Trade-offs with telemetry-derived contact networks for infectious disease studies in wildlife

Abstract

1. Network analysis of infectious disease in wildlife can reveal traits or individuals critical to pathogen transmission and help inform disease management strategies. However, estimates of contact between animals are notoriously difficult to acquire. Researchers commonly use telemetry technologies to identify animal associations; but such data may have different sampling intervals and often captures a small subset of the population. The objectives of this study were to outline best practices for telemetry sampling in network studies of infectious disease by determining (1) the consequences of telemetry sampling on our ability to estimate network structure, (2) whether contact networks can be approximated using purely spatial contact definitions, and (3) how wildlife spatial configurations may influence telemetry sampling requirements.

2. We simulated individual movement trajectories for wildlife populations using a home range-like movement model, creating full location datasets and corresponding “complete” networks. To mimic telemetry data, we created “sample” networks by subsampling the population (10-100% of individuals) with a range of sampling intervals (every minute to every three days). We varied the definition of contact for sample networks, using either spatiotemporal or spatial overlap, and varied the spatial configuration of populations (random, lattice, or clustered). To compare complete and sample networks, we calculated seven network metrics important for disease transmission and assessed mean ranked correlation coefficients and percent error between complete and sample network metrics.

3. Telemetry sampling severely reduced our ability to calculate global node-level network metrics, but had less impact on local and network-level metrics. Even so, in populations with infrequent associations, high intensity telemetry sampling may still be necessary. Defining contact in terms of spatial overlap generally resulted in overly connected networks, but in some instances, could compensate for otherwise coarse telemetry data.

4. By synthesizing movement and disease ecology with computational approaches, we characterized trade-offs important for using wildlife telemetry data beyond ecological studies of individual movement, and found that careful use of telemetry data has the potential to inform network models. Thus, with informed application of telemetry data, we can make significant advances in leveraging its use for a better understanding and management of wildlife infectious disease.

Introduction

Outbreaks of infectious disease in wildlife can have significant impacts on population health and may also have detrimental effects on domestic animals and humans as a result of cross-species transmission (Jones et al., 2008; Plowright et al., 2017). Disease modeling has proven an illuminating tool in understanding transmission dynamics within and between wildlife populations (Lloyd-Smith et al., 2009). However, disease models rely upon estimates of transmission, which require estimates of contact between individuals, particularly for directly or sexually transmitted pathogens (Anderson & May, 1991; Begon et al., 2002). Further, contact heterogeneity within a population has significant impacts on epidemic outcomes (Lloyd-Smith, Schreiber, Kopp, & Getz, 2005; Keeling & Eames, 2005), which may alter the approach needed to appropriately model a pathogen system. Network analysis (including social network analysis and network modeling) incorporates contact heterogeneity which can help address this challenge, but network tools are data hungry and further dependent on quality estimates of contact rates (Keeling & Eames, 2005).

The cost and effort required to monitor free-ranging populations, the size or secretive nature of a species, or inhospitable habitats can all make contacts in wildlife challenging to observe (Krause et al., 2013). Estimates of contact in wildlife populations, therefore, increasingly utilize remote or automated detection of animal associations via animal tracking devices (Cross et al., 2012; Krause et al., 2013). Among such approaches, arguably the most direct approximation of contact is to identify co-location in both space and time (spatiotemporal overlap) via proximity loggers (e.g., Hamede, Bashford, McCallum, & Jones, 2009). However, proximity loggers are not a perfect solution; a short battery life can limit the duration of observation, and the larger size of these loggers is inappropriate for some species (Krause et al., 2013). Alternatively, GPS or VHF telemetry technologies have also been used to detect spatiotemporal overlap as a proxy for contact (e.g., Perkins, Cagnacci, Stradiotto, Arnoldi, & Hudson, 2009; Godfrey, Ansari, Gardner, Farine, & Bull, 2014; Schauber, Nielsen, Kjær, Anderson, & Storm, 2015), but the localization error associated with these tools may affect their contact detection accuracy (Hulbert & French, 2001).

