Collective detection based on visual information in animal groups

Abstract

We investigate key principles underlying individual, and collective, visual detection of stimuli, and how this relates to the internal structure of groups. While the individual and collective detection principles are generally applicable, we employ a model experimental system of schooling golden shiner fish (Notemigonus crysoleucas) to relate theory directly to empirical data, using computational reconstruction of the visual fields of all individuals. This reveals how the external visual information available to each group member depends on the number of individuals in the group, the position within the group, and the location of the external visually detectable stimulus. We find that in small groups, individuals have detection capability in nearly all directions, while in large groups, occlusion by neighbours causes detection capability to vary with position within the group. To understand the principles that drive detection in groups, we formulate a simple, and generally applicable, model that captures how visual detection properties emerge due to geometric scaling of the space occupied by the group and occlusion caused by neighbours. We employ these insights to discuss principles that extend beyond our specific system, such as how collective detection depends on individual body shape, and the size and structure of the group.

Keywords: collective behaviour; detection; vision.

Figure 1.

External visual detection of individuals. (a) A focal individual has external detection in a given direction if neighbours do not block vision in that direction. Computationally, this is implemented by considering a set of discrete locations outside of the group, which are located far away and thus represent detection in a certain direction (figure 10). (b–d) External visual detection coverage over all possible directions of a single individual located at the centre of a school of 70 fish. Shown is the detection coverage determined using different parameters. Directions where the left eye has external detection capability are shown in blue, and that for the right eye in red. (b) Full visual blockage and a full 360° field of view. (c) Including a blind angle where fish cannot see behind themselves, with otherwise full blockage from neighbours. The blind angle area is highlighted by the dotted lines, and detection directions omitted due to the blind angle are shown in grey. (d) Blind angle along with out-of-plane effects, where neighbours considered as out-of-plane (shown in grey) do not block the external view in a certain direction. Because tracking is in two dimensions, we approximate this effect by randomly choosing neighbours to designate as out-of-plane, here using a 25% probability that a neighbour will be out-of-plane. Additional detection directions due to out of plane effects are shown in darker colours (compare with c).

Figure 2.

Collective detection capabilities of the group. Illustration of the external visual field of the entire group at a single frame. Each heatmap shows detection capability obtained by summing the overlapping regions of the external visual fields of all individuals, using results with a blind angle and out-of-plane effects (25% out-of-plane probability). Results are displayed by scaling to show either (a) absolute detection capability in terms of the number of individuals with detection capability or (b) the fraction of the maximum possible total detection capability among group members.

Figure 3.

Individual detection coverage. The detection coverage is the fraction of the external visual field that an individual can see. (a) Example snapshot of the external detection coverage for groups with different numbers of individuals. (b) Distributions of individual detection coverage for the different groups, combining all individuals during a trial, calculated using different settings: full blockage–full field (dashed line), full blockage–blind angle (dotted line), full blockage–blind angle with detection capability any time over a 1/3 second time window (dashed-dotted line), and out-of-plane effects (25% out-of-plane probability)–blind angle. (c) Detection coverage, comparing individual differences to the combined distribution. Results use out-of-plane effects (25% out-of-plane probability)–blind angle. The mean and standard deviation of the combined distribution from B are shown as the large point and error bars for each group size. The mean individual detection coverages during a trial are the small points, and individual standard deviations are the shaded bars. Note that 3 trials were performed for N = (10, 30, 70), while only 1 trial was performed for N = 151. The individual points are spaced on the x-axis for display purposes. The dashed line shows the contribution from ‘consistent individual differences’ (the variance of individual means) to the overall distribution, while the dotted line shows the contribution of ‘individuals differing during a trial’ (the mean of individual variances; see Methods, equation (4.5)).

Figure 4.

Group states and detection dependence. (a) Example snapshots of a group of 70 in different configurations: polarized, milling and swarm states. (b) The fraction of time each group was observed in the different states. (c) The total number of possible detections for all individuals in the group, for groups with different values of N, showing results for all group states compared to polarized, milling, swarm and other states. Points show the median, and error bars show the lower and upper quartiles of the total number of possible detections among all group members in a certain direction at an instant in time. (d) The distribution of spatial area occupied by the group, for different states, showing the median (points) and inter-quartile range (error bars). The high upper quartile values for the group of 151 in the swarm state are due to instances where the group is not a single cohesive unit.

