1
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Malishev M, Kramer-Schadt S. Movement, models, and metabolism: Individual-based energy budget models as next-generation extensions for predicting animal movement outcomes across scales. Ecol Modell 2021. [DOI: 10.1016/j.ecolmodel.2020.109413] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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2
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López-Incera A, Ried K, Müller T, Briegel HJ. Development of swarm behavior in artificial learning agents that adapt to different foraging environments. PLoS One 2020; 15:e0243628. [PMID: 33338066 PMCID: PMC7748156 DOI: 10.1371/journal.pone.0243628] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 11/24/2020] [Indexed: 11/25/2022] Open
Abstract
Collective behavior, and swarm formation in particular, has been studied from several perspectives within a large variety of fields, ranging from biology to physics. In this work, we apply Projective Simulation to model each individual as an artificial learning agent that interacts with its neighbors and surroundings in order to make decisions and learn from them. Within a reinforcement learning framework, we discuss one-dimensional learning scenarios where agents need to get to food resources to be rewarded. We observe how different types of collective motion emerge depending on the distance the agents need to travel to reach the resources. For instance, strongly aligned swarms emerge when the food source is placed far away from the region where agents are situated initially. In addition, we study the properties of the individual trajectories that occur within the different types of emergent collective dynamics. Agents trained to find distant resources exhibit individual trajectories that are in most cases best fit by composite correlated random walks with features that resemble Lévy walks. This composite motion emerges from the collective behavior developed under the specific foraging selection pressures. On the other hand, agents trained to reach nearby resources predominantly exhibit Brownian trajectories.
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Affiliation(s)
- Andrea López-Incera
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria
| | - Katja Ried
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria
| | - Thomas Müller
- Fachbereich Philosophie, Universität Konstanz, Konstanz, Germany
| | - Hans J. Briegel
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria
- Fachbereich Philosophie, Universität Konstanz, Konstanz, Germany
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3
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D’Elia J, Brandt J, Burnett LJ, Haig SM, Hollenbeck J, Kirkland S, Marcot BG, Punzalan A, West CJ, Williams-Claussen T, Wolstenholme R, Young R. Applying circuit theory and landscape linkage maps to reintroduction planning for California Condors. PLoS One 2020; 14:e0226491. [PMID: 31891594 PMCID: PMC6938332 DOI: 10.1371/journal.pone.0226491] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Accepted: 11/26/2019] [Indexed: 11/21/2022] Open
Abstract
Conservation practitioners are increasingly looking to species translocations as a tool to recover imperiled taxa. Quantitative predictions of where animals are likely to move when released into new areas would allow managers to better address the social, institutional, and ecological dimensions of conservation translocations. Using >5 million California condor (Gymnogyps californianus) occurrence locations from 75 individuals, we developed and tested circuit-based models to predict condor movement away from release sites. We found that circuit-based models of electrical current were well calibrated to the distribution of condor movement data in southern and central California (continuous Boyce Index = 0.86 and 0.98, respectively). Model calibration was improved in southern California when additional nodes were added to the circuit to account for nesting and feeding areas, where condor movement densities were higher (continuous Boyce Index = 0.95). Circuit-based projections of electrical current around a proposed release site in northern California comported with the condor’s historical distribution and revealed that, initially, condor movements would likely be most concentrated in northwestern California and southwest Oregon. Landscape linkage maps, which incorporate information on landscape resistance, complement circuit-based models and aid in the identification of specific avenues for population connectivity or areas where movement between populations may be constrained. We found landscape linkages in the Coast Range and the Sierra Nevada provided the most connectivity to a proposed reintroduction site in northern California. Our methods are applicable to conservation translocations for other species and are flexible, allowing researchers to develop multiple competing hypotheses when there are uncertainties about landscape or social attractants, or uncertainties in the landscape conductance surface.
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Affiliation(s)
- Jesse D’Elia
- Pacific Regional Office, U.S. Fish and Wildlife Service, Portland, Oregon, United States of America
- * E-mail:
| | - Joseph Brandt
- California Condor Recovery Office, U.S. Fish and Wildlife Service, Ventura, California, United States of America
| | - L. Joseph Burnett
- Ventana Wildlife Society, Monterey, California, United States of America
| | - Susan M. Haig
- Forest and Rangeland Ecosystem Science Center, U.S. Geological Survey, Corvallis, Oregon, United States of America
| | - Jeff Hollenbeck
- The Northwest Habitat Institute, Corvallis, Oregon, United States of America
| | - Steve Kirkland
- California Condor Recovery Office, U.S. Fish and Wildlife Service, Ventura, California, United States of America
| | - Bruce G. Marcot
- Pacific Northwest Research Station, U.S. Forest Service, Portland, Oregon, United States of America
| | - Arianna Punzalan
- Department of Ecosystem Science and Sustainability, Colorado State University, Fort Collins, Colorado, United States of America
| | - Christopher J. West
- Wildlife Program, Yurok Tribe, Klamath, California, United States of America
| | - Tiana Williams-Claussen
- Wildlife Program, Yurok Tribe, Klamath, California, United States of America
- Department of Wildlife, Humboldt State University, Arcata, California, United States of America
| | - Rachel Wolstenholme
- Pinnacles National Park, U.S. National Park Service, Paicines, California, United States of America
| | - Rich Young
- Pacific Regional Office, U.S. Fish and Wildlife Service, Portland, Oregon, United States of America
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4
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Sims DW, Humphries NE, Hu N, Medan V, Berni J. Optimal searching behaviour generated intrinsically by the central pattern generator for locomotion. eLife 2019; 8:e50316. [PMID: 31674911 PMCID: PMC6879304 DOI: 10.7554/elife.50316] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 10/24/2019] [Indexed: 01/01/2023] Open
Abstract
Efficient searching for resources such as food by animals is key to their survival. It has been proposed that diverse animals from insects to sharks and humans adopt searching patterns that resemble a simple Lévy random walk, which is theoretically optimal for 'blind foragers' to locate sparse, patchy resources. To test if such patterns are generated intrinsically, or arise via environmental interactions, we tracked free-moving Drosophila larvae with (and without) blocked synaptic activity in the brain, suboesophageal ganglion (SOG) and sensory neurons. In brain-blocked larvae, we found that extended substrate exploration emerges as multi-scale movement paths similar to truncated Lévy walks. Strikingly, power-law exponents of brain/SOG/sensory-blocked larvae averaged 1.96, close to a theoretical optimum (µ ≅ 2.0) for locating sparse resources. Thus, efficient spatial exploration can emerge from autonomous patterns in neural activity. Our results provide the strongest evidence so far for the intrinsic generation of Lévy-like movement patterns.
