paper/manuscript.md

In robitalec/ScaleInMultilayerNetworks: Package Accompanying: The Problem And Promise Of Scale In Multilayer Animal Social Networks.

Considering scale in multilayer animal social networks

Alec L. Robitaille1*, Quinn M.R. Webber2, Julie W. Turner1, Eric Vander Wal1,2 1Department of Biology, Memorial University of Newfoundland, Canada 2Cognitive and Behavioural Ecology Interdisciplinary Program, Memorial University of Newfoundland *Corresponding author: Alec L. Robitaille ([e-mail])

Abstract

Scale remains a foundational concept in ecology. Spatial scale, for instance, has become a central consideration in the way we understand landscape ecology and animal space use. Meanwhile, social processes can range from fine-scale interactions to co-occurrence and overlapping home ranges. Multilayer networks promise the explicit integration of the social, spatial and temporal contexts. Given the complex interplay of sociality and animal space use in heterogeneous landscapes, there remains an important gap in our understanding of the influence of scale on animal social networks. We discuss ways of considering social, spatial and temporal scale in the context of multilayer caribou social networks. Effective integration of social and spatial processes, including biologically meaningful scales, within the context of animal social networks is an emerging area of research. We incorporate perspectives on how the social environment and spatial processes are linked across scales in a multilayer context.

Keywords

Social network analysis, Landscape ecology, Movement ecology, Space use

Introduction

Our inference regarding the processes underlying ecological patterns are directly linked to the scale at which they are observed (Levin 1992; Allen and Hoekstra 2015). Animals are influenced across scales through ecological processes such as trophic interactions, resource availability (Legendre 1993; Chave 2013), and global climate and productivity (Field et al. 2009). Multiscale ecology has been integrated into species distribution modelling (Elith and Leathwick 2009), habitat selection (Mayor et al. 2007), and food webs (Sugihara, Schoenly and Trombla 1989). We posit that it is important to consider the scale-dependence of animal behaviour within the social environment to effectively understand complex social systems.

Social interactions exists across both temporal and spatial scales (Whitehead 2008). For example, grooming requires close spatial proximity between conspecifics and occurs over brief time periods (e.g. Carter, Lee and Marshall 2015), whereas social associations over long time periods represent shared space use by members of the same social group (Figure 1, Franks, Ruxton and James 2009). Individuals must share space to interact or associate and thus have overlapping home ranges (Vander Wal, Laforge and McLoughlin 2014). Home range overlap is an example of how animals share space over coarser spatial and temporal scales (e.g. Piza-Roca et al. 2018). Although the social environment clearly scales spatially and temporally, it remains unclear whether coarser scales of social interactions, such as social association and home range overlap, vary predictably (Castles et al. 2014; Farine 2015). We define social scale as the explicit definition and measurement of social relationships (Farine 2015).

Social network analysis is a well-developed tool used to measure the relationships of individuals and organization of social systems (Wey et al. 2008; Krause, Lusseau and James 2009; Croft et al. 2011). It provides insight into the structure of social communities, which can influence population dynamics and evolutionary processes (Pinter-Wollman et al. 2013; Kurvers et al. 2014). Despite the widespread use and innovation of traditional social network analysis (Webber and Vander Wal 2019), it typically considers sociality in a singular context, drastically simplifying the complexity of animal social systems (Finn et al. 2019).

Extending traditional monolayer social networks, multilayer networks explicitly consider social systems across scale-dependent contexts (Pilosof et al. 2017). Multilayer networks are composed of multiple layers, each representing (i) different classes of individuals, e.g. male or female, (ii) types of behaviours, e.g. grooming, travelling, or foraging, (iii) spatial areas, e.g. local or regional, (iv) or temporal windows, e.g. daily or seasonal (Kivela et al. 2014; Porter 2018). Multilayer networks are relatively novel to studies of animal behaviour (Silk et al. 2018; Finn et al. 2019) and integrating scale within these remains an unexplored opportunity to develop novel understanding of animal social systems.

