Inferring social network structure in ecological systems from spatio-temporal data streams

Abstract

We propose a methodology for extracting social network structure from spatio-temporal datasets that describe timestamped occurrences of individuals. Our approach identifies temporal regions of dense agent activity and links are drawn between individuals based on their co-occurrences across these 'gathering events'. The statistical significance of these connections is then tested against an appropriate null model. Such a framework allows us to exploit the wealth of analytical and computational tools of network analysis in settings where the underlying connectivity pattern between interacting agents (commonly termed the adjacency matrix) is not given a priori. We perform experiments on two large-scale datasets (greater than 10(6) points) of great tit Parus major wild bird foraging records and illustrate the use of this approach by examining the temporal dynamics of pairing behaviour, a process that was previously very hard to observe. We show that established pair bonds are maintained continuously, whereas new pair bonds form at variable times before breeding, but are characterized by a rapid development of network proximity. The method proposed here is general, and can be applied to any system with information about the temporal co-occurrence of interacting agents.

Figure 1.

(a) We plot the network load for various time window sizes, spanning from 10 s to half an hour. We can see that especially for early increases of Δt, there is a large inclusion of links in the network. We also mark three cases of different time window sizes (dashed vertical line) and show in (b) how the graph topology changes based on the Δt value. (Online version in colour.)

Figure 2.

We plot bird arrivals as recorded at a specific location over the course of 3 h period. We can see that the visitation profile is temporally focused, consisting of bursts of bird activity. Our goal is to identify such regions of increased observation density and examine which individuals participate in these gathering events. (Online version in colour.)

Figure 3.

We calculate the time difference between every pair of consecutive observations at each location in our two data streams (seasons 2007–2008 and 2008–2009) and plot the histogram of those values on a logarithmic scale. The that refer to pairs where z − 1 is the last observation of day d − 1 and z the first observation of day d have been omitted, in order to avoid bias in the results (there is no bird feeding activity during night-time). Open circles, dataset 2007–2008; plus symbols, dataset 2008–2009. (Online version in colour.)

Figure 4.

Our method identifies gathering events from the bursts in our observation stream as seen in (a). Then individuals are assigned to such events creating a bipartite network. In part (b), we recover the bird-to-bird social network, via an appropriate one-mode projection, based on the co-participation of individuals to these events. (Online version in colour.)

Figure 5.

In (a), we show a segment of our data stream profile for a duration of 4 days. We pick a single day ‘data-chunk’ of observations and break it down into separate streams that refer to bird records at each particular location, as shown in (b). For each location-specific stream, we use our method to identify gathering events, as shown in coloured nodes on the right of the bipartite graph in (c). We assign birds (black nodes on the left of the graph) into such events based on their participation strength. We project the bird-to-event bipartite graph of (c) into an one-mode network based on co-occurrences in gathering events, as shown in (d). We remove any links (marked with double lines) that can be explained away by the null model. (Online version in colour.)

Figure 6.

The Wytham woods Parus major wild bird social network at 9 September 2007, with N = 240 nodes, M = 491 edges, created by integrating all location-specific subgraphs shown in figure 5d. Note that not all 770 birds of the 2007–2008 season have been recorded during that day and also individuals no connections have been removed from the network. (Online version in colour.)

Figure 7.

We plot the co-membership values of on a base-2 logarithmic scale. Each value (x-axis) denotes the total number of days a random pair is observed in the same community. We can see that is sparse and the vast majority co-membership values are zero. This shows that if we pick a random dyad in the population, it will most probably be never seen in the same social circle. Asterisks with continuous line, season 2007–2008; open square with continuous line, season 2008–2009. (Online version in colour).

Figure 8.

We plot the cumulative co-membership distributions for three different dyad types: random pairs, mating pairs formed in previous seasons and pairs that formed in the current season. Although for the majority of random bird pairs in the network co-membership values are concentrated around zero, breeding individuals tend to participate much more frequently into the same flocks. (Online version in colour.)

Figure 9.

We compare the co-membership distributions versus (red triangles, line) and versus (green squares, line) in a month-by-month basis, using a Kolmogorov–Smirnov test. Values above the proposed α = 0.05 significance threshold imply that the two distributions under comparison are similar. We can see that from very early in the year old pairs differentiate themselves from random, by starting to participate frequently in the same communities. On the other hand, members of new pairs in the beginning of the year treat each other as random, while preferential mechanism that makes them flock together, starts to build-up during early winter. (a,b) Triangles with solid line, random versus old pairs; squares with solid line, random versus new pairs. (Online version in colour.)