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Affiliation(s)
- David W Sims
- The Marine Biological Association of the United KingdomPlymouthUnited Kingdom
- Ocean and Earth Science, National Oceanography Centre SouthamptonUniversity of SouthamptonSouthamptonUnited Kingdom
- Centre for Biological SciencesUniversity of SouthamptonSouthamptonUnited Kingdom
| | - Nicolas E Humphries
- The Marine Biological Association of the United KingdomPlymouthUnited Kingdom
| | - Nan Hu
- Department of ZoologyUniversity of CambridgeCambridgeUnited Kingdom
| | - Violeta Medan
- Departamento de Fisiología, Biología Molecular y CelularFacultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad UniversitariaBuenos AiresArgentina
- Instituto de Fisiología, Biología Molecular y Neurociencias (IFIBYNE-UBA-CONICET)Buenos AiresArgentina
| | - Jimena Berni
- Department of ZoologyUniversity of CambridgeCambridgeUnited Kingdom
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5
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Gallotti R, Louf R, Luck JM, Barthelemy M. Tracking random walks. J R Soc Interface 2019; 15:rsif.2017.0776. [PMID: 29436509 DOI: 10.1098/rsif.2017.0776] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Accepted: 01/11/2018] [Indexed: 11/12/2022] Open
Abstract
In empirical studies, trajectories of animals or individuals are sampled in space and time. Yet, it is unclear how sampling procedures bias the recorded data. Here, we consider the important case of movements that consist of alternating rests and moves of random durations and study how the estimate of their statistical properties is affected by the way we measure them. We first discuss the ideal case of a constant sampling interval and short-tailed distributions of rest and move durations, and provide an exact analytical calculation of the fraction of correctly sampled trajectories. Further insights are obtained with simulations using more realistic long-tailed rest duration distributions showing that this fraction is dramatically reduced for real cases. We test our results for real human mobility with high-resolution GPS trajectories, where a constant sampling interval allows one to recover at best 18% of the movements, while over-evaluating the average trip length by a factor of 2. Using a sampling interval extracted from real communication data, we recover only 11% of the moves, a value that cannot be increased above 16% even with ideal algorithms. These figures call for a more cautious use of data in quantitative studies of individuals' movements.
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Affiliation(s)
- Riccardo Gallotti
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), CSIC-UIB, Campus UIB, ES-07122 Palma de Mallorca, Spain
| | - Rémi Louf
- Centre for Advanced Spatial Analysis (CASA), University College London, London W1T 4TJ, UK
| | - Jean-Marc Luck
- Institut de Physique Théorique, Université Paris-Saclay, CEA and CNRS, 91191 Gif-sur-Yvette, France
| | - Marc Barthelemy
- Institut de Physique Théorique, Université Paris-Saclay, CEA and CNRS, 91191 Gif-sur-Yvette, France .,CAMS (CNRS/EHESS), 190-198, avenue de France, 75244 Paris Cedex 13, France
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6
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Ahmed DA, Petrovskii SV. Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency. Methods Ecol Evol 2019. [DOI: 10.1111/2041-210x.13207] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Danish A. Ahmed
- Department of Mathematics and Natural Sciences Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally Kuwait
| | - Sergei V. Petrovskii
- Department of Mathematics University of Leicester Leicester UK
- Peoples Friendship University of Russia (RUDN University) Moscow Russian Federation
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7
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Torney CJ, Hopcraft JGC, Morrison TA, Couzin ID, Levin SA. From single steps to mass migration: the problem of scale in the movement ecology of the Serengeti wildebeest. Philos Trans R Soc Lond B Biol Sci 2019; 373:rstb.2017.0012. [PMID: 29581397 DOI: 10.1098/rstb.2017.0012] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/24/2017] [Indexed: 11/12/2022] Open
Abstract
A central question in ecology is how to link processes that occur over different scales. The daily interactions of individual organisms ultimately determine community dynamics, population fluctuations and the functioning of entire ecosystems. Observations of these multiscale ecological processes are constrained by various technological, biological or logistical issues, and there are often vast discrepancies between the scale at which observation is possible and the scale of the question of interest. Animal movement is characterized by processes that act over multiple spatial and temporal scales. Second-by-second decisions accumulate to produce annual movement patterns. Individuals influence, and are influenced by, collective movement decisions, which then govern the spatial distribution of populations and the connectivity of meta-populations. While the field of movement ecology is experiencing unprecedented growth in the availability of movement data, there remain challenges in integrating observations with questions of ecological interest. In this article, we present the major challenges of addressing these issues within the context of the Serengeti wildebeest migration, a keystone ecological phenomena that crosses multiple scales of space, time and biological complexity.This article is part of the theme issue 'Collective movement ecology'.