We examined scale-dependent multilayer networks motivated by behavioural, landscape, and spatial ecology to and applied this framework to caribou (Rangifer tarandus) on Fogo Island, Newfoundland, Canada. First, we test to what degree the social scale of relationships, spatial scale of landscapes, and temporal scale of analysis influences our ability to interpret complex social systems. Second, we address how variation in the social, spatial, and temporal scale improves our understanding of the relationship between social association and seasonal resource availability. We conclude with potential future developments and applications of scale in multilayer networks.

Methods

Caribou socioecology

Caribou are gregarious ungulates with fission-fusion dynamics (Lesmerises, Johnson and St-Laurent 2018) that display temporal and spatial variation in social networks (Peignier et al. 2019). In winter, caribou dig holes, termed craters, to access forage beneath the snow (Bergerud 1974). Cratering is presumed to be a costly behaviour, and as a result, caribou tend to occupy and re-use craters once they are established. Importantly, craters exist on the landscape at multiple scales: the crater scale (a single crater), the feeding area scale (multiple craters in close proximity), and the winter range scale (all craters within an individual’s range) (Mayor et al. 2009). Access to forage is therefore heterogeneous in winter depending on snow cover and distribution of craters on the landscape.

Caribou location data

We used GPS location data collected from Fogo Island caribou between April 2017 and March 2019. Adult female caribou were immobilized and fitted with global positioning system (GPS) collars (Lotek Wireless Inc., Newmarket, ON, Canada, GPS4400M collars, 1,250 g) as described by Schaefer and Mahoney (2013). Collars were programmed to collect location fixes every 2 hours. Prior to analyses, we subset GPS fixes to remove all erroneous and outlier GPS fixes following (Bjørneraas et al. 2010). We did not collar all caribou in the herd; however, the proportion of marked adult females was \~10% of all adult females and \~5% of all individuals in the herd. We assumed these individuals were randomly distributed throughout the population.

Landscape data and habitat classification

Land cover data were provided by the Newfoundland and Labrador Wildlife Division (Integrated Informatics Inc. 2013). Available land cover classification included nine habitat types at 30 m resolution. We reclassified the land cover types into three categories using the R package raster (Hijmans 2019): foraging, forest, and open habitats. Foraging habitat consisted of lichen, forest habitat consisted of coniferous forest, conifer scrub, broad leaf forest, and mixed-wood forest, while open habitat consisted of wetland, rocky barrens, and anthropogenic. Water habitat was excluded from all subsequent analyses.

Caribou multilayer social networks

Network layer construction

We generated proximity-based social networks using the R package spatsoc (Robitaille, Webber and Vander Wal 2019) in R version 4.0.1 (R Core Team 2020). Typically for ungulates and other gregarious mammals, the ‘chain rule’ is used for group assignment (Croft, James and Krause 2008). For GPS data, the chain rule is applied by assigning a group identifier to the union of buffered GPS fixes at each time step. As such, individuals in a group are within the social distance threshold of at least one other though not necessarily all other individuals (Robitaille, Webber and Vander Wal 2019). Group assignment based on the chain rule has previously been applied to caribou using a temporal threshold of 5 minutes and a social distance threshold of 50 m (Lesmerises, Johnson and St-Laurent 2018; Peignier et al. 2019). In all networks, individual caribou were represented as nodes and associations between individuals in a given network layer were represented as intralayer edges.

We weighted edges of social networks by the strength of association between caribou using the simple ratio index (SRI, Cairns and Schwager 1987):

[ SRI = \frac{x}{x + y_{AB} + y_{A} + y_{B}} ]

where x is the number of fixes where individuals A and B were in the same group, (y_{A}) is the number of fixes from individual A when individual B did not have a simultaneous fix, (y_{B}) is the number of fixes from individual B when individual A did not have a simultaneous fix, and (y_{AB}) is the number of simultaneous fixes from individuals A and B that were separated by more than the social distance threshold (Farine and Whitehead 2015).

