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A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling
A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling
1) A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns.
2) Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data.
3) We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such.
4) By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude.
5) Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.
albatross, cell tracking, correlated random walk, fractal path analysis, Lévy flight, optimal foraging theory, power-law distribution, random walk, satellite tracking, scale-free movement
2041-210X
930-938
Humphries, Nicolas E.
9246d06a-396a-4c05-9721-dc340e75a4d0
Weimerskirch, Henri
fb5128e3-1789-4c1b-91b7-cabd1d8d7547
Sims, David W.
7234b444-25e2-4bd5-8348-a1c142d0cf81
Freckleton, Robert
e6aa5dc7-a1f7-41a1-8e36-90deba70c3b8
Humphries, Nicolas E.
9246d06a-396a-4c05-9721-dc340e75a4d0
Weimerskirch, Henri
fb5128e3-1789-4c1b-91b7-cabd1d8d7547
Sims, David W.
7234b444-25e2-4bd5-8348-a1c142d0cf81
Freckleton, Robert
e6aa5dc7-a1f7-41a1-8e36-90deba70c3b8

Humphries, Nicolas E., Weimerskirch, Henri, Sims, David W. and Freckleton, Robert (2013) A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling. Methods in Ecology and Evolution, 4 (10), 930-938. (doi:10.1111/2041-210X.12096).

Record type: Article

Abstract

1) A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns.
2) Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data.
3) We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such.
4) By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude.
5) Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.

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More information

Published date: October 2013
Keywords: albatross, cell tracking, correlated random walk, fractal path analysis, Lévy flight, optimal foraging theory, power-law distribution, random walk, satellite tracking, scale-free movement
Organisations: Ocean and Earth Science

Identifiers

Local EPrints ID: 359561
URI: http://eprints.soton.ac.uk/id/eprint/359561
ISSN: 2041-210X
PURE UUID: 720d59ed-83e7-43cd-9377-3bae8755af7a

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Date deposited: 04 Nov 2013 13:58
Last modified: 27 Apr 2022 04:10

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Contributors

Author: Nicolas E. Humphries
Author: Henri Weimerskirch
Author: David W. Sims
Author: Robert Freckleton

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