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Affiliation(s)
- Colin J Torney
- School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8SQ, UK
| | - J Grant C Hopcraft
- Institute of Biodiversity, Animal Health and Comparative Medicine, University of Glasgow, Glasgow G12 8QQ, UK
| | - Thomas A Morrison
- Institute of Biodiversity, Animal Health and Comparative Medicine, University of Glasgow, Glasgow G12 8QQ, UK
| | - Iain D Couzin
- Department of Collective Behaviour, Max Planck Institute for Ornithology, 78464 Konstanz, Germany.,Chair of Biodiversity and Collective Behaviour, Department of Biology, University of Konstanz, 78464 Konstanz, Germany
| | - Simon A Levin
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA
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8
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Tsalyuk M, Kilian W, Reineking B, Getz WM. Temporal variation in resource selection of African elephants follows long‐term variability in resource availability. ECOL MONOGR 2019. [DOI: 10.1002/ecm.1348] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Miriam Tsalyuk
- Department of Environmental Sciences, Policy & Management University of California Berkeley 130 Mulford Hall #3114 Berkeley California 94720‐3114 USA
| | - Werner Kilian
- Etosha Ecological Institute PO Box 6 Okaukuejo via Outjo Namibia
| | - Björn Reineking
- Universite Grenoble Alpes, Irstea, UR LESSEM, BP 76 38402 St‐Martin‐d'Hères France
- Biogeographical Modelling Bayreuth Center for Ecology and Environmental Research BayCEER University of Bayreuth Universitätstraße 30 95447 Bayreuth Germany
| | - Wayne Marcus Getz
- Department of Environmental Sciences, Policy & Management University of California Berkeley 130 Mulford Hall #3114 Berkeley California 94720‐3114 USA
- School of Mathematical Sciences University of KwaZulu‐Natal Private Bag X54001 Durban 4000 South Africa
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9
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Ross CT, Winterhalder B. Evidence for encounter-conditional, area-restricted search in a preliminary study of Colombian blowgun hunters. PLoS One 2018; 13:e0207633. [PMID: 30540780 PMCID: PMC6291100 DOI: 10.1371/journal.pone.0207633] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Accepted: 11/02/2018] [Indexed: 11/21/2022] Open
Abstract
Active search for prey is energetically costly, so understanding how foragers optimize search has been central to foraging theory. Some theoretical work has suggested that foragers of randomly distributed prey should search using Lévy flights, while work on area-restricted and intermittent search strategies has demonstrated that foragers can use the information provided by prey encounters to more effectively adapt search direction and velocity. Previous empirical comparisons of these search modes have tended to rely on distribution-level analyses, due to the difficulty of collecting event-level data on encounters linked to the GPS tracks of foragers. Here we use a preliminary event-level data-set (18.7 hours of encounter-annotated focal follows over 6 trips) to show that two Colombian blowgun hunters use adaptive encounter-conditional heuristics, not non-conditional Lévy flights, when searching for prey. Using a theoretically derived Bayesian model, we estimate changes in turning-angle and search velocity as a function of encounters with prey at lagged time-steps, and find that: 1) hunters increase average turning-angle in response to encounters, producing a more tortuous search of patches of higher prey density, but adopt more efficient uni-directional, inter-patch movement after failing to encounter prey over a sufficient period of time; and, 2) hunters reduce search velocity in response to encounters, causing them to spend more of their search time in patches with demonstrably higher prey density. These results illustrate the importance of using event-level data to contrast encounter-conditional, area-restricted search and Lévy flights in explaining the search behavior of humans and other organisms.
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Affiliation(s)
- Cody T. Ross
- Max Planck Institute for Evolutionary Anthropology, Department of Human Behavior, Ecology and Culture, Leipzig, Germany
- * E-mail:
| | - Bruce Winterhalder
- University of California Davis, Department of Anthropology, Davis, CA, United States of America
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10
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Ross C, Pacheco-Cobos L, Winterhalder B. A general model of forager search: Adaptive encounter-conditional heuristics outperform Lévy flights in the search for patchily distributed prey. J Theor Biol 2018; 455:357-369. [PMID: 30053387 DOI: 10.1016/j.jtbi.2018.07.031] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Revised: 07/20/2018] [Accepted: 07/23/2018] [Indexed: 10/28/2022]
Abstract
A theoretical and applied literature has suggested that foragers search using Lévy flights, since Lévy flights can maximize the efficiency of search in the absence of information on the location of randomly distributed prey. Foragers, however, often have available to them at least some information about the distribution of prey, gained either through evolved mechanisms, experience and memory, or social transmission of information. As such, we might expect selection for heuristics that make use of such information to further improve the efficiency of random search. Here we present a general model of random search behavior that includes as special cases: area-restricted search, correlated random walks, Brownian search, and Lévy flights. This generative model allows foragers to adjust search parameters based on encounter-conditional and other heuristics. Using a simulation model, we demonstrate the efficiency gains of these search heuristics, and illustrate the resulting differences in the distributions of step-size and heading angle change they imply, relative to Lévy flights. We conclude by presenting a statistical model that can be fit to empirical data and a set of testable, quantitative predictions that contrast our model of adaptive search with the Lévy flight foraging hypothesis.
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Affiliation(s)
- Cody Ross
- Department of Human Behavior, Ecology, and Culture, Max Planck Institute for Evolutionary Anthropology, Deutscher Platz 6, Leipzig 04103, Germany.
| | - Luis Pacheco-Cobos
- Facultad de Biología, Cuerpo Académico Biología y Ecología del Comportamiento, Universidad Veracruzana, México.
| | - Bruce Winterhalder
- Department of Anthropology and Graduate Group in Ecology, University of California, Davis, United States.
