Predicting oscillatory dynamics in the movement of territorial animals

Abstract

Understanding ecological processes relies upon the knowledge of the dynamics of each individual component. In the context of animal population ecology, the way animals move and interact is of fundamental importance in explaining a variety of observed patterns. Here, we present a theoretical investigation on the movement dynamics of interacting scent-marking animals. We study how the movement statistics of territorial animals is responsible for the appearance of damped oscillations in the mean square displacement (MSD) of the animals. This non-monotonicity is shown to depend on one dimensionless parameter, given by the ratio of the correlation distance between successive steps to the size of the territory. As that parameter increases, the time dependence of the animal's MSD displays a transition from monotonic, characteristic of Brownian walks, to non-monotonic, characteristic of highly correlated walks. The results presented here represent a novel way of determining the degree of persistence in animal movement processes within confined regions.

Quantifying Behavioral Changes in Territorial Animals Caused by Sudden Population Declines

“…Making use of a reaction-diffusion formalism where the position densities of two neighboring packs are coupled with density profiles of the scent marks and with a predetermined knowledge of the locations of the coyote den sites, compared the steady state position distributions of the animals before and after the removal. This approach, however, cannot be used in our context because the tendency to drift toward the den site is either not present in Bristol's foxes or not sufficiently strong to generate steady state position distributions, since the mean square displacement of the animals increases with time and never settles (Giuggioli et al 2011a). Neither was the habitat spatially confined, as in Briscoe et al (2002).…”

“…Stochastic simulations were performed based on the twodimensional (2-D) territorial random walk model of Giuggioli et al (2011a) but employing one of two different movement processes: nearest-neighbor random walks (NNRWs) and ballistic walks (BWs). The NNRW process is described in Giuggioli et al (2011a), whereas ballistically moving animals will always continue in a straight line, unless they encounter foreign scent, causing them to turn at random.…”

“…The presence/absence nature of the scent implies that the system is intrinsically stochastic, so deterministic representation via reaction-diffusion formalisms may be unable to account for the discrete nature of the interaction events (e.g., see Durrett and Levin 1994;McKane and Newman 2004). A recent modeling framework (Giuggioli et al 2011a(Giuggioli et al , 2011bPotts et al 2011Potts et al , 2012 that accounts for the discrete nature of the scentmediated interaction events is employed here to interpret E74 The American Naturalist observations of the Bristol fox population before and during the 1994-1996 mange epizootic.…”

“…Neither was the habitat spatially confined, as in Briscoe et al (2002). One of the fundamental advancements of the stochastic framework proposed by Giuggioli et al (2011a) is the ability to quantify the (discrete) longevity of scent cues and the movements in territory borders, a key notion implicit in the elastic disc hypothesis. See Potts et al (2012) for a detailed comparison of the two approaches.…”

“…Variations in mean territory size, the amount of directional persistence in the animal movement process, and the animal velocity are also quantified, enabling behavioral changes due to a sudden population decline to be assessed. Additionally, we analyze agent-based simulations of systems of moving and interacting animals (Giuggioli et al 2011a), to determine the longevity of territorial scent marks, the active scent time , from the information provided in the T AS parameter K. Animals are modeled to move at random (Okubo and Levin 2002) but constrained to roam within areas that do not contain scent of conspecifics. As each animal moves, it deposits scent, but once the scent has been present for time , it is no longer considered by others T AS to be fresh and so is ignored.…”