# Chapter 15 Summary

1. Network analysis examines the pattern of pooled relationships between all animals in a group or population. Relationships can be estimated by tallying interactions between each pair; inferring relationships through joint attendance in specified contexts is called the gambit of the group. All combinations of relationships can be tabulated in an association matrix or visualized in a two-dimensional network graph in which each individual is assigned one node, and edges link all pairs with recorded relationships. Weighted edges can be used to indicate relationship strengths, signed edges to indicate beneficial versus detrimental relationships, and pairs of directed edges to accommodate asymmetrical relationships. Where directed edges of three or more nodes form a continuous path in the same direction, the network is said to be cyclic. Complex relationships such as alliances and coalitions may require hyperedges on graphs with more than two dimensions.
2. Connectivity measures reflect the amount of linkage in a network. Edge density is the ratio of the number of edges in a network to that expected were the network complete (every node connected to every other node). Networks with low edge densities are said to be sparse. Path length is the average of the shortest topological distance between a focal node and all other nodes in the network; average path length is the mean path length across all nodes; and network diameter is the largest path length in the network. Topological distance is measured as the number of traversed edges in unweighted networks; reciprocals of weights are used for weighted networks, and the mean of reciprocal sums is called network closeness.
3. Centrality measures indicate the heterogeneity of a network’s linkage. A network with no heterogeneity is said to be regular. Irregular networks show heterogeneity at different scales, and different centrality measures focus on these different levels. At the most local level, one can compare nodes according to the number of attached edges (degree) in unweighted networks or the sum of their attached edge weights (intensity) in weighted networks. Reach is the number of nodes within a fixed number of edges of a focal node. Central nodes have greater reach than noncentral nodes. Nodes of high degree or intensity (hubs) whose linked neighbors are also hubs will exhibit high eigenvector centrality. Clustering coefficients measure the level of local connectivity in adjacent trios of nodes. Network heterogeneity can also be generated if individuals selectively form links according to type: such assortativity may be based on sex, age, alliances, or even node degree. The highest levels of heterogeneity will be reflected in the shape of a network’s degree distribution, or by identifying clusters of nodes called communities, modules, or cliques, which differ from each other in the relative amounts of inter-cluster and within-cluster linkage. Nodes that link separate clusters have high values of betweenness and information centrality. Clusters that have no connection to other clusters are called components.
4. Several key types of networks recur in many different contexts. Networks with edge densities above a threshold largely consist of a giant component, while lower edge densities result in many isolated components. Adding a few random shortcuts to a regular network can reduce average path length and turn it into a small world. Completely random networks have no significant transitivity, associativity, or community structure, but are usually small worlds. Heavy-tailed networks have more high-degree and low-degree nodes than a random network, and are called scale-free if their degree distribution plot is linear. Modular networks that show similar linkage patterns at multiple scales are said to be fractal. There is usually a trade-off between a network being small world and fractal.
5. An event at one or more nodes can generate effects that percolate within the network. The percentage of nodes affected is the percolation fraction, and the time it takes to affect these nodes is the percolation time. Percolation fractions are small for sparse networks without a giant component and high for those with a giant component. Percolation times are short for small worlds but longer for fractal networks with limited between-module connectivity. Robust networks retain initial percolation properties even after some original edges or nodes are removed. Networks that are heavy-tailed are usually robust to random edge or node removal, but not to targeted hub removals unless they are also fractal and modular in structure. In general, network structures that favor high percolation fractions and low percolation times have low robustness, and vice versa. Most biological systems appear to be selected for an optimal weighting in this trade-off.
6. Effect propagation in many networks is nonlinear, and this results in emergent properties and self-organized patterns that are not the linear sum of each node’s actions. An example is the emergent synchrony of repetitive actions by a network’s nodes. Sufficient edge strength is a key condition for the emergence of synchrony as well as its spread throughout a network. Even for a given edge strength, some network structures promote synchrony more than others. Regular networks usually fail to synchronize unless sufficient shortcuts are present to make them into small worlds. Heavy-tailed networks start to synchronize at lower edge strengths than random networks, but have trouble both achieving full synchrony and maintaining it for long periods at higher edge strengths. Full synchrony can be achieved in such networks if edges are weighted and input intensities are equalized (isothermal) for all nodes.
