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Animal interactions and the emergence of territoriality - PubMed

Animal interactions and the emergence of territoriality

Luca Giuggioli et al. PLoS Comput Biol. 2011 Mar.

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).

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Graphical illustration of the scent-mediated avoidance interaction.

This plot shows the possible movement of an animal inside its own territory and when it encounters a foreign scent mark. The figure represents an hypothetical snapshot in time of the position of two animals, the red and blue dots, and their own scent profile, the red and blue open circles, respectively. Wherever red (blue) open circles are present it means that the red (blue) animal has walked over that location in the past formula image timesteps, where formula image is the period during which scent remains active. The absence of any scent marks at coordinates (5,1) and (2,4) implies that no animal has occupied those coordinates within a time formula image. The interaction occurs whenever an animal is occupying a site with a foreign scent as displayed for the blue animal at position (4,2). Since the blue animal has deposited scent at (4,2), this point will eventually become blue territory if the red animal does not re-scent it before the red scent becomes inactive. The subsequent allowed locations where the blue animal can move are those for which no red scent is present, i.e. towards the coordinates (5,2) or (4,3), with the actual movement picked at random from these two possibilities. On the other hand, in the absence of an interaction, an animal such as the red one at coordinates (2,2) can move randomly in any of the four possible directions.

Figure 2
Figure 2. Contour level plot of the utilization distribution.

2D plot of the relative frequency distribution of 16 animals' locations with periodic boundary conditions observed up to time formula image (density is 0.0016 animals per site). The positions formula image and formula image are spatial coordinates normalized to the size of the box. On moving away from foreign scent, the animals perform a correlated random walk with turning angles drawn from a 2-sided exponential distribution with a parameter proportional to formula image, where formula image is the number of steps since last encountering foreign scent. The coloured crosses represent the initial animal locations from which their trajectories started to be recorded. This initial condition is obtained from a single run of the simulation up to time formula image, starting from uniformly distributed animals with no initial scent.

Figure 3
Figure 3. Mean square displacement of the locations of the animals and territorial boundaries.

Boundaries are represented by dotted lines, animal 1 by solid lines and animal 2 by dashed lines. In (a) we have plotted the time dependence of the MSD of an animal, formula image (formula image represents an average over the stochastic realizations of multiple trajectories starting with the same initial conditions), and the sum of the left and right boundaries, each formula image, adjusted to correspond to a 90% MCP estimation (see the ‘Relationship between home range size and overlap and mean square displacement’ section of Materials and Methods). Both animals exhibit the same time-dependent MSD so only one is plotted. The choice of the observation time span, from zero up to time formula image in the figure, determines the degree of territoriality one may infer from the data, the ratio of the adjusted boundary and animal mean square displacements being proportional to the square-ratio of the overlap to the size of a home range (see Materials and Methods). The probability distribution as a function of the spatial position formula image, relative to the box size, of the locations of the boundaries and animals at time formula image are plotted in (b) and (c), representing the different types of reaction to the encounter of foreign scent marks corresponding to the two versions of our movement model: (b) a random walk movement after retreat and (c) a correlated random walk, where the probability of continuing straight is formula image, where formula image is the number of steps since the animal last encountered foreign scent. These side plots illustrate the role the type of movement performed by the animals may have on the shape of their probability distribution.

Figure 4
Figure 4. Exclusivity of space use.

Cross-over from territories with an area of exclusive use to ones without in terms of formula image versus formula image. The situation where exclusivity arises is indicated by the closed circles, whereas the absence of exclusivity is represented by the open circles. For a fixed observation time formula image, the insets indicate the probability distribution of the two animals as a function of the spatial position relative to the box size. The degree of overlap between territorial neighbours diminishes as formula image increases, as indicated by inspecting the insets (a), (b) and (c) sequentially. The reaction to the neighbouring scent encountered is the one employed in Fig. 3b and the ratio formula image as one moves from inset (a) to (c).

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