Another proxy mechanism for estimating contacts in wildlife is through the use of spatial overlap contact definitions, which assumes that the extent of spatial overlap between any two individuals is representative of the probability of contact. A number of studies have used this approach to estimate networks and contact rates from observed or telemetry-recorded locations (e.g., Schauber, Storm, & Nielsen, 2007; Godfrey, Moore, Nelson, & Bull, 2010; Lewis et al., 2017). Further, home range and subsequent spatial overlap estimation can be accomplished with lower frequency of sampling than would be required for spatiotemporal definitions of contact. However, while some studies have supported the underlying assumption that increased dyadic spatial overlap is associated with increased dyadic contact rate (Robert, Garant, & Pelletier, 2012; Vander Wal, Laforge, & McLoughlin, 2014), this assumption has not been thoroughly tested across systems (Schauber et al., 2015) and may be more likely to reflect the likelihood of shared space use rather than actual interaction frequency (Wanelik & Farine, 2019). Further, studies examining animal social networks often correct for spatial overlap (Whitehead & James, 2015), indicating that spatial overlap is, as yet, an unproven proxy for animal associations.

Perhaps the most pervasive challenge for any of these contact estimation approaches or any telemetry study more broadly is the issue of appropriate sampling effort — both the proportion of the population sampled and the frequency with which locations are recorded for each monitored individual. While some work has attempted to establish the proportion of a population that must be sampled (i.e. node sampling) for appropriate estimates of contact networks (e.g., Wey, Blumstein, Shen, & Jordán, 2008; Smith & Moody, 2013; Silk, Jackson, Croft, Colhoun, & Bearhop, 2015), less effort has been focused on the frequency with which individuals should be monitored (i.e. edge sampling, but see Davis, Crofoot, & Farine, 2018). Further, we lack realistic sampling recommendations for deriving contact networks for wildlife (Cross et al., 2012, but see Costenbader & Valente, 2003), and, to the best of the authors’ knowledge, no research has yet explored the impact of the frequency of telemetry locations on subsequent network estimation.

Despite these challenges, telemetry estimation of wildlife contacts holds great promise for informing network analysis and improving understanding of pathogen transmission in wildlife. Researchers therefore need best practices recommendations for using existing and future telemetry datasets for wildlife network estimation, particularly in light of the lack of information about necessary telemetry sampling effort.

Because sampling or directly observing an entire wildlife population and all of its resulting contacts is currently unfeasible, we employed a simulation approach to investigate the impact of telemetry sampling on contact detection and network estimation. The first objective of this study was to simulate the movement trajectories of a theoretical wildlife population to produce complete networks of known contacts and then to simulate different sampling effort regimes by “collaring” or “tagging” different proportions of the population and also varying the frequency of telemetry sampling. We hypothesized that the impact of sampling would vary based on the metrics used to describe network structure, with metrics determined by local network topology being the most resilient to reduced sampling effort (Cross et al., 2012; Davis et al., 2018).

In addition, because different approaches to detecting and defining contact, even in the same population, can result in different contact network structures (Perkins et al., 2009), our second objective was to investigate how our methodological definition of a contact (spatiotemporal overlap versus spatial overlap) affected network structure and resulting network metrics. In particular, we investigated if more sensitive, but less specific definitions of contact could compensate for reduced sampling effort.

Lastly, social systems of wildlife are highly variable, spanning from solitary to highly gregarious, and from non-territorial to territorial (Sah, Mann, & Bansal, 2018). Our third objective was therefore to determine if the underlying social system of the population has consequences for the effect of sampling on network estimation. We tested variations in the spatial configuration of simulated populations to represent a range of realistic social systems, including highly territorial populations with infrequent associations between individuals (e.g. solitary carnivores) and highly aggregated populations with frequent associations between individuals (e.g. herd species or animals aggregating around limited resources). We hypothesized that territorial populations with infrequent associations would be more sensitive to sampling, as their rare associations with limited partners are more likely to be missed with telemetry sampling.

Materials and Methods

Simulations

In order to examine the effects of telemetry sampling on subsequent network estimation, we simulated movements of individuals in wildlife populations and sampled from these movement trajectories to mimic data collection from telemetry devices (Figures 1 and S2). Hereafter, a single simulation refers to movement trajectories for a population of 100 animals. Movement trajectories were created using a simple biased correlated random walk (BCRW; (Long, Nelson, Webb, & Gee, 2014), which produces home range-like movement when the bias is directed toward the starting point of the trajectory (Van Moorter et al., 2009). A home range movement model was necessary in order to estimate home ranges and thereby test the robustness of spatial overlap as an indicator of animal associations (see “Sample Networks” below). The movement trajectories were generated on a per-minute basis, for a duration of 90 days. We considered 90 days an appropriate time frame for contact network estimation because animal social dynamics and pathogen transmission are known to vary seasonally (Reynolds, Hirsch, Gehrt, & Craft, 2015).