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11
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Gallotti R, Chialvo DR. How ants move: individual and collective scaling properties. J R Soc Interface 2018; 15:rsif.2018.0223. [PMID: 29899161 DOI: 10.1098/rsif.2018.0223] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2018] [Accepted: 05/18/2018] [Indexed: 12/20/2022] Open
Abstract
The motion of social insects is often used as a paradigmatic example of complex adaptive dynamics arising from decentralized individual behaviour. In this paper, we revisit the topic of the ruling laws behind the burst of activity in ants. The analysis, done over previously reported data, reconsiders the causation arrows, proposed at individual level, not finding any link between the duration of the ants' activity and their moving speed. Secondly, synthetic trajectories created from steps of different ants demonstrate that a Markov process can explain the previously reported speed shape profile. Finally, we show that as more ants enter the nest, the faster they move, which implies a collective property. Overall, these results provide a mechanistic explanation for the reported behavioural laws, and suggest us a formal way to further study the collective properties in these scenarios.
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Affiliation(s)
- Riccardo Gallotti
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), CSIC-UIB, Campus UIB, 07122 Palma de Mallorca, Spain.,Center for Complex Systems and Brain Sciences (CEMSC), Universidad Nacional de San Martín, 25 de Mayo 1169, San Martín, (1650), Buenos Aires, Argentina
| | - Dante R Chialvo
- Center for Complex Systems and Brain Sciences (CEMSC), Universidad Nacional de San Martín, 25 de Mayo 1169, San Martín, (1650), Buenos Aires, Argentina .,Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Godoy Cruz 2290, Buenos Aires, Argentina
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12
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The evolutionary origins of Lévy walk foraging. PLoS Comput Biol 2017; 13:e1005774. [PMID: 28972973 PMCID: PMC5640246 DOI: 10.1371/journal.pcbi.1005774] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2016] [Revised: 10/13/2017] [Accepted: 09/14/2017] [Indexed: 11/19/2022] Open
Abstract
We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks. How organisms improve the search for food, mates, etc., is a key factor to their survival. Mathematically, the best strategy to look for randomly distributed re-visitable resources—under scarce information and sparse conditions—results from Lévy distributions of move lengths (the probability of taking a step ℓ is proportional to 1/ℓ2). Today it is well established that many animal species in different habitats do perform Lévy foraging. This fact has raised a heated debate, viz., the emergent versus evolutionary hypotheses. For the former, a Lévy foraging is an emergent property, a consequence of searcher-environment interactions: certain landscapes induce Lévy patterns, but others not. In this view, the optimal strategy depends on the particular habitat. The evolutionary explanation, in contrast, is that Lévy foraging strategies are adaptations that evolved via natural selection. In this article, through simulations we exhaustively analyze the influence of distinct environments on the foraging efficiency. We find that the optimal procedure is the same in all situations, provided density is low and landscape information is scarce. So, the best search strategy is remarkably independent of details. These results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.
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13
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Abrahms B, Seidel DP, Dougherty E, Hazen EL, Bograd SJ, Wilson AM, Weldon McNutt J, Costa DP, Blake S, Brashares JS, Getz WM. Suite of simple metrics reveals common movement syndromes across vertebrate taxa. MOVEMENT ECOLOGY 2017; 5:12. [PMID: 28580149 PMCID: PMC5452391 DOI: 10.1186/s40462-017-0104-2] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2017] [Accepted: 04/28/2017] [Indexed: 05/23/2023]
Abstract
BACKGROUND Because empirical studies of animal movement are most-often site- and species-specific, we lack understanding of the level of consistency in movement patterns across diverse taxa, as well as a framework for quantitatively classifying movement patterns. We aim to address this gap by determining the extent to which statistical signatures of animal movement patterns recur across ecological systems. We assessed a suite of movement metrics derived from GPS trajectories of thirteen marine and terrestrial vertebrate species spanning three taxonomic classes, orders of magnitude in body size, and modes of movement (swimming, flying, walking). Using these metrics, we performed a principal components analysis and cluster analysis to determine if individuals organized into statistically distinct clusters. Finally, to identify and interpret commonalities within clusters, we compared them to computer-simulated idealized movement syndromes representing suites of correlated movement traits observed across taxa (migration, nomadism, territoriality, and central place foraging). RESULTS Two principal components explained 70% of the variance among the movement metrics we evaluated across the thirteen species, and were used for the cluster analysis. The resulting analysis revealed four statistically distinct clusters. All simulated individuals of each idealized movement syndrome organized into separate clusters, suggesting that the four clusters are explained by common movement syndrome. CONCLUSIONS Our results offer early indication of widespread recurrent patterns in movement ecology that have consistent statistical signatures, regardless of taxon, body size, mode of movement, or environment. We further show that a simple set of metrics can be used to classify broad-scale movement patterns in disparate vertebrate taxa. Our comparative approach provides a general framework for quantifying and classifying animal movements, and facilitates new inquiries into relationships between movement syndromes and other ecological processes.
