Hierarchically embedded scales of movement shape the social networks of vampire bats

Social structure can emerge from hierarchically embedded scales of movement, where movement at one scale is constrained within a larger scale (e.g., among branches, trees, forests). In most studies of animal social networks, some scales of movement are unobserved, and the relative importance of the observed scales of movement is unclear. Here, we asked: how does individual variation in movement, at multiple nested spatial scales, influence each individual’s social connectedness? Using existing data from common vampire bats (Desmodus rotundus), we created an agent-based model of how three nested scales of movement—among roosts, clusters, and grooming partners—each influence a bat’s grooming network centrality. In each of 10 simulations, virtual bats lacking social and spatial preferences moved at each scale at empirically-derived rates that were either fixed or individually variable and either independent or correlated across scales. We found the number of partners groomed per bat was driven more by within-roost movements than by roost switching, highlighting that co-roosting networks do not fully capture bat social structure. Simulations revealed how individual variation in movement at nested spatial scales can cause false discovery and misidentification of preferred social relationships. Our model provides several insights into how nonsocial factors shape social networks.

Methods
Empirical analyses

We analyzed existing published data to estimate how often common vampire bats switched roosts, clusters, and partners. To estimate individual rates of roost-switching, we used 1,336 observations of 81 free-ranging bats of both sexes (38 males and 43 females) that were observed >25 times across 11 tree roosts along the Rio Corobici in Guanacaste, Costa Rica (1, 2). We also made grooming networks using 1,761 grooming interactions among 29 of these bats (3). To estimate individual rates of cluster switching and partner switching, we used 4,092 observations of clusters (defined as bats roosting in the same corner of a flight cage) and 22,836 observations of grooming from 31 vampire bats of both sexes (5 males and 26 females) at a captive colony in Panama (4). Individuals in both studies were identified visually using unique combinations of distinctive wing bands.

To estimate roost-switching rates, we only used observations of the same bat or roost on consecutive days, because roost switching would be underestimated when a bat moved away and then returned to the same roost between observations (see supplement in associated paper for details). To calculate cluster-switching and partner-switching rates, we counted consecutive observations of the same bat where a switch occurred, then divided that count by the total time elapsed between those observations (see supplement for details). We only considered consecutive cluster-switching and partner-switching observations that occurred within a sampled hour. To calculate within-cluster partner-switching rates, we did not count partner switches and the associated time lapse that occurred due to partner switches between clusters.

To create co-roosting and co-clustering networks, we defined edge weights in the co-roosting and co-clustering networks as the ‘simple ratio index’ of association (5–7). To create grooming networks, we defined edge weights as total minutes of grooming. To assess within-bat correlations between movement types, we used a linear model to test if cluster-switching rates predicted within-cluster partner-switching rates.

To determine how well roost, cluster, and partner-switching rates predict the overdispersed counts of the number of bats groomed (outdegree centrality), we fit a quasi-Poisson generalized linear mixed-effects model with each of the three rates as single predictors, and bat as random intercept. We used nonparametric bootstrapping to create a 95% confidence interval (CI) around the standardized coefficient (b).

Agent-based model

We created a model using NetLogo 6.2.0 and used it to simulate movements of virtual vampire bats that lacked preferences for roosts, clusters, or partners. Each of 11 roosts contained 4 locations for potential clusters. We randomly assigned each virtual bat to a starting roost and cluster location. For each spatial scale, each bat had a switching propensity randomly sampled with replacement from empirical estimates of the probabilities of movement. Switching probabilities at every scale were conditional on the time since the last switch (see supplement).

We initially ran all the simulations with populations of 200 virtual bats, the approximate number of bats encountered and banded by Wilkinson along the Rio Corobici between 1978 and 1983 (1, 2). To explore how our results would change with fewer bats and limited partner choice, we later ran the simulation with 100 virtual bats to explore how our results would change with fewer bats, leading to smaller group sizes and limited partner choice (2.3 bats per cluster, or an average of 1.3 partners per cluster).

To isolate the effects of movement, we fixed the probability of grooming per minute for all virtual bats at 1.8% (the mean probability that a captive vampire bat groomed another bat during the sampled hours from empirical observations of captive vampire bats (4)). We included a synchronous 200-minute foraging period where bats left all roosts to forage outside the roosts. The simulations recorded observations of behaviors every minute for 15 days. 

When in a roost, virtual bats randomly decided every minute whether to groom a partner and whether they would switch partners based on an increasing probability related to the time since last switch at that scale. The decision was solely determined by the groomer initiating the exchange; the receiver did not decide whether to accept grooming. Each bat could only groom one partner at any particular minute, but multiple bats could groom the same bat during that minute. Virtual bats decided whether to switch clusters within their roost once every hour. Additionally, they decided whether to switch roosts once per day after returning from foraging.

If a bat changed its partner as a result of cluster or roost switching, we did not count this event as partner switching. Similarly, if a bat changed clusters due to roost switching, we did not count this event as cluster switching. We took this approach to test the effects of a bat’s decisions at each scale rather than the effect of what it experiences. Although we measured within-roost cluster switching and within-cluster partner switching, for brevity, these are simply referred to as ‘cluster switching’ and ‘partner switching.’

Simulations using agent-based model

We ran five types of simulation, each 100 times, and we ran those five simulation types across two different population sizes, once for 100 bats and again for 200 bats. Each of the five simulation types had switching propensities that were either fixed or individually-variable and either correlated or uncorrelated. In simulation 1, virtual bats were assigned a random propensity of roost, cluster, and partner switching; these propensities were uncorrelated within each individual bat because they were drawn independently from empirical distributions. The resulting standardized coefficients of the switching rates from this simulation measured how well each movement type predicted grooming outdegree when controlling for the other movement types.

