Elsevier

Journal of Theoretical Biology

Volume 225, Issue 4, 21 December 2003, Pages 443-451
Journal of Theoretical Biology

A model of animal movements in a bounded space

https://doi.org/10.1016/S0022-5193(03)00277-7Get rights and content

Abstract

Most studies describing animal movements have been developed in the framework of population dispersion or population dynamics, and have mainly focused on movements in open spaces. During their trips, however, animals are likely to encounter physical heterogeneities that guide their movements and, as a result, influence their spatial distribution. In this paper, we develop a statistical model of individual movement in a bounded space. We introduced cockroaches in a circular arena and quantified accurately the behaviors underlying their movement in a finite space. Close to the edges, we considered that the animals exhibit a linear movement mode with a constant probability per unit time to leave the edge and enter the central zone of the arena. Far from the walls cockroaches were assumed to move according to a diffusive random walk which enabled us to overcome the inherent problem of the quantification of the turning angle distribution. A numerical model implementing the behavioral rules derived from our experiments, confirms that the pattern of the spatial distribution of animals observed can be reliably accounted for by wall-following behaviors combined with a diffusive random walk. The approach developed in this study can be applied to model the movements of animals in various environment under consideration of spatial structure.

Introduction

Random walk and diffusion models are commonly used to describe animal movements in their environment, analyse their dispersion and predict their spatial distribution (Okubo, 1980; Kareiva and Shigesada, 1983; McCulloch and Cain, 1989; Berg, 1993; Turchin, 1998; Byers, 2001). These models have been used for instance to describe the foraging patterns of ants (Crist and McMahon, 1991), the search for resources in butterflies (Root and Kareiva, 1984) or the migration patterns of vertebrates (Bergman et al., 2000).

Land cover types and landscape spatial heterogeneities (e.g. patch boundaries or habitat edges) can affect the spatial distribution of organisms through their influence on their movement patterns (Crist et al., 1992; Johnson et al., 1992; Wiens et al., 1993; Morales and Ellner, 2002). In particular, the influence of small-scale physical heterogeneities of the environment will be important for small size walking or crawling species. For instance, it is known that ants and termites orient their movements along the structural guidelines created by rocks, crest lines or grooves (Jander and Daumer, 1974; Klotz and Reid (1992), Klotz and Reid (1993); Klotz et al., 2000). The tendency for an organism to orient itself in space by mechanical contacts has been termed thigmotaxis (Fraenkel and Gunn, 1961), and the trend to move along edges has been defined as wall-following behavior (Creed and Miller, 1990). In these cases, animals are not attracted towards physical heterogeneities by long-range stimulations (as it is the case in phototaxis or chemotaxis) but rather, they move randomly in the environment until establishing a physical contact with an obstacle that will guide their motion.

In this paper we investigate how the motion patterns of organisms are affected by the presence of physical edges in a simple situation in which the tracking and quantification of animals’ movements can be easily conducted. We study the movements of the German cockroach Blattella germanica (L.) when introduced in a circular arena. In this situation cockroaches display both exploratory and wall-following behaviors (Darchen, 1957). First, we identify and quantify the behavioral rules that were assumed to contribute to the spatial distribution of the cockroaches. We then built a statistical model of individual motion to verify that these behavioral rules can explain the spatial distribution of cockroaches in an enclosed area, qualitatively as well as quantitatively.

Section snippets

Experimental animals

Experiments were performed with first instar larvae (24-h old) of B. germanica (L.) (Dictyoptera: Blattellidae). At this stage of development the body length is about 3 mm (excluding the antennae), the body width 2 mm and the antennae length 3 mm. The experimental arena was 11 cm in diameter and 0.3 cm in height. It was covered with a glass plate to avoid air currents and to prevent larvae from escaping. The arena was cleaned before each experiment with hot soapy water and alcohol to remove any

Discussion

This study confirms that the spatial distribution of cockroaches is affected by the presence of edges through thigmotaxis. In order to characterize animal movements in a bounded space, we proposed a method of statistical modeling of individual motion. Compared to the standard procedures used to model animal movements, two points are worth noting in the method we used:

(1) Close to the edge, we assumed a linear displacement mode with a constant probability to leave the peripheral zone per unit

Acknowledgements

We thank Christian Jost for stimulating discussions and two anonymous referees for useful comments. R. Jeanson was supported by a doctoral grant from the French Ministry of Scientific Research. JL Deneubourg is a research associate of the Belgian National Foundation for Scientific Research. This work was supported in part by the European Project no: IST-2001-35506: “Artificial Life Control in Mixed-Societies ”

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