Figure 1:

Workflow for simulations, sampling, and network estimation. Green boxes indicate individual steps in the workflow, and purple boxes indicate treatments introduced to simulations, sampling, or contact detection protocols. “q1m” means “every 1 minute,” and so on.

Movement trajectories were generated using six parameter sets. Three of these varied home range sizes by altering the step length distribution scaling parameter, while leaving all other parameters constant; this produced small, medium, and large home range parameter sets (Table S1). Because the BCRW is a simple, tractable movement model, step length distributions based on empirical movement data do not necessarily produce appropriate home range sizes for a chosen species. Rather, the BCRW allowed us to test the sensitivity of our findings to changes in movement model parameters without the decreased transparency associated with more complex movement models. With these benefits in mind, we tested three additional parameter sets which kept home range size roughly constant with the small home range model while varying other BCRW parameters (Table S1).

To mimic different spatial configurations, with a given parameter set, we varied the starting locations (and thus the home range centers) of individuals, testing random, lattice, and clustered spatial configurations (Figure S1). Random configurations were a “null” spatial layout. Lattice configurations maintained approximately the same degree of home range overlap, independent of home range size, and represented highly territorial, solitary species such as many large carnivores (e.g. jaguars, Ethiopian wolves; Zubiri & Gottelli, 1995; de Azevedo & Murray, 2007). Clustered configurations placed individuals in one, five, or ten equally sized clusters, thereby representing highly social species (e.g. social ungulates such as white-tailed deer or American bison; Schauber et al., 2015) or animals aggregated around heterogeneous resources (e.g. urban racoons; Hirsch, Prange, Hauver, & Gehrt, 2013). Further details on simulation methods can be found in Supplementary Materials. We performed all simulations in R, version 3.5.0 (R Core Team, 2018).

Complete Networks

We constructed complete contact networks by detecting contact events between all 100 individual movement trajectories in a given simulated population. For complete networks, contact was always determined by spatiotemporal overlap, with contacts defined as simultaneous locations within a given distance threshold. We varied the distance threshold used to construct complete networks; because movement simulations were scale-free, we refer to the thresholds as small, medium, or large thresholds (hereafter, small thresholds, etc.), with these resulting in three complete networks for any given simulation. The distance thresholds should be considered relative to the step length distributions used in the movement model. For example, even with the smallest step length distribution, an individual’s cumulative steps would surpass the largest contact threshold within about 8-10 steps (i.e. minutes), meaning that even our large contact threshold is fairly strict (see Supplementary Materials for further details).

Sample Networks

To construct sample networks, we first mimicked sampling a subset of the population by randomly selecting a portion of the simulated individuals to “collar.” We varied the sampling effort from 10-100% of the population at 10% intervals (hereafter, proportion of the population sampled). In reality, the proportion of a wildlife population sampled is often unknown, but is likely to be on the lower end of this range (i.e. <50%; Cross et al., 2012). With those monitored individuals, we then varied the frequency of location sampling by recording individual locations at an interval of every 1 minute, 15 minutes, 60 minutes, 3 hours, 12 hours, 24 hours, or 72 hours (hereafter, frequency of sampling). This range spans functionally continuous sampling (every 1 minute), which is rare in wildlife studies, to much more common frequencies of GPS sampling (every 12-72 hours). The composite of the proportion of the population sampled and frequency of sampling is hereafter referred to collectively as sampling effort.

We then estimated spatiotemporal overlap using simultaneous locations within large, medium, or small distance thresholds for each sample dataset. For sample networks, we also detected contacts as determined by spatial overlap, which we calculated using the utilization distribution overlap index (UDOI) of the 95% bivariate normal kernel density estimate (KDE) home range (Fieberg, Kochanny, & Lanham, 2005). Spatial overlap contacts were defined as UDOI greater than zero (using both binary and weighted edges). Because KDE approaches assume independent locations (Worton, 1989), we only calculated spatial overlap contacts for telemetry frequencies of every 24 or 72 hours. Spatial overlap was calculated using the adehabitatHR package in R (Calenge, 2006).