Network metrics

We used a series of metrics to characterize the multilayer networks, focusing on the role of individuals within layers and the similarity of edges across layers. Within each layer, we calculated degree centrality, the number of direct connections an individual has, and graph strength, the degree weighted by the strength of association. We calculated multidegree, the sum of degree centrality of individuals across layers, an extension of degree centrality to multiple layers (Berlingerio et al. 2012; Kivela et al. 2014). Finally, we measured the similarity of layers by calculating edge overlap. Edge overlap is defined as the proportion of edges present in each network layer out of all observed edges (Battiston, Nicosia and Latora 2014). Network metrics were calculated using the R packages igraph (Csardi and Nepusz 2006), asnipe (Farine 2019), spatsoc (Robitaille, Webber and Vander Wal 2019) and data.table (Dowle and Srinivasan 2019).

Varying scale in multilayer networks

Social scale

We generated multilayer networks across a series of social distance thresholds for group assignment. Social distance thresholds (5, 25, 50, 75, 100, 250 and 500 m) represent a range of sensory modalities of caribou from visual to olfactory and auditory. Multilayer networks consisted of the social association between 21 individuals across three habitat layers (foraging, forest, and open) for the entire study period. At the finest scale, individuals within 5 m of one another were considered in the same group, whereas at the coarsest scale, individuals within 500 m of one another were considered in the same group. Increasing social distance threshold is a proxy for potential behavioural interactions that occur across these distances. For every social distance threshold, we calculated individual graph strength within each habitat layer, and edge overlap and multidegree across habitat layers.

Spatial scale

To assess the influence of spatial scale, we aggregated the land cover raster using the R package grainchanger (Graham 2019) across a series of scales (100 - 1000 m by steps of 100 m). The land cover raster was aggregated using a modal moving window method using a circular window corresponding to the above scales (Graham et al. 2019). We assume 30 m and 100 m represents fine-scale decision making for caribou, while 500 - 1000 m represents the scale at which caribou tend to select and avoid habitat (Bastille-Rousseau et al. 2018). Multilayer networks consisted of the social associations between 21 individuals across three habitat layers (foraging, forest and open) for the entire study period. For each land cover resolution, we calculated individual graph strength within each habitat layer, and edge overlap and multidegree across habitat layers.

Temporal scale

Time windows

We used a temporal multilayer network to assess the seasonality of caribou sociality. Multilayer networks consisted of the social associations between 21 individuals across 20 ordinal sample periods from the entire study period. For each time window, we calculated individual graph strength within each time window, and edge overlap and multidegree across time windows.

Number of observations

Studies of social network analysis vary in the number and frequency of observations as well as the data collection technique used to generate networks, ranging from directly observed to remotely sensed (Davis, Crofoot and Farine 2018; Webber and Vander Wal 2019). Remotely sensed GPS data is commonly collected at a fixed rate, e.g. every (x) minutes or hours, continuously throughout the study period. Fix rate is a reflection of number of observations an individual would have been observed and recorded in traditional ethological studies. To investigate the influence of number of observations, we generated multilayer networks of social association between 21 individuals across three habitat layers (foraging, forest, and open) using (n) randomly selected observations. We first generated a maximum of 1000 timesteps and iteratively used (n) of these ((n) = 10 - 1000 observations by steps of 10), to ensure previously included timesteps, and resulting associations, were accumulated with subsequent observations to mimic collection of observational data. Within each multilayer network with (n) observations, we calculated individual graph strength and multidegree. We calculated edge overlap across the entire series of networks to determine proportion of total edges as number of observations increased.

