Visual sensory networks and effective information transfer in animal groups

Abstract

Social transmission of information is vital for many group-living animals, allowing coordination of motion and effective response to complex environments. Revealing the interaction networks underlying information flow within these groups is a central challenge. Previous work has modeled interactions between individuals based directly on their relative spatial positions: each individual is considered to interact with all neighbors within a fixed distance (metric range), a fixed number of nearest neighbors (topological range), a 'shell' of near neighbors (Voronoi range), or some combination (Figure 1A). However, conclusive evidence to support these assumptions is lacking. Here, we employ a novel approach that considers individual movement decisions to be based explicitly on the sensory information available to the organism. In other words, we consider that while spatial relations do inform interactions between individuals, they do so indirectly, through individuals' detection of sensory cues. We reconstruct computationally the visual field of each individual throughout experiments designed to investigate information propagation within fish schools (golden shiners, Notemigonus crysoleucas). Explicitly considering visual sensing allows us to more accurately predict the propagation of behavioral change in these groups during leadership events. Furthermore, we find that structural properties of visual interaction networks differ markedly from those of metric and topological counterparts, suggesting that previous assumptions may not appropriately reflect information flow in animal groups.

Figure 1

The spread of information through fish schools. (A) Different models for the neighbors with whom a given fish interacts, shown for one example image from our dataset. Metric: all individuals within a certain distance. Topological: a fixed number of nearest neighbors. Voronoi: those individuals sharing a boundary in a Voronoi tessellation of the group. Visual: all individuals that occupy an angular area on the retina of the focal fish that is greater than a threshold value. (B) A wave of behavioral responses spreads through the group during leadership events. An image from the end of a leadership event is shown. Superimposed on this image, each filled circle marks the location of a single fish when it responded, and colors represent the time of that response. Black borders around circles denote informed (trained) fish. (C) Empirical support for different models of information transfer. Higher marginal likelihood indicates more support (note the log scale). Marginal likelihoods of each model (computed via numerical integration) represent the product of the likelihoods over all uninformed individuals and all trials. Plotted values are the mean of 10 runs, each using 10,000 random samples from parameter space. Standard deviations of these estimates are smaller than data markers. (D) Network efficiency (the speed with which information can flow through the network) vs. average degree (number of neighbors) for the different models of interaction networks. (E) Network transitivity (the extent to which individuals who share a neighbor are neighbors themselves) vs. average degree for the different interaction networks. Higher transitivity indicates a greater likelihood of one’s neighbors being mutually connected, and hence a greater level of redundant information available to each individual. Colors and marker shapes are as given in panel A. For each data point, network measurements represent mean values taken over 250 networks randomly sampled from our data (10 samples from each leadership event). Different parameterizations are generated by adjusting the interaction radius, number of nearest neighbors, or visual threshold. Because of its inherently fixed interaction range, only one data point is shown for the Voronoi model. Shaded areas show the standard deviation along the first principal component of the error distribution. Non-filled markers indicate the average degree associated with the best fit to the data. Full definitions of network measurements are given in Supplemental information.