Social network analysis has become a vital tool for studying patterns of individual interactions that influence a variety of processes in behavior, ecology, and evolution. Taxa in which interactions are indirect or whose social behaviors are difficult to observe directly are being excluded from this rapidly expanding field. Here, we introduce a method that uses a probabilistic and spatially implicit technique for delineating social interactions. Kernel density estimators (KDE) are nonparametric techniques that are often used in home range analyses and allow researchers studying social networks to generate interaction matrices based on shared space use. We explored the use of KDE analysis and the effects of altering KDE input parameters on social network metrics using data from a natural population of the spatially persistent forked fungus beetle, Bolitotherus cornutus.
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We would like to thank Mountain Lake Biological Station faculty and staff, especially M. Larsen, for logistical support throughout the field season. We would also like to thank A. Wilkinson, J. McGlothlin, E. Liebgold, L. Avila, M. Formica, P. Fields, J. Krause, and two anonymous reviewers for helpful discussions on earlier versions of this manuscript. Many field assistants, graduate students, and REU students at MLBS assisted in the nocturnal data collection, and we are very grateful for their help. We are especially indebted to D.L. Gaggia for his tireless assistance in the field. A. Snedden and Wet-A-Hook technologies provided materials and advice for beetle labeling. Funding was provided by the University of Virginia, Mountain Lake Biological Station, the Norman A. Meinkoth Field Biology Award from the Department of Biology at Swarthmore College, Swarthmore College chapter of Sigma Xi, the Howard Hughes Medical Institute grant to Swarthmore College Biology Department, and the National Science Foundation REU grant to MLBS (DBI-0453380).
Communicated by J. Krause
Definitions and descriptions of common weighted social network metrics (for an in-depth discussion and mathematical explanations, see Whitehead 2008).
Strength: the sum of the weights of edges connected to a node. This is the weighted number of interactants that an individual experiences. For our data set, strength represents the sum of weighted association indices, which essentially represents the frequency of potential social interactions. Depending on the data used to construct the social network, strength might represent the conspecific density experienced by an individual, the number of aggressive encounters it has participated in, or the frequency of matings.
Reach: the sum of the strengths of an individual’s social partners. Reach is a measure of how well the social partners of a focal individual are connected. A focal individual may only have a few social partners, but if those partners are well connected in the network, then the focal individual will have a high reach. Reach can be thought of as an indirect measure of connectedness, and Flack et al. (2006) suggest that reach can access the ability of a behavioral contagion (e.g., aggression) to spread from individuals.
Affinity: the ratio of how well connected a focal individual is to how well connected its social partners are. Affinity examines a focal individual’s connectedness by taking into account the weights of connections to social partners and then how well connected those social partners are to the rest of the network. Mathematically, this becomes the weighted mean strength of a node or an individual’s reach divided by its strength.
Eigenvector centrality: a more abstract metric that relates how highly connected an individual is within the entire network. Eigenvector centrality does not discriminate whether has many social partners or associates with highly connected social partners. Mathematically, eigenvector centrality is the first eigenvector of the weighted association matrix.
Clustering coefficient (CC): how well connected a focal individual’s social partners are to each other. An individual’s (or node’s) CC score is calculated as the sum of the weights on all three connections of each triangle (between three individuals) divided by the maximum weight in the network. In other words, the clustering coefficient measures how many and how often the focal individual’s social partners are themselves social partners.
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Formica, V.A., Augat, M.E., Barnard, M.E. et al. Using home range estimates to construct social networks for species with indirect behavioral interactions. Behav Ecol Sociobiol 64, 1199–1208 (2010). https://doi.org/10.1007/s00265-010-0957-5
- Social networks
- Kernel density estimation
- Home range
- Bolitotherus cornutus
- Indirect behavioral interactions