Results

Individuals in multilayer networks became more connected as the social distance threshold increased. Mean graph strength was higher in foraging and open layers than in forest layers (Figure 2). Individual graph strength increased sharply between 5 m and 100 m in all three habitat classes followed by a plateau in the rate of increase after 100 m (Figure 2). These results suggest the optimal social scale at which groups should be assigned is between \~20 - 100 m based on the rate at which variance in graph strength decreased. GPS data allows (e.g. from this study and Peignier et al. 2019; Lesmerises, Johnson and St-Laurent 2018) us to confirm the use of 50 m buffer that has long been used for studies in the field (Clutton-Brock, Guinness and Albon 1982; Lingle 2003).

Increasing land cover resolution resulted in decreased availability of foraging habitat and corresponding low connectivity of individuals in foraging layers at higher land cover resolutions. Edge overlap decreased sharply between 30 m and 600 m in foraging layers, afterwards remaining stable to 1000 m (Figure 3 D). In contrast, edge overlap was relatively consistent in forest and open layers as land cover resolution increased (Figure 3 D). Graph strength was more variable within foraging habitat layers across land cover resolutions than open and forest habitat layers (Figure 3 E). The proportion of relocations in forest (38.68% at 30 m - 50.27% at 1000 m) and open (37.39% at 30 m - 48.18% at 1000 m) habitats increased with increasing spatial resolution, while decreasing in foraging habitat (23.93% at 30 m - 1.55% at 1000 m). These results indicate the importance of matching land cover resolution to scale of habitat selection and choosing a land cover product with a resolution sufficient to detect less common habitats.

The temporal multilayer network indicated within-year time windows where social network metrics increased. Edge overlap was higher in time windows 1, 6-11 and 15-20 than in time windows 2-5 and 12-15 (Figure 4 A). Time windows of higher edge overlap, between approximately October and June, also had higher graph strength compared to time windows of lower edge overlap, between approximately June and October (Figure 4 C). Graph strength peaked across the time series between January 2018 and April 2018. These results highlight the importance of carefully selecting the temporal scale of analysis to effectively capture within- and across-year variation in sociality.

As the number of observations used to generate multilayer networks increased, individuals became more connected and variance in metrics decreased. Edge overlap increased across all three habitat layers with increasing number of observations (Figure 5 B). Similarly, multidegree for all individuals increased quickly between 10 and 100 observations, and continued to increase until 1000 observations (Figure 5 C). Graph strength across individuals in all three habitat layers was highly variable at low number of observations and variance decreased after \~100 observations (Figure 5 A). Since the variance in these multilayer metrics decreases after a certain number of observations, this sensitivity method could be useful for determining the number of observations necessary for sufficiently describing social dynamics across contexts.

An illustrative multilayer network was generated, informed by previous social, spatial and temporal scale results (Figure 6). Relocations were predominantly in open (37.39%) and forest (38.68%) habitats compared to foraging habitats (23.93%). Despite this, individuals were more strongly connected in foraging and open habitats than in forest (mean graph strength in habitat layers; foraging: 0.21, forest: 0.11, open: 0.23). There was a seasonal difference in association with individuals more connected between approximately October - June (mean graph strength in time windows; 2: 0.37, 4: 0.18) than between approximately June - October (mean graph strength in time windows; 1: 0.04, 3: 0.03). The time windows were aggregated from the finer scale time windows presented above (time window 1: 2-5, time window 2: 6-11, time window 3: 12-15, time window 4: 16-20).

Discussion

Animal social systems are characterized and influenced by scale. Three types of scale to consider are social, spatial, and temporal scale. Social scale defines the type and measurement of social relationships and directly impacts observed social connectivity between individuals. Spatial scale can reflect the resolution of the habitat within which social interactions occur. Finally, temporal scale is related to both study design and seasonal differences in social processes. By partitioning social associations into discrete contexts using multilayer networks, we highlight the influence of social, spatial and temporal scales on animal social systems, demonstrating the importance of considering biologically relevant and robust scales.

