterior standard deviation, for each of the four possums, as a function of sub-sampling interval. State 1 is indicated with dashed lines, and State 2 with dotted lines. As expected, the movement rates decrease with increasing sub-sampling interval.</p

Posterior mean vectors of turning-angle distributions of possum #1882.

<p>The figure shows the posterior mean vectors of the wrapped Cauchy distribution of turning angles, for each sub-sampling interval and behavioural state. Circles around each arrow head have radius equal to the posterior standard deviation of the mean vector.</p

Mean vectors of posterior turning-angle distributions.

<p>Mean vectors are represented for subsampling intervals of 5, 15, 30 and 60 min, for both behavioural modes (red is State 1, green is State 2), for each of the four possums. Each arrow and circle represents one behavioural mode for one possums. Circles around arrow heads have radii equal to the posterior standard deviation of mean vectors. The dashed arrow in (a) is of length 0.4 (the maximum possible length for a mean vector is 1, which corresponds to a point distribution).</p

Movement-rate and turning-angle distributions of one set of trajectories (possum #1882).

<p>Each sub-figure shows, for each state in the two-state model, movement-rate (top, in m/s) and turning-angle (bottom, in degrees) distributions, at subsampling frequencies of (a) 5 min, (b) 15 min, (c) 30 min and (d) 60 min. Lines and colors are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057640#pone-0057640-g002" target="_blank">Fig. 2</a>.</p