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Affiliation(s)
- Briana Abrahms
- NOAA Southwest Fisheries Science Center, Environmental Research Division, 99 Pacific Street, Monterey, CA 93940 USA
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, CA 95060 USA
| | - Dana P. Seidel
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
| | - Eric Dougherty
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
| | - Elliott L. Hazen
- NOAA Southwest Fisheries Science Center, Environmental Research Division, 99 Pacific Street, Monterey, CA 93940 USA
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, CA 95060 USA
| | - Steven J. Bograd
- NOAA Southwest Fisheries Science Center, Environmental Research Division, 99 Pacific Street, Monterey, CA 93940 USA
| | - Alan M. Wilson
- Structure & Motion Lab, Royal Veterinary College, University of London, London, UK
| | | | - Daniel P. Costa
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, CA 95060 USA
| | - Stephen Blake
- Max Planck Institute for Ornithology, Radolfzell, Germany
| | - Justin S. Brashares
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
| | - Wayne M. Getz
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
- School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa
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14
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Reyna-Hurtado R, Teichroeb JA, Bonnell TR, Hernández-Sarabia RU, Vickers SM, Serio-Silva JC, Sicotte P, Chapman CA. Primates adjust movement strategies due to changing food availability. Behav Ecol 2017. [DOI: 10.1093/beheco/arx176] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- Rafael Reyna-Hurtado
- El Colegio de la Frontera Sur, ECOSUR, Avenida Rancho s/n, Lerma, Campeche, México
| | - Julie A Teichroeb
- Department of Anthropology, University of Toronto Scarborough, Scarborough, Toronto, Ontario, Canada
| | - Tyler R Bonnell
- Department of Psychology, University of Lethbridge, Lethbridge, Alberta, Canada
| | - Raul Uriel Hernández-Sarabia
- Instituto de Neuroetología, Universidad Veracruzana, Av. Dr. Luis Castelazo, Industrial de las ánimas, Xalapa, Veracruz, Mexico
| | - Sofia M Vickers
- Department of Anthropology, University of California Santa Cruz, Santa Cruz, CA, USA
| | - Juan Carlos Serio-Silva
- Instituto de Ecología, INECOL, A.C.El Haya, Camino Antiguo a Coatepec, Emiliano Zapata, Xalapa, Veracruz, Mexico
| | - Pascale Sicotte
- Department of Anthropology, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, Canada
| | - Colin A Chapman
- Department of Anthropology, McGill School of Environment, McGill University, Montreal, Quebec, Canada, USA
- Wildlife Conservation Society, Bronx, NY, USA
- Primate Research Institute, Kyoto University, Inuyama, Aichi, Japan
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15
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Abrahms B, Seidel DP, Dougherty E, Hazen EL, Bograd SJ, Wilson AM, Weldon McNutt J, Costa DP, Blake S, Brashares JS, Getz WM. Suite of simple metrics reveals common movement syndromes across vertebrate taxa. MOVEMENT ECOLOGY 2017. [PMID: 28580149 DOI: 10.5441/001/1.hm5nk220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
BACKGROUND Because empirical studies of animal movement are most-often site- and species-specific, we lack understanding of the level of consistency in movement patterns across diverse taxa, as well as a framework for quantitatively classifying movement patterns. We aim to address this gap by determining the extent to which statistical signatures of animal movement patterns recur across ecological systems. We assessed a suite of movement metrics derived from GPS trajectories of thirteen marine and terrestrial vertebrate species spanning three taxonomic classes, orders of magnitude in body size, and modes of movement (swimming, flying, walking). Using these metrics, we performed a principal components analysis and cluster analysis to determine if individuals organized into statistically distinct clusters. Finally, to identify and interpret commonalities within clusters, we compared them to computer-simulated idealized movement syndromes representing suites of correlated movement traits observed across taxa (migration, nomadism, territoriality, and central place foraging). RESULTS Two principal components explained 70% of the variance among the movement metrics we evaluated across the thirteen species, and were used for the cluster analysis. The resulting analysis revealed four statistically distinct clusters. All simulated individuals of each idealized movement syndrome organized into separate clusters, suggesting that the four clusters are explained by common movement syndrome. CONCLUSIONS Our results offer early indication of widespread recurrent patterns in movement ecology that have consistent statistical signatures, regardless of taxon, body size, mode of movement, or environment. We further show that a simple set of metrics can be used to classify broad-scale movement patterns in disparate vertebrate taxa. Our comparative approach provides a general framework for quantifying and classifying animal movements, and facilitates new inquiries into relationships between movement syndromes and other ecological processes.
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Affiliation(s)
- Briana Abrahms
- NOAA Southwest Fisheries Science Center, Environmental Research Division, 99 Pacific Street, Monterey, CA 93940 USA
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, CA 95060 USA
| | - Dana P Seidel
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
| | - Eric Dougherty
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
| | - Elliott L Hazen
- NOAA Southwest Fisheries Science Center, Environmental Research Division, 99 Pacific Street, Monterey, CA 93940 USA
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, CA 95060 USA
| | - Steven J Bograd
- NOAA Southwest Fisheries Science Center, Environmental Research Division, 99 Pacific Street, Monterey, CA 93940 USA
| | - Alan M Wilson
- Structure & Motion Lab, Royal Veterinary College, University of London, London, UK
| | | | - Daniel P Costa
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, CA 95060 USA
| | - Stephen Blake
- Max Planck Institute for Ornithology, Radolfzell, Germany
| | - Justin S Brashares
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
| | - Wayne M Getz
- Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 USA
- School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa
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16
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Pedersen JN, Li L, Grădinaru C, Austin RH, Cox EC, Flyvbjerg H. How to connect time-lapse recorded trajectories of motile microorganisms with dynamical models in continuous time. Phys Rev E 2016; 94:062401. [PMID: 28085401 DOI: 10.1103/physreve.94.062401] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Indexed: 01/29/2023]
Abstract
We provide a tool for data-driven modeling of motility, data being time-lapse recorded trajectories. Several mathematical properties of a model to be found can be gleaned from appropriate model-independent experimental statistics, if one understands how such statistics are distorted by the finite sampling frequency of time-lapse recording, by experimental errors on recorded positions, and by conditional averaging. We give exact analytical expressions for these effects in the simplest possible model for persistent random motion, the Ornstein-Uhlenbeck process. Then we describe those aspects of these effects that are valid for any reasonable model for persistent random motion. Our findings are illustrated with experimental data and Monte Carlo simulations.
