Global network structure of dominance hierarchy of ant workers

Abstract

Dominance hierarchy among animals is widespread in various species and believed to serve to regulate resource allocation within an animal group. Unlike small groups, however, detection and quantification of linear hierarchy in large groups of animals are a difficult task. Here, we analyse aggression-based dominance hierarchies formed by worker ants in Diacamma sp. as large directed networks. We show that the observed dominance networks are perfect or approximate directed acyclic graphs, which are consistent with perfect linear hierarchy. The observed networks are also sparse and random but significantly different from networks generated through thinning of the perfect linear tournament (i.e. all individuals are linearly ranked and dominance relationship exists between every pair of individuals). These results pertain to global structure of the networks, which contrasts with the previous studies inspecting frequencies of different types of triads. In addition, the distribution of the out-degree (i.e. number of workers that the focal worker attacks), not in-degree (i.e. number of workers that attack the focal worker), of each observed network is right-skewed. Those having excessively large out-degrees are located near the top, but not the top, of the hierarchy. We also discuss evolutionary implications of the discovered properties of dominance networks.

Keywords: directed networks; dominance hierarchy; social network analysis.

Figure 1.

Observed dominance networks. Each panel corresponds to a colony. The largest connected component is drawn for each colony. A circle represents a worker. The workers are aligned according to their hierarchical ranks as determined by the bottom-up leaf-removal algorithm. An arrow represents aggressive behaviour exerted by an attacking worker towards an attacked worker. The two bidirectional links in C5 are shown by the red thick bidirectional arrows. (Online version in colour.)

Figure 2.

Complementary cumulative distributions of the in-degree and out-degree in dominance networks. The fraction of nodes with the in-degree and out-degree larger than or equal to the value shown on the horizontal axis is plotted for the six dominance networks. The solid and dashed lines correspond to the in-degree and out-degree, respectively. (Online version in colour.)

Figure 3.

Dependence of the average out-degree on the worker's rank. The out-degree averaged over the workers possessing the same rank is plotted against the rank for each colony. The squares and circles represent the results for the observed dominance networks and the corresponding thinned linear tournament averaged over 10³ realizations, respectively. The error bars accompanying the circles represent the standard deviation. (Online version in colour.)

Figure 4.

Dependence of the average out-strength on the worker's rank. The out-strength, i.e. the sum of the link weights over the outgoing links of a worker, averaged over the workers possessing the same rank is plotted against the rank for each colony. (Online version in colour.)

Figure 5.

Results of the motif analysis. We calculated the Z score for the frequency of each three-node network against each null model (i.e. thinned linear tournament or randomized DAG). Asterisks indicate significance levels (*p < 0.05, i.e. |Z| > 1.96; **p < 0.01, i.e. |Z| > 2.58).