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Net displacement and temporal scaling: Model fitting, interpretation and implementation

Garrett M. Street, Tal Avgar, Luca Borger Orcid Logo

Methods in Ecology and Evolution

Swansea University Author: Luca Borger Orcid Logo

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DOI (Published version): 10.1111/2041-210X.12978

Abstract

Net displacement is an integral component of numerous ecological processes and is critically dependent on the tortuosity of a movement trajectory and hence on the temporal scale of observation. Numerous attempts have been made to quantitatively describe net displacement while accommodating tortuosit...

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Published in: Methods in Ecology and Evolution
ISSN: 2041210X
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39319
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Numerous attempts have been made to quantitatively describe net displacement while accommodating tortuosity, typically evoking a power law, but scale&#x2010;dependency in tortuosity limits the utility of approaches based on power law relationships that must assume scale&#x2010;invariant tortuosity. We describe a phenomenological model of net displacement that permits both scale&#x2010;variant and scale&#x2010;invariant movement. Movement trajectories are divided into pairs of relocations specifying start&#x2010; and end&#x2010;points, and net displacements between points are calculated across a vector of time intervals. A bootstrap is implemented to create new datasets that are independent both across and within time intervals, and the model is fitted to the bootstrapped dataset using log&#x2013;log regression. We apply this model to simulated trajectories and both fine&#x2010;grain and coarse&#x2010;grain trajectories obtained from an Aldabra giant tortoise Aldabrachelys gigantea, African elephants Loxodonta africana, black&#x2010;backed jackals Canis mesomelas and Northern elephant seals Mirounga angustirostris. The model was able to quantify the characteristics of net displacement from simulated movement trajectories corresponding to both scale&#x2010;variant (e.g. correlated random walks) and scale&#x2010;invariant (e.g. random walk) movement models. Furthermore, the model produced identical outputs across time vectors corresponding to different intervals and absolute ranges of time for scale&#x2010;invariant models. The model characterized the tortoise as generally exhibiting long scale&#x2010;invariant steps, which was corroborated by visual comparison of model outputs to observed trajectories. Elephants, jackals and seals exhibited movement parameters consistent with their known movement behaviours (nomadism, territoriality and widely ranging searching). We describe how the model may be used to compare movements within and between species, for example by partitioning movement into scale&#x2010;variant and scale&#x2010;invariant components, and by calculating a unitless net displacement scaled to the basal movement capacities of an animal. 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spelling 2021-07-16T14:43:21.8681433 v2 39319 2018-04-05 Net displacement and temporal scaling: Model fitting, interpretation and implementation 8416d0ffc3cccdad6e6d67a455e7c4a2 0000-0001-8763-5997 Luca Borger Luca Borger true false 2018-04-05 SBI Net displacement is an integral component of numerous ecological processes and is critically dependent on the tortuosity of a movement trajectory and hence on the temporal scale of observation. Numerous attempts have been made to quantitatively describe net displacement while accommodating tortuosity, typically evoking a power law, but scale‐dependency in tortuosity limits the utility of approaches based on power law relationships that must assume scale‐invariant tortuosity. We describe a phenomenological model of net displacement that permits both scale‐variant and scale‐invariant movement. Movement trajectories are divided into pairs of relocations specifying start‐ and end‐points, and net displacements between points are calculated across a vector of time intervals. A bootstrap is implemented to create new datasets that are independent both across and within time intervals, and the model is fitted to the bootstrapped dataset using log–log regression. We apply this model to simulated trajectories and both fine‐grain and coarse‐grain trajectories obtained from an Aldabra giant tortoise Aldabrachelys gigantea, African elephants Loxodonta africana, black‐backed jackals Canis mesomelas and Northern elephant seals Mirounga angustirostris. The model was able to quantify the characteristics of net displacement from simulated movement trajectories corresponding to both scale‐variant (e.g. correlated random walks) and scale‐invariant (e.g. random walk) movement models. Furthermore, the model produced identical outputs across time vectors corresponding to different intervals and absolute ranges of time for scale‐invariant models. The model characterized the tortoise as generally exhibiting long scale‐invariant steps, which was corroborated