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Affiliation(s)
- Jonas N Pedersen
- Department of Micro- and Nanotechnology, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Liang Li
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Cristian Grădinaru
- Department of Micro- and Nanotechnology, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
| | - Robert H Austin
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Edward C Cox
- Department of Molecular Biology, Princeton University, Princeton, New Jersey 08544, USA
| | - Henrik Flyvbjerg
- Department of Micro- and Nanotechnology, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
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17
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Auger-Méthé M, Derocher AE, DeMars CA, Plank MJ, Codling EA, Lewis MA. Evaluating random search strategies in three mammals from distinct feeding guilds. J Anim Ecol 2016; 85:1411-21. [DOI: 10.1111/1365-2656.12562] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2015] [Accepted: 05/29/2016] [Indexed: 11/28/2022]
Affiliation(s)
- Marie Auger-Méthé
- Department of Biological Sciences; University of Alberta; Edmonton AB Canada T6G 2E9
| | - Andrew E. Derocher
- Department of Biological Sciences; University of Alberta; Edmonton AB Canada T6G 2E9
| | - Craig A. DeMars
- Department of Biological Sciences; University of Alberta; Edmonton AB Canada T6G 2E9
| | - Michael J. Plank
- School of Mathematics and Statistics; University of Canterbury; Christchurch Private Bag 4800 New Zealand
| | - Edward A. Codling
- Department of Mathematical Sciences; University of Essex; Colchester CO4 3SQ UK
| | - Mark A. Lewis
- Department of Biological Sciences; University of Alberta; Edmonton AB Canada T6G 2E9
- Department of Mathematical and Statistical Sciences; Centre for Mathematical Biology; University of Alberta; Edmonton AB Canada T6G 2G1
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18
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A framework for analyzing the robustness of movement models to variable step discretization. J Math Biol 2016; 73:815-45. [PMID: 26852021 DOI: 10.1007/s00285-016-0969-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Revised: 09/22/2015] [Indexed: 10/22/2022]
Abstract
When sampling animal movement paths, the frequency at which location measurements are attempted is a critical feature for data analysis. Important quantities derived from raw data, e.g. travel distance or sinuosity, can differ largely based on the temporal resolution of the data. Likewise, when movement models are fitted to data, parameter estimates have been demonstrated to vary with sampling rate. Thus, biological statements derived from such analyses can only be made with respect to the resolution of the underlying data, limiting extrapolation of results and comparison between studies. To address this problem, we investigate whether there are models that are robust against changes in temporal resolution. First, we propose a mathematically rigorous framework, in which we formally define robustness as a model property. We then use the framework for a thorough assessment of a range of basic random walk models, in which we also show how robustness relates to other probabilistic concepts. While we found robustness to be a strong condition met by few models only, we suggest a new method to extend models so as to make them robust. Our framework provides a new systematic, mathematically founded approach to the question if, and how, sampling rate of movement paths affects statistical inference.
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19
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Benhamou S, Collet J. Ultimate failure of the Lévy Foraging Hypothesis: Two-scale searching strategies outperform scale-free ones even when prey are scarce and cryptic. J Theor Biol 2015; 387:221-7. [PMID: 26463680 DOI: 10.1016/j.jtbi.2015.09.034] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2015] [Revised: 09/15/2015] [Accepted: 09/23/2015] [Indexed: 11/30/2022]
Abstract
The "Lévy Foraging Hypothesis" promotes Lévy walk (LW) as the best strategy to forage for patchily but unpredictably located prey. This strategy mixes extensive and intensive searching phases in a mostly cue-free way through strange, scale-free kinetics. It is however less efficient than a cue-driven two-scale Composite Brownian walk (CBW) when the resources encountered are systematically detected. Nevertheless, it could be assumed that the intrinsic capacity of LW to trigger cue-free intensive searching at random locations might be advantageous when resources are not only scarcely encountered but also so cryptic that the probability to detect those encountered during movement is low. Surprisingly, this situation, which should be quite common in natural environments, has almost never been studied. Only a few studies have considered "saltatory" foragers, which are fully "blind" while moving and thus detect prey only during scanning pauses, but none of them compared the efficiency of LW vs. CBW in this context or in less extreme contexts where the detection probability during movement is not null but very low. In a study based on computer simulations, we filled the bridge between the concepts of "pure continuous" and "pure saltatory" foraging by considering that the probability to detect resources encountered while moving may range from 0 to 1. We showed that regularly stopping to scan the environment can indeed improve efficiency, but only at very low detection probabilities. Furthermore, the LW is then systematically outperformed by a mixed cue-driven/internally-driven CBW. It is thus more likely that evolution tends to favour strategies that rely on environmental feedbacks rather than on strange kinetics.
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Affiliation(s)
- Simon Benhamou
- Centre d׳Ecologie Fonctionnelle et Evolutive, CNRS, 34293 Montpellier, France.
| | - Julien Collet
- Centre d׳Ecologie Fonctionnelle et Evolutive, CNRS, 34293 Montpellier, France; Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69007 Lyon, France.
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20
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Tromer RM, Barbosa MB, Bartumeus F, Catalan J, da Luz MGE, Raposo EP, Viswanathan GM. Inferring Lévy walks from curved trajectories: A rescaling method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022147. [PMID: 26382383 DOI: 10.1103/physreve.92.022147] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2015] [Indexed: 06/05/2023]
Abstract
An important problem in the study of anomalous diffusion and transport concerns the proper analysis of trajectory data. The analysis and inference of Lévy walk patterns from empirical or simulated trajectories of particles in two and three-dimensional spaces (2D and 3D) is much more difficult than in 1D because path curvature is nonexistent in 1D but quite common in higher dimensions. Recently, a new method for detecting Lévy walks, which considers 1D projections of 2D or 3D trajectory data, has been proposed by Humphries et al. The key new idea is to exploit the fact that the 1D projection of a high-dimensional Lévy walk is itself a Lévy walk. Here, we ask whether or not this projection method is powerful enough to cleanly distinguish 2D Lévy walk with added curvature from a simple Markovian correlated random walk. We study the especially challenging case in which both 2D walks have exactly identical probability density functions (pdf) of step sizes as well as of turning angles between successive steps. Our approach extends the original projection method by introducing a rescaling of the projected data. Upon projection and coarse-graining, the renormalized pdf for the travel distances between successive turnings is seen to possess a fat tail when there is an underlying Lévy process. We exploit this effect to infer a Lévy walk process in the original high-dimensional curved trajectory. In contrast, no fat tail appears when a (Markovian) correlated random walk is analyzed in this way. We show that this procedure works extremely well in clearly identifying a Lévy walk even when there is noise from curvature. The present protocol may be useful in realistic contexts involving ongoing debates on the presence (or not) of Lévy walks related to animal movement on land (2D) and in air and oceans (3D).