Network Comparisons

Complete and sample networks were compared based on contact definitions (Figure S2). The complete networks with a large contact threshold were therefore compared to sample networks with the same large threshold, and so on. In addition, we compared complete networks with a medium threshold to corresponding sample networks with a large threshold to assess the effect of using a more sensitive but less specific spatiotemporal contact definition in the sample network. Lastly, we compared the three types of complete networks (large, medium, or small threshold) to sample networks derived from the spatial overlap contact definition. Hereafter, sample networks with the same contact definition as their corresponding complete network are referred to as strict contact definitions, while sample networks with more sensitive/less specific spatiotemporal or spatial overlap contact definitions are referred to as less precise contact definitions.

For all complete and sample networks, we calculated seven structural network metrics which can be important for pathogen transmission. We followed Silk et al. (2015) and Davis et al. (2018) in selecting the node-level metrics of degree, strength, betweenness, and transitivity; we also calculated network-level metrics of density, proportion isolates, and modularity (see Supplementary Materials for modularity details). As in Davis et al. (2018), we characterized our node-level metrics as local or global. Degree and strength are determined by local connectivity, and individuals with high degree or strength have more or stronger connections. Such well-connected individuals may therefore be candidates as “superspreaders” in studies of pathogen transmission (Lloyd-Smith et al., 2005). Betweenness and transitivity are determined by global network topology; individuals with high betweenness may be important “firebreak” individuals for interrupting pathogen transmission (VanderWaal, Atwill, Isbell, & McCowan, 2014), and transitivity is a measure of clustering in a network (Farine & Whitehead, 2015) which can have significant impacts on epidemic outcomes (Keeling & Eames, 2005). Network analysis was performed with the R package igraph (Csardi & Nepusz, 2006).

To compare node-level metrics between complete and sample networks, we followed Davis et al. (2018) in calculating the ranked correlation coefficient between metrics from individuals in the sample network to corresponding individuals from the complete network. We calculated mean and 95% confidence intervals for ranked correlation coefficients as averaged across variations in movement model parameterization and sampling effort. Sample networks often became very poorly connected with low sampling effort, meaning that fewer networks had measurable node-level metrics, with subsequently greater variation in mean ranked correlation coefficients. We therefore conservatively used the lower limit of the 95% confidence interval, rather than the mean, to interpret results. Target correlations were between 0.80 and 1.00, following Smith and Moody (2013). When networks were completely unconnected at a given level of sampling effort, we classified them as “disconnected.”

To compare agreement between sample and complete networks for the network-level metrics (density, proportion isolates, modularity), we calculated the percent error of mean metric values between complete and sample networks across given simulation variations. Here percent error is the difference between the network metric of the sample and complete networks, divided by the metric of the complete network, and multiplied by 100%. For proportion isolates, we assessed the percent error of the complement of proportion isolates (i.e., proportion connected or effective number of nodes; Sah et al., 2018) as connected individuals are of primary interest in pathogen transmission studies. Percent error of mean density and proportion isolates describes agreement in overall network connectivity; a positive percent error equates to more connections in the sample network than the complete network. For modularity, a positive percent error indicates higher modularity in the sample networks, suggesting stronger community structure.

Results

We completed a total of 11,994 simulations, each with three definitions of contact (large, medium, or small threshold) used to construct complete networks, for a total of 35,982 complete networks. Simulation variations did not yield substantial changes in the patterns reported here, but more extensive results are reported in supplementary materials (Figures S1–S12). Here we highlight key results for medium home range simulations which are illustrative of our overall findings.

Local metrics outperform global metrics

When using spatiotemporal definitions of contact, all metrics performed best (highest correlation coefficients and smallest percent error) for comparisons of complete and sample networks with large threshold contact definitions, and all metrics performed poorly with small thresholds. This finding was consistent across all simulation variations, and was likely driven by fewer associations with the small thresholds. In general, the local metrics (strength, degree) consistently outperformed the global metrics (betweenness, transitivity; Figures 2 and S1–S8). Strength showed the highest resilience to sampling of all metrics with the best performance in clustered populations. However, even among the local metrics, high sampling effort was still required to achieve high correlation scores in some instances (e.g. for lattice spatial configurations, as in Figure 2).