by visual comparison of model outputs to observed trajectories. Elephants, jackals and seals exhibited movement parameters consistent with their known movement behaviours (nomadism, territoriality and widely ranging searching). We describe how the model may be used to compare movements within and between species, for example by partitioning movement into scale‐variant and scale‐invariant components, and by calculating a unitless net displacement scaled to the basal movement capacities of an animal. We also identify several useful derived quantities and realistic parameter ranges and discuss how the model may be implemented in a variety of ecological studies. Journal Article Methods in Ecology and Evolution 2041210X bootstrap, fractal, movement, power law, random walk, regression, validation, 4 6 2018 2018-06-04 10.1111/2041-210X.12978 https://besjournals.onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.12978 COLLEGE NANME Biosciences COLLEGE CODE SBI Swansea University 2021-07-16T14:43:21.8681433 2018-04-05T22:43:03.6990238 Professional Services ISS - Uncategorised Garrett M. Street 1 Tal Avgar 2 Luca Borger 0000-0001-8763-5997 3 0039319-05042018225000.pdf StreetetalNetDisplacementRevision1.pdf 2018-04-05T22:50:00.2100000 Output 36205985 application/pdf Accepted Manuscript true 2019-04-05T00:00:00.0000000 12 month embargo. true eng 20 true true
title Net displacement and temporal scaling: Model fitting, interpretation and implementation
spellingShingle Net displacement and temporal scaling: Model fitting, interpretation and implementation
Luca Borger
title_short Net displacement and temporal scaling: Model fitting, interpretation and implementation
title_full Net displacement and temporal scaling: Model fitting, interpretation and implementation
title_fullStr Net displacement and temporal scaling: Model fitting, interpretation and implementation
title_full_unstemmed Net displacement and temporal scaling: Model fitting, interpretation and implementation
title_sort Net displacement and temporal scaling: Model fitting, interpretation and implementation
author_id_str_mv 8416d0ffc3cccdad6e6d67a455e7c4a2
author_id_fullname_str_mv 8416d0ffc3cccdad6e6d67a455e7c4a2_***_Luca Borger
author Luca Borger
author2 Garrett M. Street
Tal Avgar
Luca Borger
format Journal article
container_title Methods in Ecology and Evolution
publishDate 2018
institution Swansea University
issn 2041210X
doi_str_mv 10.1111/2041-210X.12978
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url https://besjournals.onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.12978
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description Net displacement is an integral component of numerous ecological processes and is critically dependent on the tortuosity of a movement trajectory and hence on the temporal scale of observation. Numerous attempts have been made to quantitatively describe net displacement while accommodating tortuosity, typically evoking a power law, but scale‐dependency in tortuosity limits the utility of approaches based on power law relationships that must assume scale‐invariant tortuosity. We describe a phenomenological model of net displacement that permits both scale‐variant and scale‐invariant movement. Movement trajectories are divided into pairs of relocations specifying start‐ and end‐points, and net displacements between points are calculated across a vector of time intervals. A bootstrap is implemented to create new datasets that are independent both across and within time intervals, and the model is fitted to the bootstrapped dataset using log–log regression. We apply this model to simulated trajectories and both fine‐grain and coarse‐grain trajectories obtained from an Aldabra giant tortoise Aldabrachelys gigantea, African elephants Loxodonta africana, black‐backed jackals Canis mesomelas and Northern elephant seals Mirounga angustirostris. The model was able to quantify the characteristics of net displacement from simulated movement trajectories corresponding to both scale‐variant (e.g. correlated random walks) and scale‐invariant (e.g. random walk) movement models. Furthermore, the model produced identical outputs across time vectors corresponding to different intervals and absolute ranges of time for scale‐invariant models. The model characterized the tortoise as generally exhibiting long scale‐invariant steps, which was corroborated by visual comparison of model outputs to observed trajectories. Elephants, jackals and seals exhibited movement parameters consistent with their known movement behaviours (nomadism, territoriality and widely ranging searching). We describe how the model may be used to compare movements within and between species, for example by partitioning movement into scale‐variant and scale‐invariant components, and by calculating a unitless net displacement scaled to the basal movement capacities of an animal. We also identify several useful derived quantities and realistic parameter ranges and discuss how the model may be implemented in a variety of ecological studies.
published_date 2018-06-04T03:49:55Z
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