A multiplex centrality metric for complex social networks: sex, social status, and family structure predict multiplex centrality in rhesus macaques

Abstract

Members of a society interact using a variety of social behaviors, giving rise to a multi-faceted and complex social life. For the study of animal behavior, quantifying this complexity is critical for understanding the impact of social life on animals' health and fitness. Multilayer network approaches, where each interaction type represents a different layer of the social network, have the potential to better capture this complexity than single layer approaches. Calculating individuals' centrality within a multilayer social network can reveal keystone individuals and more fully characterize social roles. However, existing measures of multilayer centrality do not account for differences in the dynamics and functionality across interaction layers. Here we validate a new method for quantifying multiplex centrality called consensus ranking by applying this method to multiple social groups of a well-studied nonhuman primate, the rhesus macaque. Consensus ranking can suitably handle the complexities of animal social life, such as networks with different properties (sparse vs. dense) and biological meanings (competitive vs. affiliative interactions). We examined whether individuals' attributes or socio-demographic factors (sex, age, dominance rank and certainty, matriline size, rearing history) were associated with multiplex centrality. Social networks were constructed for five interaction layers (i.e., aggression, status signaling, conflict policing, grooming and huddling) for seven social groups. Consensus ranks were calculated across these five layers and analyzed with respect to individual attributes and socio-demographic factors. Generalized linear mixed models showed that consensus ranking detected known social patterns in rhesus macaques, showing that multiplex centrality was greater in high-ranking males with high certainty of rank and females from the largest families. In addition, consensus ranks also showed that females from very small families and mother-reared (compared to nursery-reared) individuals were more central, showing that consideration of multiple social domains revealed individuals whose social centrality and importance might otherwise have been missed.

Keywords: Animal behavior; Complex societies; Multilayer networks; Network analysis; Nonhuman primates; Social behavior.

Figure 1. The method for assigning rank tiers is illustrated.

Hierarchical clustering was performed on the centrality values for a given network layer. The hierarchical clustering tree shown in (A) maps onto the plot of centrality values ordered from largest to smallest shown in (B) such that all members of the same cluster are assigned the same rank tier (different rank tiers denoted by alternating colors green and purple in the bar graph in (B)). Plot (C) shows 1 − r² (the correlation between the original and tiered centralities) with respect to the number of tiers. The final number of rank tiers selected (i.e., the height at which the clustering tree is cut) is the first one which falls below the threshold line (where 99% of the variance is explained). Illustrated is the aggression layer for group B.

Figure 2. Heatmap of layer correlations for all groups.

Spearman correlations were calculated for all pairs of network layers, using the centrality rankings of each layer, across all study groups. The lettered labels (A–G) correspond to group IDs.

Figure 3. Data Mechanics heatmap.

Heatmap showing the block structure revealed by Data Mechanics and the associated hierarchical clustering trees on the columns (layers) and the rows (individuals) for group B. Row clusters group together individuals with similar centrality ranks across the five layers, and column clusters group together layers with similar values across all individuals. Darker colors in the heatmap represent larger values (i.e., low centrality ranks within each layer) and lighter colors represent smaller values (i.e., high centrality ranks within each layer). The grayscale bars on the y-axis indicate animals’ dominance rank (left) and Borda rank (right). Lighter colors represent smaller values (i.e., high rank) and darker represents larger values.

Figure 4. Model predicted values of reverse Borda ranks relative to rank, sex and dominance certainty, based upon Model 1.

Predicted reverse Borda ranks for (A) females and (B) males, calculated at two levels of dominance certainty from the observed range of values: high dominance certainty (transformed DC = 0.1) and low dominance certainty (transformed DC = 0.3). Predicted values are based upon Model 1 of reversed Borda ranks.

Figure 5. Histograms of model coefficients from network randomizations.

Histograms of coefficients for each predictor generated from fitting Model 1 to the network randomizations. For each randomization (n = 1, 000), all the node labels in the original network (e.g., sex, age, rank) were shuffled; then the same model (reversed Borda rank ∼ rank*sex*DC + matriline size category*sex + rearing) was run for each randomized network. The vertical red line shows the value of the model coefficient for each predictor from the observed network data. (A–G) correspond to histograms of the coefficients for the following model predictors of reversed Borda rank: (A) dominance rank, (B) sex (males), (C) dominance certainty, (D) rearing history (nursery-reared), (E) matriline size category (medium-sized families vs. small families), (F) matriline size category (large families vs. small families), (G) dominance rank by sex (male) interaction, (H) sex (male) by dominance certainty interaction, (I) dominance certainty by rank interaction, (J) matriline size category (medium-sized families) by sex (male) interaction, (K) matriline size category (large families) by sex (male) interaction, and (L) dominance certainty by rank by sex (male) interaction.

Figure 6. Model predicted values of reverse grooming layer ranks relative to dominance rank and matriline size.

Predicted reversed rank in the grooming layer with respect to dominance rank (proportion of others outranked) and matriline size category. Predicted values are based upon Model 1 of grooming layer rank.

Figure 7. Raw data plots of reverse Borda ranks against dominance rank for all study groups.

Reversed Borda ranks (i.e., 1 = low) plotted against dominance rank (proportion of others outranked) for all seven study groups. (A–G) correspond to group IDs. Red dots represent females; turquoise dots represent males.