Figure 2:

Heat maps demonstrating the lower limit of the 95% confidence interval for mean correlation coefficient results for betweenness and strength, the best performing global and local node-level network metrics, respectively. Yellow and light green cells indicate the highest correlation categories. Results here represent a comparison of complete networks and sample networks generated with large threshold contact definitions. Results shown are for medium home range movement simulations across four variations in spatial configurations (random, lattice, one cluster, and ten clusters). For telemetry sampling frequencies, “q1m” means “every 1 min,” and so on.

Density, proportion isolates, and modularity performed intermediately as compared to the other metrics. Density, especially, required higher frequency of sampling to achieve a smaller percent error. As with the node-level metrics, both density and proportion isolates performed best (smallest percent errors) in clustered populations, with random and lattice spatial configurations more sensitive to sampling (Figures S9–S12). Modularity, on the other hand, showed strong positive percent error in clustered configurations, and greater variability in results overall (Figures S13–S14).

Frequency of sampling has major consequences for network estimation

As expected, reducing the proportion of the population sampled resulted in reduced metric performance for most metrics, but with the notable exception of density (Figures S9–S10). Density was largely unaffected by the proportion of the population sampled, regardless of simulation variations, though this was likely a result of the random sampling procedure used. Surprisingly, frequency of telemetry sampling had at least as much impact on metric performance as the proportion of the population sampled (Figure 2). This was especially notable for global metrics, density, lattice spatial configurations, and more restrictive contact definitions (medium or small thresholds), where seemingly minor reductions in the frequency of sampling resulted in rapid decreases in correlation scores and more negative percent error.

Less precise contact definitions produce overly connected networks

We also examined metric performance when less precise contact definitions were used in the sample networks in order to determine if such approaches could compensate for reduced sampling effort. We found mixed results when using less precise contact definitions. As with the spatiotemporal contact definitions, global metrics performed poorly across all simulation variations. The local metrics, however, occasionally recovered surprising levels of correlation performance with our less precise contact definitions (Figures 3 and S5–S8), especially when compared to the equivalent sampling effort with a standard spatiotemporal contact definition (Figure 3). The correlation score improvements were the most pronounced for spatial overlap definitions of contact when the complete networks were defined by a large threshold. Even with the local metrics, improvements in correlation scores varied across types of spatial configurations: clustered configurations showed the most improvement with less precise contact definitions, but lattice layouts displayed no major increase in correlation scores. The network-level metrics, density and proportion isolates (evaluated as proportion connected), showed increased positive percent error, demonstrating that these less precise definitions of contact produced overly connected networks (Figures S9–S12).

Figure 3:

Heat maps of network strength (lower limit of the 95% confidence interval for mean correlation coefficient), which showed the strongest improvement with a spatial overlap contact definition, for medium home range simulations at the coarsest frequencies of sampling. The top panel represents the comparison between complete and sample networks each generated with large threshold spatiotemporal contact definitions (Spatiotemporal Overlap). The lower panel shows results for the comparison between complete networks with a large threshold spatiotemporal contact definition and sample networks with a spatial overlap contact definition (Spatial Overlap).

Spatial configuration has significant impacts on network estimation

The performance for all social network metrics varied with spatial configuration (degree shown for illustrative purposes in Figure 4; see also Figures S1–S12). Lattice layouts, in particular, consistently showed poor metric performance, while dense, frequently interacting populations (i.e. one cluster) had the best metric performance. In general, the lattice and random layout populations had fewer associations than clustered populations (Table S2; from 1-20% of the mean number of contacts for single cluster configurations), supporting our hypothesis that infrequently interacting populations would be more sensitive to telemetry sampling. However, even in instances in which lattice populations had greater than or equivalent mean numbers of contacts per dyad (Table S2), correlation scores in lattice populations remained low compared to other spatial configurations, suggesting that sampling sensitivity is not entirely mediated by the strength of an association. The global metrics showed less variation in performance with spatial configuration, although these metrics generally performed poorly across all variations.

Figure 4:

Heat maps of the lower limit of the 95% confidence interval of mean correlation coefficient for degree. Yellow and green represent the highest correlation values; results are shown across two movement model variations (small and large home ranges; Small HR and Large HR, respectively) and four spatial configurations (random, lattice, one cluster, and ten clusters), with large threshold contact definitions.