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Affiliation(s)
- R M Tromer
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal-RN, 59078-970, Brazil
| | - M B Barbosa
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal-RN, 59078-970, Brazil
- Centre d'Estudis Avançats de Blanes (CEAB), CSIC, Blanes, 17300, Spain
| | - F Bartumeus
- Centre d'Estudis Avançats de Blanes (CEAB), CSIC, Blanes, 17300, Spain
- CREAF, Campus UAB, Cerdanyola, 08193, Spain
| | - J Catalan
- Centre d'Estudis Avançats de Blanes (CEAB), CSIC, Blanes, 17300, Spain
- CREAF, Campus UAB, Cerdanyola, 08193, Spain
| | - M G E da Luz
- Departamento de Física, Universidade Federal do Paraná, Curitiba-PR, 81531-980, Brazil
| | - E P Raposo
- Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil
| | - G M Viswanathan
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal-RN, 59078-970, Brazil
- National Institute of Science and Technology of Complex Systems, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil
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21
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Bertrand S, Joo R, Fablet R. Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements. PLoS One 2015; 10:e0132231. [PMID: 26172045 PMCID: PMC4501722 DOI: 10.1371/journal.pone.0132231] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2014] [Accepted: 06/12/2015] [Indexed: 12/02/2022] Open
Abstract
How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW) models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD). GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS), both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1) providing a synthetic and pattern–oriented description of movement, (2) using top predators as ecosystem indicators and (3) studying the variability of spatial behaviour among species or among individuals with different personalities.
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Affiliation(s)
- Sophie Bertrand
- Institut de Recherche pour le Développement (IRD), UMR212 EME, Centre de Recherche Halieutique Méditerranéenne et Tropicale, Avenue Jean Monnet, BP 171, 34203 Sète Cedex, France
- * E-mail:
| | - Rocío Joo
- Institut de Recherche pour le Développement (IRD), UMR212 EME, Centre de Recherche Halieutique Méditerranéenne et Tropicale, Avenue Jean Monnet, BP 171, 34203 Sète Cedex, France
- IMARPE, Esquina Gamarra y General Valle S/N Chucuito, Callao, Lima, Peru
| | - Ronan Fablet
- Institut TELECOM; TELECOM Bretagne; UMR CNRS 3192 Lab-STICC, Technopôle Brest Iroise CS 83818, 29238 Brest cedex, France
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22
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Auger‐Méthé M, Derocher AE, Plank MJ, Codling EA, Lewis MA. Differentiating the Lévy walk from a composite correlated random walk. Methods Ecol Evol 2015. [DOI: 10.1111/2041-210x.12412] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Marie Auger‐Méthé
- Department of Biological Sciences University of Alberta Edmonton Canada
| | | | - Michael J. Plank
- Department of Mathematics and Statistics University of Canterbury Christchurch New Zealnd
| | - Edward A. Codling
- Department of Mathematical Sciences University of Essex Colchester UK
| | - Mark A. Lewis
- Department of Biological Sciences University of Alberta Edmonton Canada
- Centre for Mathematical Biology Department of Mathematical and Statistical Sciences University of Alberta Edmonton Canada
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23
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Breed GA, Severns PM, Edwards AM. Apparent power-law distributions in animal movements can arise from intraspecific interactions. J R Soc Interface 2015; 12:rsif.2014.0927. [PMID: 25519992 DOI: 10.1098/rsif.2014.0927] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight.
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Affiliation(s)
- Greg A Breed
- Department of Biological Sciences, University of Alberta, Edmonton, Canada AB T6G 2E9
| | - Paul M Severns
- Department of Botany and Plant Pathology, Oregon State University, 2082 Cordley Hall, Corvallis, OR, USA
| | - Andrew M Edwards
- Marine Ecosystems and Aquaculture Division, Pacific Biological Station, Fisheries and Oceans Canada, 3190 Hammond Bay Road, Nanaimo, British Columbia, Canada V9T 6N7
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24
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Kenkre VM, Sugaya S. Theory of the transmission of infection in the spread of epidemics: interacting random walkers with and without confinement. Bull Math Biol 2014; 76:3016-27. [PMID: 25403272 DOI: 10.1007/s11538-014-0042-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2014] [Accepted: 11/05/2014] [Indexed: 11/29/2022]
Abstract
A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in [Formula: see text] dimensions. The motion of an animal pair is taken to obey a Smoluchowski equation in [Formula: see text]-dimensional space that combines diffusion with confinement of each animal to its particular home range. An additional (reaction) term that comes into play when the animals are in close proximity describes the process of infection. Analytic solutions are obtained, confirmed by numerical procedures, and shown to predict a surprising effect of confinement. The effect is that infection spread has a non-monotonic dependence on the diffusion constant and/or the extent of the attachment of the animals to the home ranges. Optimum values of these parameters exist for any given distance between the attractive centers. Any change from those values, involving faster/slower diffusion or shallower/steeper confinement, hinders the transmission of infection. A physical explanation is provided by the theory. Reduction to the simpler case of no home ranges is demonstrated. Effective infection rates are calculated, and it is shown how to use them in complex systems consisting of dense populations.
