Animal Interactions and the Emergence of Territoriality

Abstract

Inferring the role of interactions in territorial animals relies upon accurate recordings of the behaviour of neighbouring individuals. Such accurate recordings are rarely available from field studies. As a result, quantification of the interaction mechanisms has often relied upon theoretical approaches, which hitherto have been limited to comparisons of macroscopic population-level predictions from un-tested interaction models. Here we present a quantitative framework that possesses a microscopic testable hypothesis on the mechanism of conspecific avoidance mediated by olfactory signals in the form of scent marks. We find that the key parameters controlling territoriality are two: the average territory size, i.e. the inverse of the population density, and the time span during which animal scent marks remain active. Since permanent monitoring of a territorial border is not possible, scent marks need to function in the temporary absence of the resident. As chemical signals carried by the scent only last a finite amount of time, each animal needs to revisit territorial boundaries frequently and refresh its own scent marks in order to deter possible intruders. The size of the territory an animal can maintain is thus proportional to the time necessary for an animal to move between its own territorial boundaries. By using an agent-based model to take into account the possible spatio-temporal movement trajectories of individual animals, we show that the emerging territories are the result of a form of collective animal movement where, different to shoaling, flocking or herding, interactions are highly heterogeneous in space and time. The applicability of our hypothesis has been tested with a prototypical territorial animal, the red fox (Vulpes vulpes).

Predicting oscillatory dynamics in the movement of territorial animals

“…When residents and intruders belong to the same species, this response mechanism is called conspecific avoidance. A recent theoretical study, validated with experimental observations on urban foxes, has elucidated the role of conspecific avoidance and scent-mediated interaction in the collective formation of territorial patterns [4]. The study has shown that conspecific avoidance at the level of the individual generates an exclusion process [5] at the level of the territories, making it apparent that territoriality is a complex emergent phenomenon.…”

“…Compared with figure 5, the shape of the curve in figure 6b, separating the monotonic from the non-monotonic regime in parameter space, appears to be inversely proportional. This does not come as a surprise because preliminary results for Brownian walkers have determined that the diffusion constant of the boundaries, here called K crw because the walkers are correlated, decreases exponentially with Z [4]. In one dimension, this exponential dependence has been shown to arise from a similar exponential dependence in the probability of a territory to extend into interstitial range, as opposed to shrinking further [7].…”

“…To compare the analytical predictions of the previous sections to the many-bodied system of territorial correlated random walkers, we generalize the territorial random walk model in Giuggioli et al [4], so that animals move as correlated random walkers rather than diffusive walkers. We implement stochastic simulations of N animals whereby each animal moves as a correlated random walker inside a square terrain of side S with periodic boundary conditions.…”

“…Previous work in one dimension [4,6] has shown that the relative rate of displacement of a territory boundary compared with that of an animal is solely controlled by the parameter Z. We thus study the dynamics of the MSD of a territorial random walker by varying not only j but also Z as well.…”

What do territory owners defend against?

“…A conflict over territory borders for example implies the ability to remember ownership of the locations of their habitat. Furthermore, this structure is not static but the emergent result of the individuals' activities, namely the history of their movements and interactions [108], a process that we have only recently begun to understand [16,23,109]. If border conflicts are being studied in isolation, these mechanisms can be abstracted away from the single actions of individuals and cognition can be made implicit in the model structure (e.g.…”