A wrap-around movement path randomization method to distinguish social and spatial drivers of animal interactions

Abstract

Studying the spatial-social interface requires tools that distinguish between social and spatial drivers of interactions. Testing hypotheses about the factors determining animal interactions often involves comparing observed interactions with reference or 'null' models. One approach to accounting for spatial drivers of social interactions in reference models is randomizing animal movement paths to decouple spatial and social phenotypes while maintaining environmental effects on movements. Here, we update a reference model that detects social attraction above the effect of spatial constraints. We explore the use of our 'wrap-around' method and compare its performance to the previous approach using agent-based simulations. The wrap-around method provides reference models that are more similar to the original tracking data, while still distinguishing between social and spatial drivers. Furthermore, the wrap-around approach results in fewer false-positives than its predecessor, especially when animals do not return to one place each night but change movement foci, either locally or directionally. Finally, we show that interactions among GPS-tracked griffon vultures (Gyps fulvus) emerge from social attraction rather than from spatial constraints on their movements. We conclude by highlighting the biological situations in which the updated method might be most suitable for testing hypotheses about the underlying causes of social interactions. This article is part of the theme issue 'The spatial-social interface: a theoretical and empirical integration'.

Keywords: GPS telemetry; animal movement; null models; randomization; social network analysis; spatial constraints.

Figure 1.

A schematic comparison of the path shuffling and wrap-around randomization methods. Five individuals (A–E) are shown tracked over 5 days, represented conceptually as coloured circles connected by black lines, with hues progressing from dark to light over time (a). In the path shuffling method (b), the order of days is permuted for each individual, resulting in a large number of ‘teleportation’ events (grey slashed lines). In the wrap-around method (c), trajectories are shifted forward or backward by a number of days selected from a uniform distribution between −2 and 2 (the time-shift range), with each individual’s time-shift shown to the right of its trajectory. This method creates a maximum of one ‘teleportation’ event per individual and maintains the order of consecutive days.

Figure 2.

Examples of movement trajectories of home ranges and agents in the ABM. The home range centres to which agents are attracted are either static (a(i); b(i), b(ii), changing locally (a(ii); b(iii), b(iv)), or changing in a directional manner (a(iii); b(v), b(vi)). In (a(i)), the home range centre is shown as a large black circle and in (a(ii), (iii)) the numbers on the large circles of home range centres represent five days. Lines are the walking trajectory of an agent attracted to these home range centres, with line colour corresponding to the colour of each day’s home range centre. The movements of each agent in the ABM are based on correlated random walks in which individuals are either non-sociable (b(i), (iii), (v)) or sociable and attracted to their nearest neighbour (social weight = 0.7, b(ii), (iv), (vi)) when home range centres are static (b(i),(ii)), changing locally (b(iii), (iv), or changing in a directional manner (b(v), (vi)). In (b), the walking trajectories of 10 randomly selected agents throughout the 50 days of a single simulation are shown in colour and the 20 trajectories of the remaining individuals are in light grey. Note the different spatial scales across (b(i)-(vi)).

Figure 3.

Comparing the path shuffling and wrap-around randomization methods using ABMs. In each plot, agents are ordered by their observed value of degree (a) or strength (b) (open circles), which are shown on the y-axes. Agents are either non-sociable ((i), (iii), (v)) or sociable ((ii), (iv), (vi)) and their home range centres are static ((i), (ii)), change locally ((iii), (iv)) or change in a directional manner ((v), (vi)). The degree or strength values of each agent from 100 iterations of the shuffled (orange) or the wrap-around (blue) randomizations (with a maximum time-shift of 10 days, or 20% of the simulation duration) are shown as boxplots which range to the 25 percentile, with whisker lengths as 1.5 times the interquartile range and outliers as small points. The inset in each panel shows the distribution of degree (a) or strength (b) values for all agents in all 100 simulation iterations of the shuffled (orange) or the wrap-around (blue) randomizations; the dashed black lines are the average degree or strength values of the ‘observed’ agents.

Figure 4.

Comparing different time-shift ranges of the wrap-around randomization using ABMs. Distribution of population mean degree (a) and strength (b) values from 100 randomization iterations when agent’s movement trajectories are shuffled each day (orange lines) or when trajectories are shifted using the wrap-around method (blue lines). Each blue line represents a different allowed time-shift range, as a proportion of the total simulation duration. The proportion of shifting ranges from 4% (darkest blue; as much as ±1 day out of 50 days) to 100% (lightest blue; as much as ±25 days out of 50 days). Dashed lines are the 'observed' mean degree or strength of the population of simulated agents, which are either non-sociable ((i), (iii), (v)) or sociable ((ii), (iv), (vi)). The agents' home range centres are static ((i), (ii)), change locally ((iii), (iv)), or change in a directional manner ((v), (vi)). For a visualization of just the means of the distributions shown here, see the electronic supplementary material, figure S2.

Figure 5.

Effect of sampling frequency on the false-positive rate. The likelihood of detecting a social effect (social attraction or avoidance) in the non-sociable simulations, i.e. when there was no underlying social attraction simulated, for the two randomization methods, different time-shift ranges and four sampling frequencies (10%, 20%, 50% and 100% of observed points). Owing to computational constraints, observed values are compared with 50 randomization iterations in this figure. Path shuffling randomization is in orange and blue lines are for the wrap-around method, with shades of blue indicating time-shift ranges, with the proportion of shifting ranging from 4% (darkest blue) to 100% (lightest blue), analogous to figure 4. The grey horizontal lines represent a 95% likelihood (p = 0.05). Coloured lines that go above this grey line indicate that a randomization detected sociality even though a social process was not simulated—i.e. a false positive. Panels on the left show false positives for degree, and panels on the right show false positives for strength. Home range centres are static (a, b), change locally (c, d), or change in a directional manner (e, f).

Figure 6.

Vulture interactions emerge from social attraction rather than from spatial constraints. Number of unique individuals a vulture interacts with—degree (a, b) and number of interactions—strength (c, d) of free living vultures during summer 2022 (black open circles). Individual vultures are ordered along the x-axis by their observed degree (a, b) or strength (c, d). The observed values are compared with the degree (a, b) and strength (c, d) expected by chance when shuffling the trajectory of each day (orange) and when shifting trajectories up to 12 days in either direction (a total time-shift range of 24 days) in (a, c) and by 1 day in each direction (total time-shift range of 2 days) in (b, d) using the wrap-around method (blue).