Social scale is an essential consideration for social network analysis (Castles et al. 2014; Carter, Lee and Marshall 2015; Farine 2015). For example, networks can be constructed based on fine-scale social interactions (e.g. grooming or aggression), social associations (e.g. group membership or proximity), or spatial or home range overlap. Here, we define social associations using a series of social distance thresholds to generate proximity-based social networks. Across habitat layers, increasing the social distance threshold resulted in an increase in graph strength (Figure 2). Specifically, open and foraging layers showed a larger increase in graph strength as well as greater variation across individuals with larger social distance thresholds. These results emphasize that multilayer network metrics are directly influenced by social scale. An extension of this analysis could be to incorporate behavioural states to explore the influence of social scale on patterns of association or interaction across habitat and behavioural layers (e.g. using focal observations or hidden Markov Models see Muller et al. 2018; Jones et al. 2020).

Habitat selection, the use of available resources or landscape features by animals (Manly, McDonald and Thomas 1993; Boyce and McDonald 1999), is a scale-dependent process (Mayor et al. 2009). Social structure and habitat selection are intimately related and individuals must share space to interact (Webber and Vander Wal 2018). We found edge overlap was stable in open and forest layers but decreasing in foraging layers with increasing spatial scale (Figure 3 D). Graph strength had greater individual variation in open and foraging layers than in forest layers (Figure 3 E). We observed a decrease in the proportion of relocations in foraging habitat with increasing spatial resolution (23.93% at 30 m - 1.55% at 1000 m). As the foraging layer had similar edge overlap and graph strength as the open layer at 30 m spatial resolution, this highlights the importance of considering spatial scale when including habitat in multilayer networks. Johnson (1980) identified four orders of habitat selection: (1) the geographical range of a species, (2) the home range of an individual, the (3) habitat patches within the home range and (4) specific resources within a habitat patch. Scales of habitat selection could be relevant for multilayer networks and our integration of habitat within a multilayer context could be an important first step. Specifically, if individuals select habitats at the home range scale, it may be relevant to assess social structure using home range overlap. By contrast, in cases where individuals select habitats at the patch-scale, fine-scale measures of sociality may be more relevant. Moving past this hierarchical perspective, Mayor et al. (2007) emphasized the importance of considering a broad continuum of scales to reveal scale-dependent selection and avoid the bias of predefined scales assumed to be associated with certain behaviours.

The emergent relationship between habitat and sociality has been explored by the temporal distribution and phenology of resources and use of social information. We found increased edge overlap and graph strength in fall, winter and spring (approximately October - June) than in summer (approximately June - October) (Figure 4 A, C). These periods of increased sociality correspond to seasons of heterogeneous resource availability (Peignier et al. 2019). This analysis could be extended using time-aggregated networks and a moving-window approach for informing time window size and sampling effort (Farine 2017; Bonnell and Vilette 2020). By explicitly considering the temporal context of social interactions in separate layers, multilayer networks provide a detailed and dynamic perspective of animal social systems. For example, female mandrill (Mandrillus sphinx) sociality is more completely represented by temporal multilayer networks than aggregated networks (Pereira et al. 2020). Evans et al. (2020) observed seasonal differences in the multilayer social structure of mice (Mus musculus domesticus) related to temperature and breeding activity. Finally, it is crucial to include sufficient data within sampling periods or time windows to construct robust networks (Farine 2017; Proskurnikov and Tempo 2017). With increasing number of observations, we found variance decreased in edge overlap and multidegree across habitat layers as well as in graph strength within habitat layers (Figure 5). In addition, less common relationships were recorded with increasing number of observations, demonstrating the value of this form of sensitivity analysis.

Recognition of scale as a fundamental concept in ecology (Levin 1992) has lead to an increased attention to the scale at which ecological processes are observed (Schneider 2001; Chave 2013). Recent technological advances in remotely sensed imagery (Drusch et al. 2012) and animal tracking devices (Wikelski et al. 2007; Börger 2016; Börger et al. 2020) have increased the availability of complex, high resolution data. We highlight ways in which scale should be considered when building social networks from both observed and remotely-sensed data. Our multilayer network analysis of caribou sociality incorporating high resolution GPS telemetry data and spatial land cover data is grounded in the context of observed animal behaviour as the scales we chose to explore, e.g., number of observations and sociality across space and time, are ones that have also traditionally been done in ethology.