Simulated home range size varied from 5 × 10⁶ (small) to 4 × 10⁷ (large) square units (equivalent to 5 to 40 square “kilo-units”; a mean area increase of 800%, Table S1). Home range size also impacted metric performance, with a general trend toward reduced performance as home range size increased . For density, this trend resulted in large home range simulations having larger positive percent error when using a spatial overlap definition of contact in sample networks. This is notable for lattice simulations, which were designed to keep roughly equivalent amounts of spatial overlap between individuals across simulations (see Supplementary Materials for details on simulations), meaning it is unlikely that large home range simulations had proportionally more overlap than small home range simulations. Rather, the higher positive percent error in the lattice scenarios suggests that large home range simulations generally had fewer associations between individuals, making these simulations more sensitive to sampling across metrics and simulation variations (Table S2).

Discussion

Wildlife telemetry data can be a powerful tool for remotely detecting animal associations for use in network estimation, social network analysis, and pathogen transmission modeling (Robitaille, Webber, & Vander Wal, 2019). However, regardless of study objective, variations in telemetry sampling effort can have a significant impact on the structure of subsequent contact networks. Our results suggest that the impact of telemetry sampling effort varies with contact definition, spatial configuration, and the chosen network metrics, and we provide best practices recommendations for telemetry sampling design for network studies of wildlife infectious disease below.

Prioritize local network metrics and consider maximizing sampling frequency

Across all simulation variations, we found that local network metrics consistently outperformed global metrics. However, the local metrics still required intensive sampling under some conditions, especially lattice layout populations. Further, the frequency of telemetry sampling was often at least as important as the proportion of the population sampled in order to achieve high metric correlation values. In the context of networks, the proportion of the population monitored can be thought of as “node sampling,” while the frequency of telemetry sampling relates to the “edges” of the network. Given the profound impact of undersampling the edges of the network which we observed here, we suggest that researchers may choose to maximize frequency of telemetry locations over the proportion of the population sampled, especially for territorial species or those with infrequent interactions (e.g. solitary species such as puma; Elbroch & Quigley, 2016). This recommendation expands upon work by Franks et al. (2010), who argued for emphasizing edge sampling over node sampling when observing gambit of the group associations in resource-limited circumstances. In infectious disease studies, estimates of local metrics may be important for identifying highly connected individuals (i.e. “superspreaders”), but also for determining if phenotypic traits are associated with connectedness. For example, traits like sex, age, or social rank may be associated with high node degree, allowing for more efficient vaccination protocols, interventions, or management strategies (Rushmore et al., 2014). The population sample sizes necessary to achieve the statistical power to identify such associations may therefore need to be balanced against the frequency of locations necessary to accurately estimate local network metrics, and our simulation results suggest this conflict will be most profound for territorial or infrequently interacting species.

In more extreme situations, researchers may also consider using a smaller number of intensively monitored individuals to develop movement and association models in order to simulate contacts in populations. Such an approach may be particularly useful if global network metrics are critical to the research objective (e.g. using high betweenness to identify important “firebreak” individuals for vaccination or quarantine), as these metrics tended only to perform well with exceptionally high sampling effort which is generally not feasible for wildlife populations. Alternatively, many network metrics tend to be highly correlated with each other, including betweenness and degree (VanderWaal et al., 2014; Farine & Whitehead, 2015), which could further depend on spatial configuration. Researchers may therefore consider if a local network metric is able to accomplish their research objectives, rather than attempting to manage the sampling challenges needed to achieve reliable global metrics.

Spatial overlap is a viable contact definition in clustered spatial configurations

We also examined the effect of using less precise contact definitions on network estimation. First, we examined the effects of using a large spatiotemporal threshold in sample networks, as compared to a medium threshold in the complete network. While simulating location error was beyond the scope of the present study, a less precise spatiotemporal contact definition approximates some of the precision lost with telemetry location error. The less precise spatiotemporal contact definitions showed modest improvement in local metric correlation scores suggesting location error may have limited effects on network estimation. However, further research more specifically into the effects of location errors are necessary to refine this conclusion.

Importantly, in some instances, less precise spatial overlap contact definitions were able to compensate for coarse sampling by still identifying the relative connectedness of individual nodes in our simulations. Thus, if the research objective is to identify the most connected individuals in a population (Craft, 2015; Farine & Whitehead, 2015; White, Forester, & Craft, 2017), less precise contact definitions like spatial overlap may be a viable strategy. However, because these contact definitions simultaneously produced overly dense networks, caution should be applied if using these contact definitions for metrics at the network level or in the context of pathogen transmission simulations. It may be possible to correct for overly dense networks when using a less precise contact definition by “thresholding” at the network level — for example, only counting as contacts those pairs that reach a specified level of spatial or spatiotemporal overlap — however excluding edges below a given weight is generally not recommended in network studies (Farine & Whitehead, 2015), and determining the exact threshold to use may be ambiguous or lack biological motivation.

