The ecology of movement and behaviour: a saturated tripartite network for describing animal contacts

Abstract

Ecologists regularly use animal contact networks to describe interactions underlying pathogen transmission, gene flow, and information transfer. However, empirical descriptions of contact often overlook some features of individual movement, and decisions about what kind of network to use in a particular setting are commonly ad hoc Here, we relate individual movement trajectories to contact networks through a tripartite network model of individual, space, and time nodes. Most networks used in animal contact studies (e.g. individual association networks, home range overlap networks, and spatial networks) are simplifications of this tripartite model. The tripartite structure can incorporate a broad suite of alternative ecological metrics like home range sizes and patch occupancy patterns into inferences about contact network metrics such as modularity and degree distribution. We demonstrate the model's utility with two simulation studies using alternative forms of ecological data to constrain the tripartite network's structure and inform expectations about the harder-to-measure metrics related to contact.

Keywords: Lagrangian movement; contact network; network projection; pathogen transmission; tripartite tagging network.

Figure 1.

From movement processes to contact patterns. Overarching ecological processes in (a) drive a set of (realized) individual movement trajectories (b). These can in turn be summarized through a set of ecological features in c, which are fully determined by the movement trajectories describing individual identity (I), location in space (S), and position in time (T). Some ecological features can then be measured (with noise) to produce various ecological datasets (d). Other ecological metrics, in particular, those describing contact networks, are derived from observed ecological data (e). These derived network metrics are then used as a basis for simulation studies of transmission (f). A key question is how well these forecasted transmission dynamics match those realized in the system (g).

Figure 2.

Network constructions project the full tripartite structure. (a) The full tripartite network shows how six individuals (I) occupy six spatial patches (S) over five time steps (T). Stack heights represent how often each patch was occupied, and colours indicate the occupying individuals. Curves pass through the time step of each occupation. Individuals occupy one patch at a time, but can visit the same patch multiple times. Multiple individuals can occupy the same patch simultaneously. (b) The individual-space bipartite network connects individuals to spatial patches they occupy. (c) The individual-aggregation bipartite network connects individuals to aggregations (points in space–time) in which they occur. (d–g) are unipartite projections of the bipartite networks in (b) and (c).

Figure 3.

Animal behaviour motifs generate consistent correlations in individual identity (I), spatial location (S), and time (T). Venn diagrams show mutual information between variable pairs. Completely overlapping circles contain no independent information, whereas entirely separated circles are completely independent (see the electronic supplementary material for calculation details). (a) Fission–fusion societies may have low mutual information between I, S, and T. (b) In societies with stable social groups, locations in space and time are correlated among group members (individuals 1, 2, and 3 in one group; and 4, 5, and 6 in the other), so that an (I, S × T) bipartite network captures much of the information in the full tripartite network. (c) In some migratory societies, locations in space are associated with positions in time, with all individuals located at the same patch in a given time. (d) In territorial societies, individual identity is correlated with position in space, so that unipartite projections of either individuals or locations in space capture most of the information on spatio-temporal patterns of contact. (Online version in colour.)

Figure 4.

Home range size and patch quality data inform expectations about network topology. In the null model (white), simulated networks were not subject to any marginal constraints, but in two contrasting models (light and dark grey), networks were simulated subject to constraints from ‘observed’ individual home range sizes and patch occupancy patterns. In the light grey model, the system was constrained toward highly varied patch quality (distribution shown in b), whereas in the dark grey model, the system was constrained toward consistent patch quality (distribution shown in c). Each histogram contains modularity estimates from 1 000 simulated individual association networks. Panels (b) and (c) show the simulator’s capacity to recapture input parameters in the overdispersed (b) and underdispersed (c) scenarios. Dashed lines in (b) and (c) show distributions based on the 2.5th and 97.5th quantiles, respectively, of maximum likelihood fits to the emergent patch quality distribution; solid lines indicate the patch quality distribution specified at the simulation's outset.

Figure 5.

Aggregation size and home range size relate consistently to network modularity. (a) Aggregation size distribution constrained modularity of the individual association network, so that systems with larger group sizes had lower modularities. (b) Modularity increased with increasing home range size. (c) Mean group size and mean home range size were strongly related, with larger group sizes occurring in systems with small home ranges. Colours represent values of the shape parameter in the aggregation size distribution used for network simulation (red = 0.5 to blue = 50; the distribution is exponential when the shape parameter is 1, skewness declines as the value of the shape parameter increases).