Multilayer networks remain a nascent but powerful tool in animal behavioural ecology. Silk et al. (2018) summarized some key multilayer questions in animal behaviour research and, based on our study of scale, we conclude by posing an additional set of questions on the future of multilayer networks through the lens of scale and behavioural, landscape, and spatial ecology:

1. How do social phenotypes vary across social, spatial, and temporal scales and at which scale might these influence fitness? Are some scales better predictors for different fitness metrics?

2. Why do individuals associate more strongly with certain conspecifics in some habitats? What is the role of movement in the context of habitat networks?

3. How, and why, does the spatial scale of perception influence, e.g. auditory, visual, or chemotaxis, influence the social environment? What is the role of memory, and by extension social and spatial cognition, as animals navigate their environment and make decisions about where to move next?

We show that multilayer social networks are (1) scale-dependent, and (2) useful for identifying spatially or temporally specific social associations. When employing multilayer networks, it is critical to consider a broad continuum of social, spatial and temporal scales to fully capture ecological processes and to establish a clear link between biologically relevant scales of observation.

Box 1

Social phenotype has been increasingly linked to individual fitness, including in primates (Brent, Ruiz-Lambides and Platt 2017; Thompson 2019), dolphins (Stanton, Gibson and Mann 2011; Stanton and Mann 2012), and birds (McDonald 2007; Royle et al. 2012). Social and temporal scales have emerged as important variables for understanding the fitness consequences of social network position (Holekamp et al. 2011; Berger et al. 2015; Almeling et al. 2016; Brent, Ruiz-Lambides and Platt 2017).

Varying social scales can have different fitness repercussions for individuals. Rhesus macaques (Macaca mulatta) had higher survivorship when they had fewer but stronger and more stable social associates and grooming partners rather than simply more associates (Ellis et al. 2019). It is a common trope that individuals must be associating to interact, and many studies assume that proximity is proxy for interacting (Farine 2015). For instance, baboons must be within proximity of each other for grooming yet other animals interact using communication such as long-distance vocalization or olfactory signals (Carter, Lee and Marshall 2015). It is possible to record social interactions that do not require proximity using, for example, microphone arrays to construct long-distance communication networks (Snijders and Naguib 2017).

Multilayer networks enable researchers to look at similarities and differences between discrete temporal windows. Changing social phenotypes over ontogeny can affect fitness (Berger et al. 2015; Brent, Ruiz-Lambides and Platt 2017). Individuals progress through development at different rates (Tarka et al. 2018) and this variation can complicate the selection of time windows. Considering fine temporal scales provides insight across developmental stages that may otherwise be missed (Turner et al. 2020). Thus, it is critical to carefully consider the effect of scale on the relationship between an individual’s social network position and fitness using a temporal scale based on the hypotheses being tested and logistical constraints.

Acknowledgements

We thank all members of the Wildlife Evolutionary Ecology Lab, including J. Hendrix, K. Kingdon, S. Boyle, J. Balluffi-Fry, C. Prokopenko, I. Richmond, J. Hogg, and L. Newediuk for their comments on previous versions of this manuscript as well as D. C. Schneider for inspiration and helpful discussions about scale. Funding for this study was provided by a Vanier Canada Graduate Scholarship to QMRW and a NSERC Discovery Grant to EVW.

