Individual Analyses of Lévy Walk in Semi-Free Ranging Tonkean Macaques (Macaca tonkeana)

Cédric Sueur,Léa Briard,Odile Petit,Sharon Gursky-Doyen

doi:10.1371/journal.pone.0026788

Abstract

Animals adapt their movement patterns to their environment in order to maximize their efficiency when searching for food. The Lévy walk and the Brownian walk are two types of random movement found in different species. Studies have shown that these random movements can switch from a Brownian to a Lévy walk according to the size distribution of food patches. However no study to date has analysed how characteristics such as sex, age, dominance or body mass affect the movement patterns of an individual. In this study we used the maximum likelihood method to examine the nature of the distribution of step lengths and waiting times and assessed how these distributions are influenced by the age and the sex of group members in a semi free-ranging group of ten Tonkean macaques. Individuals highly differed in their activity budget and in their movement patterns. We found an effect of age and sex of individuals on the power distribution of their step lengths and of their waiting times. The males and old individuals displayed a higher proportion of longer trajectories than females and young ones. As regards waiting times, females and old individuals displayed higher rates of long stationary periods than males and young individuals. These movement patterns resembling random walks can probably be explained by the animals moving from one location to other known locations. The power distribution of step lengths might be due to a power distribution of food patches in the enclosure while the power distribution of waiting times might be due to the power distribution of the patch sizes.

Highlights

All animals have to adapt their activity and movements patterns to their environment in order to maximize their nutrient intakes and their fitness [1,2,3,4]
The distribution of maximum waiting time is not uniform between individuals (Z = 2.00, p = 0.01). This is the first study to examine the possible effects of sociodemographic variables on the individual distributions of step lengths and waiting times
We found an effect of age and sex of individuals on the power distribution of their step lengths and of their waiting times

Summary

Introduction

All animals have to adapt their activity and movements patterns to their environment in order to maximize their nutrient intakes and their fitness [1,2,3,4]. Levy walks are a special class of random walks in which movement displacements (step lengths) and stationary periods (waiting times) are not constant but follow a probability distribution with a power-law tail [6,16]. The opposite is seen in the Brownian walk, where the probability of showing a certain step length is constant, and its distribution follows an exponential law [11,13,17]. One study alone showed that Levy walks differed between male and female spider monkeys (Ateles geoffroyi) [21] Authors suggested that this difference was due to a different space-use strategy, with males ranging over wider areas than females in order to control the boundaries of their home range. We assess whether individuals from a semi freeranging group of Tonkean macaques (Macaca tonkeana) show different movement patterns and whether these differences depend on socio-demographic variables

Methods

Results

Conclusion