Figure 8.

Tank configuration and different numbers of fish. Snapshots showing groups with different numbers of fish in the experimental tank. See also electronic supplementary material video for a short clip, and Data availability to access full videos.

Figure 5.

Area occupied and collective detection. (a) Distributions of the total spatial area occupied by groups of different numbers of individuals. Points denote the median of the distribution. (b) The spatial area per individual, calculated using Voronoi tesselation, for groups of different numbers of individuals. Points denote the median of the distribution. See figure 9 for information on how the total group area and the individual area are calculated. (c) The total instantaneous detection capability among all group members, averaged over all possible directions over time, plotted as a function of the total area of the group at that time. The line shows the mean and the shading shows the standard deviation of the number of possible detections. The transparency of the lines is proportional to the probability that the group has a certain area value (see distributions in a).

Figure 6.

Detection relative to group heading direction. (a) The number of possible detections in the group at different angles with respect to the group heading direction. Results are calculated using instances when the group is moving aligned in a polarized state. Lines show the mean number of individuals with detection capability in a certain direction, and shaded area shows the standard deviation. (b) Illustration of front and side detection using a snapshot of a group of 70, showing where individuals have open lines of sight to either a location to the front (brown lines) or to the side (grey lines) of the group. The front and side edges of the group are defined by the furthest individual in these respective directions. Computationally, a location far away is used to represent detection in a certain direction (figure 10). (c) Average individual detection capability in a direction to the front of the group, plotted as a function of individual distance from the front edge of the group. (d) Analogous results to (c), but for average individual detection capability in a direction to the side of the group, plotted as a function of individual distance from the corresponding side edge of the group. For (c,d), the transparency of the points is proportional to the number of observations of individuals at that distance from the front or side.

Figure 7.

Model of external visual detection coverage. (a) Illustration of the quantities in the model. (b) Individual detection coverage in the model compared to the data. The baseline blockage probability λ₀ and the scaling exponent q are fitted to the average detection coverage in the data, yielding λ₀ = 0.129 and = 0.58. The error bars show the standard deviations of the distributions from the data, and the grey shaded area shows the standard deviation for the model. (c) Total number of detections in the group in the model compared to the data. The parameter σ, which represents the standard deviation of the radius of the group in the model, is fitted to the standard deviation of the number of possible detections in the data (error bars), leading to σ = 0.263. The grey shaded area shows the standard deviation of total detections in the model. (d,e) Average detection capability for different model parameters and number of individuals in a group. In each, the points show the values from the data, the solid lines are obtained numerically from the model, and the dashed lines are the series approximation in equation (2.2). The solid brown line shows the best fit from model, which is obtained using numerical evaluation. (d) Average detection capability for different values of the scaling exponent q, with λ₀ set to the best fit value. (e) Average detection capability for different values of the baseline blocking probability λ₀, with q set to the best fit value. See Methods for model details and fit procedure.

Figure 9.

Group and individual area calculations. (a) The area of the group is calculated by a convex hull that contains the head positions of all group members (grey shading). Individual area is calculated using a Voronoi tesselation, keeping only Voronoi polygons that are enclosed in the overall group boundaries (coloured areas).

Figure 10.

Polygon representation of fish and detection analysis quantities. (a) Example zoomed-in video frame from a group of 10 fish with the four-sided fish polygon model shown as the red overlay. (b) By setting the origin at the group centroid and the group travel direction along the x-axis, we define the (ξ, ν) coordinate system. The front–back coordinate is ξ, and the side–side coordinate is ν. The front, back, left side and right side of the group (ξ_F, ξ_B, ν_L and ν_R, respectively) are defined as the head position of the individual farthest away from the group centroid in that direction. The group direction of travel is along the x-axis. (c) To examine detection, we consider m points placed at a distance of L from the group centroid; we used values of m = 200 and $L=1200\hspace{0.17em}\mathrm{pixels}$ (135 cm), and note that none of the results depend on these exact values; we use this representation for simplicity to represent detection with respect to different locations. The angle θ_k defines the angular location of an external point with respect to the group travel direction.