A major caveat of using less precise contact definitions to compensate for coarse sampling, however, is that the performance of these contact definitions varied across spatial configurations. For example, lattice layout populations surprisingly showed no major improvement in correlation scores with less precise contact definitions. Thus, we recommend using empirical data or system-specific movement simulations to justify using less precise contact definitions as proxies of direct contact (as in Brandell et al., unpublished data), particularly in highly territorial populations.

Our results are largely consistent with prior work which has found that spatial overlap may be used as a proxy for direct contact (Robert et al., 2012). However, such findings have not been consistent across all studies (e.g., Schauber et al., 2007) and spatial overlap is often corrected for in social network studies (Whitehead & James, 2015), suggesting that the utility of spatial overlap as a proxy of direct contact may be system specific. Further, in our simulations, spatial overlap was more representative of less restrictive contact definitions (large threshold), and may therefore be more appropriate when studying host-pathogen systems in which the pathogen is transmitted over larger distances or longer time periods (e.g. long-distance aerosol, vector, or persistent environmental transmission; Tissot-Dupont, Amadei, Nezri, & Raoult, 2004; Burgin et al., 2013). Because less precise contact definitions may be able to make the most of otherwise low frequency sampling, this approach may allow researchers to sample edges with reduced effort. While any remote contact detection approaches may struggle to determine the exact nature of an association (e.g. aggressive vs. passive; Krause et al., 2013), the less precise contact definitions are even more limited. Spatial overlap, for example, cannot directly characterize the duration or frequency of associations, both of which may be important for pathogen transmission (Sah et al., 2018). Thus, less precise contact definitions may augment but should not replace stricter, more specific definitions.

Spatial configurations influence telemetry sampling requirements

Our final objective was to determine if the effect of telemetry sampling varied with population spatial configuration. We found that random and lattice configured populations, which had lower density networks and less frequent associations, required high sampling effort to achieve high correlations between complete and sample network metrics, especially compared to clustered populations. Lattice layouts, which are most representative of highly territorial populations with limited associations such as many large carnivore species (e.g. jaguars; de Azevedo & Murray, 2007) or between groups of some social species (e.g. Ethiopian wolves; Zubiri & Gottelli, 1995), were generally the most sensitive to the effects of telemetry sampling and may therefore require especially high sampling effort to accurately estimate network metrics. Further, relatively solitary species tend to have higher variation in their number of contacts (Sah et al., 2018), which may make these populations more sensitive to undersampling, particularly if the distribution of contacts is highly skewed (Wilson et al., 2002; Perkins et al., 2009).

This increased effort may be especially important as the rare or infrequent associations between solitary animals may be pivotal for pathogen transmission, and would be easily missed with sampling effort deemed adequate for other species (social species or species aggregating over heterogeneous resources, e.g. deer or urban racoons). For instance, among our lattice simulations, even local metrics required a frequency of sampling of every 1 to 15 minutes to achieve moderate correlation scores; this level of sampling effort is quite high, even for GPS collars, and is likely to be beyond the level of effort used in many wildlife monitoring studies. VHF telemetry, in particular, tends to capture animal locations far less frequently, such that our locations every 72 hours represent a high level of effort for VHF telemetry (Krause et al., 2013). When using spatiotemporal contact definitions, VHF telemetry is therefore unlikely to adequately capture network structure for territorial, solitary species. Further, GPS telemetry for these species is likely to require higher than average frequency of sampling when the study objective is to estimate contact networks for disease transmission. Our simulations are limited in their system specificity, however, so actual sampling effort should be determined by empirical data or species-specific simulations. Importantly, spatial overlap definitions of contact performed poorly for these infrequently interacting species, meaning that spatial overlap is unlikely to be able to compensate for their higher sampling needs. Spatial overlap contact definitions may be more appropriate in heterogeneous landscapes or instances of resource provisioning where animals are expected to congregate (Becker & Hall, 2014) — a scenario approximated by our clustered simulations.