Figure 1: Space-time diagram representing variation the relative spatial and temporal extent required for different types of social and communication processes for four species, including spotted hyaena, passerine birds, sleepy lizards, and elephants. Spatial and temporal extent for social interactions, e.g. mating, grooming, or aggression, are similar for most species because physical contact between two individuals is required for many social interactions. The logical extension is that spatial and temporal extent for social interaction is hierarchically nested within the spatial and temporal extent for social association because individuals must share space to interact. By contrast, different species have potential for greater spatial and temporal extents, for example, temporal extent for vocal communication is similar for most species because most vocal calls only persist in the environment for seconds, but spatial extent for vocal communication is highly variable with elephant calls extending the great distance and passerine calls extending the shortest distance.

Figure 2: Varying scale in social distance threshold. For each social distance threshold (100 - 1000 m by steps of 100 m), multilayer networks were constructed of caribou social associations (n = 21 females) on Fogo Island, Newfoundland between April 2017 and March 2019 within three habitat layers (foraging, forest, and open). Graph strength (mean of individuals in bold) showed a sharp increase between 5 m and 100 m for all habitat classes. After 100 m, graph strength continued to increase at a slower rate. Foraging and open layers showed higher variation in graph strength between individuals while forest layers had less variation and lower mean graph strength.

Figure 3: Varying spatial scale of land cover raster. For each land cover resolution (5, 25, 50, 75, 100, 250 and 500 m), multilayer networks were constructed of caribou social associations (n = 21 females) on Fogo Island, Newfoundland between April 2017 and March 2019 within three habitat layers (foraging, forest, and open). A, B, C) Three land cover rasters: the original resolution (30 m) and two aggregated rasters (500 m and 1000 m). D) Edge overlap of habitat layers across spatial resolutions. Open and forest layers show consistent edge overlap with increasing spatial resolution while foraging shows a sharp decline in edge overlap between 30 m and 600 m. Above 600 m, edge overlap in foraging layers is stable. E) Graph strength (mean of individuals in bold) within habitat layers across spatial resolution. Foraging layers showed high variation in graph strength with many individuals dropping to 0 after 500 m and others increasing with spatial resolution. Open layers and forest layers were relatively stable across spatial resolutions, with higher mean graph strength in open compared to forest layers.

Figure 4: Varying temporal scale in multilayer networks. Multilayer networks were generated of caribou social associations (n = 21 females) on Fogo Island, Newfoundland within time windows (20 ordinal sample periods) between April 2017 and March 2019. A) Edge overlap across time windows showed two periods of low overlap (time windows 2-5 and 12-15), and three periods of high overlap (time windows 1, 6-11, 15-20). B) Ordinal network layers showing unweighted edges between individuals within time windows. Like edge overlap, individuals were more connected in time windows 1, 6-11, and 15-20, compared to 2-5 and 12-15. Number of individuals in each time window is reported below each layer. C) Graph strength within time windows showing individuals as thin grey lines and mean across individuals as thick black lines. Graph strength peaked in time window 9, with noticeable higher strength than the following year.

Figure 5: Varying scale in number of observations. Multilayer networks were generated using a subset of observations (10 - 1000 observations by steps of 10) of caribou social associations (n = 21 females) on Fogo Island, Newfoundland between April 2017 and March 2019 within three habitat layers (foraging, forest, and open). A) Edge overlap increased for all habitat layers with increasing number of observations. Foraging and open layers had higher edge overlap than forest layers. B) Graph strength was highly variable at low number of observations (less than 100) for all habitat layers and relatively stable after \~200 observations. C) Multidegree increased for all individuals with increasing number of observations. Individuals showed high variability (2 - 51) at the maximal number of observations (1000).

Figure 6: Multilayer network representing social association of caribou on Fogo Island, Newfoundland between May 2017 and February 2019. Individual caribou (n = 21 females) are represented as nodes in a constant location in layers they were observed. Twelve layers represent combinations of four time windows and three habitat classes (foraging, forest, and open) informed by previous social, spatial and temporal scale analyses. Intralayer edges represent association between individuals and line thickness is scaled by strength of association (SRI).

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robitalec/ScaleInMultilayerNetworks documentation built on Dec. 22, 2021, 5:14 p.m.