In simulations 2-4, one type of movement varied among bats while the two others were fixed (to the mean observed from the empirical data). In simulation 2, only partner-switching propensity varied across individuals. In simulation 3, only cluster-switching propensity varied across individuals. In simulation 4, only roost-switching propensity varied across individuals.

Using simulations 2-4, we estimated the reference effects, defined as the median standardized coefficients of the switching rate when switching propensity was not variable between bats. The reference effects measure how well one movement type predicts grooming outdegree when it lacks individual variation in switching propensity. We estimated the isolated effects of individual variation in each switching propensity, defined as the difference between the standardized coefficient of the switching rate when only it was variable between bats and the reference effect. The isolated effect measures how well individual variation in only one movement propensity predicts grooming outdegree while accounting for the reference effect.

Simulation 5 was similar to simulation 1 except that the three switching propensities were positively correlated, such that virtual bats that moved most frequently at one scale also moved most frequently at other scales (see supplement). By comparing the results of simulations 1 and 5, we could therefore assess the effect of switching propensities being correlated (simulation 5) or uncorrelated (simulation 1).

In sum, our model allowed us to ‘switch on and off’ the existence of realistic individual variation in movement at each spatial scale to isolate the social consequences for the individuals, while eliminating the confounding effects of social and spatial preferences found in real vampire bats. By adding or removing individual variation in movement at each scale or across all scales, and by making these movements correlated or not across scales, these simulations allowed us to isolate the causal effects of individually variable movement on grooming network centrality.

Note that a bat’s assigned probability of switching (its switching propensity) is not the same as the number of times it actually switched during the simulation (its switching rate). When switching propensity was fixed, all bats with the same time since last switch also had the same probability of switching at that time step. However, as the model was randomized, the realized number of switching events differed, even when bats had the same switching propensity. This can be seen in Eq. 1 and Eq. 2, where o is the odds of a switch at that time step, p is the probability of a switch, a is the intercept of a logistic mixed effects model (which could be set to be variable or equal for all bats), b is the slope of the logistic mixed effects model (which was always the same across bats), and t is the number of time steps since last switch. When a particular switching propensity was fixed, a was the same for all bats (and, consequently, p if t was also the same). However, every time step, the virtual bats generated an independent value, r, which, if less than p, signaled the bat should try to switch partners. Because each bat generated a different r every time step, the realized partner switching rate was different by bat.

(1)  ln(o) = a + bt

(2)  p = o / (1 + o)

The goal of these simulations was to manipulate the switching propensity (which cannot be measured from the empirical data) and then assess the relative effect of the resulting individual differences in observed switching rate. For a more detailed description of the agent-based model, see the Overview, Design Concepts, Details (ODD) in the supplement.

Analysis of simulated data

Over the course of 15 simulated days, we counted cases of roost, cluster, and partner switching. We used grooming rates to create the grooming network. We measured two measures of grooming network centrality: outdegree, the number of grooming recipients groomed by the focal bat, and pagerank, which estimates connectedness using both direct ties (grooming receivers) and indirect ties (grooming receivers of those receivers). To estimate pagerank based on grooming given rather than grooming received, we calculated it from the transposed grooming matrix. To assess how each movement type predicted grooming network centrality, we fit a Poisson generalized linear model with outdegree (count of partners groomed) as the response, and the scaled counts of roost, cluster, and partner-switching events as predictors. We did not detect evidence for over-dispersion. Effects on outdegree and pagerank centrality were almost identical (see supplement for results).

Effect of individual variation in movement and habitat structure on tests for preferred relationships

Individually variable movements and hierarchically embedded habitat structures create highly nonrandom association rates that could be taken as false evidence of social differentiation (preferred social relationships) if these features are not properly controlled for in the analysis (8). Type 1 error means that social preferences might be falsely detected, exaggerated, or inaccurate when inferences ignore the role of habitat structure and individual variation in movement. To explore this, we used permutation tests to test the significance of social differentiation, the coefficient of variation of edge weights, which is a standard method to test for social preference (5, 9). We did 50 permutation tests for detecting social differentiation using 5 randomly selected grooming networks for each of the 10 simulations. To calculate the p-value, permutation tests were repeated 100 times, each with 10,000 permutations.

To illustrate the importance of constraining permutations to account for habitat structure, we first used unconstrained permutation tests, which permuted the partners across all observed events from randomly selected simulations. Next, to investigate the effects of spatial and temporal constraints on permutations, we used two types of constrained permutation tests on the same simulation. In the semi-constrained permutation test, we created the null model by only permuting groomed partners observed in the same day and roost. In the highly constrained permutation test, we created the null model by only permuting partners observed in the same hour and cluster. Because virtual bats had no social preferences, any inferences of preferred relationships constituted type 1 error. We ran each of the demonstrative permutation tests 100 times, each with 100,000 permutations to the partner groomed.

Next, we tested which factors contributed to false appearance of preferred relationships. To do this, we used unconstrained permutation tests to check for social differentiation in data generated by four additional ‘control simulations’, each with less complexity. The first control simulation lacked hierarchically embedded scales of movement, because all virtual bats were in a single cluster. The second control simulation lacked both hierarchically embedded scales of movement and individual differences in partner-switching propensity. Although partner-switching propensity was constant across all bats, each bat still had a greater probability of grooming the same partner in series rather than grooming a new partner, which we call “byproduct partner fidelity”. The third control simulation was the same as the second but it removed byproduct partner fidelity: instead of a bat deciding whether or not to switch  partners, it selected a random available partner. Finally, the fourth control simulation was identical to the third except all bats groomed simultaneously. We used these control simulations to establish which created the false appearance of social differentiation. Again, we ran these latter demonstrative permutation tests 100 times, each with 100,000 permutations.

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