Analyzing insect movement as a correlated random walk

  title={Analyzing insect movement as a correlated random walk},
  author={Peter Kareiva and Nanako Shigesada},
SummaryThis paper develops a procedure for quantifying movement sequences in terms of move length and turning angle probability distributions. By assuming that movement is a correlated random walk, we derive a formula that relates expected square displacements to the number of consecutive moves. We show this displacement formula can be used to highlight the consequences of different searching behaviors (i.e. different probability distributions of turning angles or move lengths). Observations of… 

Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns

  • A. Reynolds
  • Biology
    Journal of The Royal Society Interface
  • 2010
It is shown that autcorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale.

Lévy or not? analysing positional data from animal movement paths

The Levy walk hypothesis asserts that the optimal search strategy for a forager under specific conditions is to make successive movement steps that have uniformly random directions and lengths drawn


This work analyzes the statistical differences between two random-walk models commonly used to fit animal movement data, the Levy walks and the correlated random walks, and quantifies their efficiencies within a random search context.

A random walk description of individual animal movement accounting for periods of rest

A composite stochastic process where the periods of active dispersal or ‘bouts’ alternate with periods of immobility is considered, and it is shown that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient.

Three-dimensional random walk models of individual animal movement and their application to trap counts modelling

This study considers three types of shape of 3D traps, which are commonly used in ecological field studies; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap, and investigates the effect of3D trap shapes and sizes and of movement diffusion on trapping efficiency.

Analysis of juvenile tuna movements as correlated random walk

We explore how a stochastic model provides the most promising avenue towards predicting fish movement. To construct a stochastic model describing fish movement, trajectories of ten juveniles in a

Random walk analysis of ranging patterns of sympatric langurs in a complex resource landscape

The identification of random walk models to characterize the movement patterns of social groups of primates, and the behavioral processes that give rise to such movement patterns, remain open

Constructing a Stochastic Model of Bumblebee Flights from Experimental Data

A model in terms of stochastic differential equations of Langevin type is used to analyse experimental search flight data of foraging bumblebees and the differences and similarities to correlated random walks are discussed.

Multi-scale properties of random walk models of animal movement: lessons from statistical inference

  • Ray KawaiS. Petrovskii
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2012
The random search problem has long attracted continuous interest owing to its broad interdisciplinary range of applications, including animal foraging, facilitated target location in biological

Covering Ground: A Look at Movement Patterns and Random Walk Behavior in Aquilonastra Sea Stars

Time-lapse photography is used to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars, to suggest that comparing the effectiveness of an organism’s paths to those from theory can give insight into the organism's actual movement strategy.



A Simulation Model of Animal Movement Patterns

Quantitative description and simulation of stochastic behaviour in dragonflies (Aeschna cyanea, odonata)

Summary1.A dynamic description model of the flight path a dragonfly takes is required in order to derive the encounter frequency of the dragonfly males visiting a pond. It is considered as the first


A simulation of the flight behavior of ovipositing P. rapae results in the placement of more eggs on isolated hosts to demonstrate the effectiveness of egg spreading in averaging out observed variations in larval survivorship and to estimate the potential advantages accrued by egg spreading.

The Food Searching Behaviour of Two European Thrushes

1. The movement path of a predator will clearly be an important determinant of its ability to encounter and subsequently attack suitable prey items. Previous work on this aspect of searching


Butterfly density tends to vary inversely with host density, despite aggregative behaviour identical to that which, in predator-prey systems, leads to a direct correlation between the densities of searcher and resource.

Random dispersal in theoretical populations.

Density, Dispersion, and Population Structure in Drosophila Pseudoobscura

Wild D. pseudoobscura flies were captured, marked, and released in relatively low numbers at nine separate, centrally located sites in each of two Colorado, U.S.A., locations in midsummer 1970 and estimates indicated that the wild Colorado flies dispersed at a rate approximately 50% greater than the laboratory flies released in California, even though the latter probably had more opportunity for dispersion.

Long-distance movement of Pieris rapae.

This method of studying animal movement overcomes several flaws inherent in previous methods, but is restricted to distances of a few km at most.

The Food Searching Behaviour of Two European Thrushes. Ii: the Adaptiveness of the Search Patterns

Although there were suggestions of differing capture rates, unforeseen errors in experimental procedure did not allow firm conclusions on the effects of thrush predation on the different prey distributions within each density, it is suggested that the increases in move lengths were an adaptive reaction by the blackbirds to increases in prey detectability.

A descriptive theory of cell migration on surfaces.