7. Evolutionary graph models of social evolution typically assume weak selection, haploid genetics, stable population sizes, and similar interaction networks and replacement networks. Most assume a structured population in which both social and demographic events are localized. They also invoke a Moran process that breaks evolutionary trajectories into a series of events in which either a birth results in a compensating death (BD) or a death results in a compensating birth (DB). The evolution of cooperative behaviors such as altruism and communication in a structured population requires that the fulfillment of the compensation step be based not on chance (drift) but on the prior fitness differences between players (selection). Models based on the assumptions that death is random but births reflect selective differences routinely predict the evolution of cooperation for DB events but not for BD events. However, real systems may vary as to which parts of a Moran event are based on selection and which on random assignments. Interestingly, inclusive fitness models for the evolution of cooperation in structured populations provide similar predictions despite using different accountings.
8. Eavesdroppers often provide a link between a communicating dyad and the larger social network outside the active space of the signals. Propagated effects need not be signals and may feed back on the original communicators. Interceptive eavesdroppers respond to signals immediately, while social eavesdroppers exploit the signal information for future decisions and actions. Senders often anticipate eavesdropping and avoid emitting signals unless primary receivers are sure to be present (first-order audience effects) or modify their signaling strategies when potential eavesdroppers are present (second-order audience effects).
9. The social networks of real animals tend to be small worlds with short path lengths, high clustering coefficients, and heavy-tailed but not scale-free degree distributions. Most fission–fusion societies have sparse networks with low edge densities and average degrees, whereas networks within cohesive groups such as monkey troops or wasp colonies have higher edge densities and average degrees. Networks in both types of society contain multiple communities if sufficiently large: the degree to which these are modular or overlapping depends upon the species. The presence and direction of associativity varies widely among species and across network topologies: when present, the most common criteria for associative linking are sex, age, and body size. Degree assortativity only occurs sporadically and may show different patterns for different subsets of the network.
10. Behavioral synchrony in animals requires two steps: individuals must adopt the same action, and they must then perform it in a coordinated way. Either step can be achieved through entrainment to external cues, attention to leader signals, as an emergent property of interactions within the network, or as some mix of these factors. A group’s collective decisions usually follow the theoretically predicted sequence of increasing emergent synchrony: advertisement of different options by different informed individuals; accretion of supporters around particular advertisers generating local pockets of synchrony; and iterative redistributions of support until some threshold synchrony is reached. Switching support may be biased by existing network affiliations and often includes mechanisms with positive feedbacks such as shifting to the currently most popular option. Network topology may be selected to produce an optimal trade-off between making correct collective choices and minimizing time spent on decisions.
11. Coordinated advertisement is an emergent pattern of behavioral synchrony seen in aggregations of animals, usually males, that display competitively. Males on avian and mammalian leks coordinate their rates of display when females are present, but they usually do not coordinate display timing. Some fiddler crabs, chorusing insects and anurans, and fireflies, however, coordinate both rate of display and the timing of signal emissions. This is apparently due to a precedence effect, in which females favor the first signaling male that they detect. Two emergent patterns that minimize the effects of precedence biases are alternation and synchrony in male signal emission.
12. A widespread case of emergent behavioral synchrony is the coordinated locomotion of schools of squid, fish, and cetaceans; flocks of flying birds; trails of ants and termites; and migrations of large mammals. The cohesion of rapidly moving bird flocks or fish schools does not require leaders, but instead relies on the existence of different types of links between a focal animal and three successively more distant shells of neighbors. The shape of the moving group and the spacing of its members depend on the relative sizes of the three zones around each individual; the zones and thus the group shape and spacing can change suddenly when the group encounters a predator or an obstacle. Rapidly moving animals rely only on cues from neighbors to pursue zoning rules, but slowly moving groups may use coordinating signals as well.
13. Dominance hierarchies and the existence of multiple personalities are additional self-organized patterns that emerge from the cumulative interactions within social networks. The linearity of dominance hierarchies arises from positive feedback loops in which individuals adjust the weights and signs of the links in their interaction network according to recent contests. In addition to their own contests, these individuals can also make adjustments after eavesdropping on the contests of others in the network. Policing by dominants can add further feedbacks that reinforce dominance differences. Multiple personalities can emerge in a similar fashion: small differences among group members or topological neighbors in physical and physiological states may favor differences in actions; positive feedbacks from the consequences of the actions then exacerbate the state differences. One result is persistent differences in personality traits such as boldness, neophobia, activity level, sociability, and aggressivity. Where an initial state difference affects multiple personality traits, one can also observe stable behavioral syndromes in animals. If animals can relocate or be selective in associations, personality differences can reshape an initial network structure into a new one. Only certain combinations of personalities may be stable equilibria (ESSs) in this case.