Challenges and future opportunities

By examining aggregated populations of individuals, our clustered simulations capture some impact of landscape heterogeneity and social biology on telemetry sampling. However, more explicit inclusion of landscape heterogeneity (e.g. through simulations based on resource selection functions, RSF; Dougherty, Seidel, Carlson, Spiegel, & Getz, 2018; White, Forester, & Craft, 2018) would be particularly useful in future work to further ascertain the effect of landscape heterogeneity on telemetry sampling and subsequent network estimation. We chose a relatively simple movement model, the BCRW, as this improved model transparency and better allowed us to determine the robustness of our results to variations in model parameterization. RSF models would be an appropriate future direction to add an additional layer of complexity and further biological realism to our findings.

Further, we utilized the same movement model across all individuals in a given simulation. In reality, animal movement varies across time of day, and between different individuals. For example, in species where males maintain larger home ranges, these individuals may require higher sampling effort, given that larger home range simulations in our study demonstrated higher sensitivity to telemetry sampling. For determining system-specific telemetry sampling needs with a simulation approach, increased biological realism should incorporate both landscape and these individual-level heterogeneities.

Contact networks used for transmission modeling should be aggregated over time frames representative of the infectious period for the pathogen of interest (White et al., 2017). Our 90-day simulation durations, therefore, make our simulations more representative of pathogens with short to moderate infectious periods (Craft, Volz, Packer, & Meyers, 2011); for longer infectious periods or populations with more rapid changes to social organization, dynamic networks might be used (Volz & Meyers, 2007; Bansal, Read, Pourbohloul, & Meyers, 2010). Future work examining the effect of telemetry sampling over dynamic networks would help refine sampling needs for populations with fission-fusion social dynamics or seasonal changes in network structure, where such temporal changes may result in significantly different epidemic outcomes (VanderWaal, Gilbertson, Okanga, Allan, & Craft, 2017).

Another key assumption of our simulations was that individuals behave independently of one another. Attraction behaviors would make animals more likely to interact or maintain associations for longer durations than is represented by our simulations. Such associations would be expected to make contact networks less sensitive to reduced telemetry sampling. In contrast, for avoidance behaviors, we would expect increased sensitivity to telemetry sampling. Our current simulation model therefore represents a “null” case for the impact of telemetry sampling on network estimation. Our results are, therefore, broadly generalizable across systems, and set an expectation for populations or research questions that may require more intensive sampling. More species-specific work in the future could clarify how association behaviors impact telemetry needs.

As with any simulation study, some events have been simplified, particularly in comparison to field conditions. Our sampling approach was truly random, but even when the goal is random sampling, this condition is often unmet in the field. For example, certain geographic study areas of populations may be more thoroughly sampled, rather than a random sample of the whole population (Craft, Volz, Packer, & Meyers, 2009; Reynolds et al., 2015). While our network density results appear to be insensitive to the proportion of the population sampled, this is likely due at least in part to our random sampling, especially given that network-level metrics are generally expected to be negatively impacted by low population sampling (Farine & Whitehead, 2015). Under field conditions, where random sampling is less likely, network density may be more sensitive to the proportion of the population sampled. Future research may examine the effect of non-random or geographically biased telemetry sampling on network metric estimation.

In addition, while we varied the distance threshold for contacts, using time lags when estimating associations was beyond the scope of this study. Given the improvement in some network metrics when using less precise contact definitions, we expect that time lags also have the potential to further maximize the utility of telemetry data for estimating wildlife contact networks. Future studies characterizing the bounds of this approach would therefore be of great practical use.

Conclusions

While some network metrics and spatial configurations are more sensitive to telemetry sampling effort, remote detection of animal contacts through telemetry technology appears to be a viable approach for estimating some network metrics. In particular, local metrics were well-approximated, particularly in clustered populations which may represent social species or animals navigating highly heterogeneous landscapes. While our results should not be used as a system-specific guide for designing telemetry protocols, they do outline several important sampling guidelines for estimating network structure in infectious disease studies. In particular, we recommend (1) using local network metrics over global metrics, (2) prioritizing frequency of sampling for territorial or infrequently interacting species, and (3) considering a spatial overlap contact definition if sampling is coarse, but only for frequently interacting, highly aggregated species (e.g. herd species). Our findings are broadly generalizable across species, but also demonstrate that future system-specific sampling efforts can be designed following our simulation approach, incorporating additional heterogeneity to inform reliable telemetry approaches for network studies of infectious disease.