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Affiliation(s)
- V M Kenkre
- Consortium of the Americas for Interdisciplinary Science, Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, 87131, USA,
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25
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Potts JR, Auger-Méthé M, Mokross K, Lewis MA. A generalized residual technique for analysing complex movement models using earth mover's distance. Methods Ecol Evol 2014. [DOI: 10.1111/2041-210x.12253] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Jonathan R. Potts
- Centre for Mathematical Biology; Department of Mathematical and Statistical Sciences; University of Alberta; Edmonton AB Canada
- School of Mathematics and Statistics; University of Sheffield; Sheffield UK
| | - Marie Auger-Méthé
- Centre for Mathematical Biology; Department of Mathematical and Statistical Sciences; University of Alberta; Edmonton AB Canada
- Department of Biological Sciences; University of Alberta; Edmonton AB Canada
| | - Karl Mokross
- School of Renewable Natural Resources; Louisiana State University Agricultural Center; Baton Rouge LA 70803 USA
- Projeto Dinâmica Biológica de Fragmentos Florestais; INPA; Av. André Araújo 2936 Petrópolis Manaus 69083-000 Brazil
| | - Mark A. Lewis
- Centre for Mathematical Biology; Department of Mathematical and Statistical Sciences; University of Alberta; Edmonton AB Canada
- Department of Biological Sciences; University of Alberta; Edmonton AB Canada
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26
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Giuggioli L, Kenkre VM. Consequences of animal interactions on their dynamics: emergence of home ranges and territoriality. MOVEMENT ECOLOGY 2014; 2:20. [PMID: 25709829 PMCID: PMC4337768 DOI: 10.1186/s40462-014-0020-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2014] [Accepted: 08/08/2014] [Indexed: 05/31/2023]
Abstract
Animal spacing has important implications for population abundance, species demography and the environment. Mechanisms underlying spatial segregation have their roots in the characteristics of the animals, their mutual interaction and their response, collective as well as individual, to environmental variables. This review describes how the combination of these factors shapes the patterns we observe and presents a practical, usable framework for the analysis of movement data in confined spaces. The basis of the framework is the theory of interacting random walks and the mathematical description of out-of-equilibrium systems. Although our focus is on modelling and interpreting animal home ranges and territories in vertebrates, we believe further studies on invertebrates may also help to answer questions and resolve unanswered puzzles that are still inaccessible to experimental investigation in vertebrate species.
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Affiliation(s)
- Luca Giuggioli
- />Bristol Centre for Complexity Sciences, Department of Engineering Mathematics and School of Biological Sciences, University of Bristol, Bristol, BS8 1UB UK
| | - V M Kenkre
- />Consortium of the Americas for Interdisciplinary Science and Department of Physics and Astronomy, University of New Mexico, Albuquerque, 87131 New Mexico USA
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27
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Petrovskii S, Petrovskaya N, Bearup D. Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks. Phys Life Rev 2014; 11:467-525. [DOI: 10.1016/j.plrev.2014.02.001] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2013] [Accepted: 02/04/2014] [Indexed: 11/25/2022]
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28
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Codling EA. Pest insect movement and dispersal as an example of applied movement ecology. Phys Life Rev 2014; 11:533-5. [DOI: 10.1016/j.plrev.2014.06.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2014] [Accepted: 06/06/2014] [Indexed: 11/29/2022]
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29
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Petrovskii S, Petrovskaya N, Bearup D. Multiscale ecology of agroecosystems is an emerging research field that can provide a stronger theoretical background for the integrated pest management. Reply to comments on "Multiscale approach to pest insect monitoring: random walks, pattern formation, synchronization, and networks". Phys Life Rev 2014; 11:536-9. [PMID: 25085502 DOI: 10.1016/j.plrev.2014.07.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Accepted: 07/01/2014] [Indexed: 10/25/2022]
Affiliation(s)
- Sergei Petrovskii
- Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
| | | | - Daniel Bearup
- ICBM, University of Oldenburg, 26111 Oldenburg, Germany
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30
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Humphries NE, Sims DW. Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions. J Theor Biol 2014; 358:179-93. [PMID: 24882791 DOI: 10.1016/j.jtbi.2014.05.032] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2014] [Revised: 05/20/2014] [Accepted: 05/21/2014] [Indexed: 10/25/2022]
Abstract
While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.
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Affiliation(s)
- Nicolas E Humphries
- Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill, Plymouth PL1 2PB, UK.
| | - David W Sims
- Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill, Plymouth PL1 2PB, UK; Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Waterfront Campus, Southampton SO14 3ZH, UK; Centre for Biological Sciences, Building 85, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK
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31
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Auger-Méthé M, Plank MJ, Codling EA. Distinguishing between Lévy walks and strong alternative models: comment. Ecology 2014; 95:1104-9. [DOI: 10.1890/13-1484.1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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32
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Anomalous diffusion and multifractality enhance mating encounters in the ocean. Proc Natl Acad Sci U S A 2014; 111:2206-11. [PMID: 24469823 DOI: 10.1073/pnas.1322363111] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
For millimeter-scale aquatic crustaceans such as copepods, ensuring reproductive success is a challenge as potential mates are often separated by hundreds of body lengths in a 3D environment. At the evolutionary scale, this led to the development of remote sensing abilities and behavioral strategies to locate, to track, and to capture a mate. Chemoreception plays a crucial role in increasing mate encounter rates through pheromone clouds and pheromone trails that can be followed over many body lengths. Empirical evidence of trail following behavior is, however, limited to laboratory experiments conducted in still water. An important open question concerns what happens in the turbulent waters of the surface ocean. We propose that copepods experience, and hence react to, a bulk-phase water pheromone concentration. Here we investigate the mating behavior of two key copepod species, Temora longicornis and Eurytemora affinis, to assess the role of background pheromone concentration and the relative roles played by males and females in mating encounters. We find that both males and females react to background pheromone concentration and exhibit both innate and acquired components in their mating strategies. The emerging swimming behaviors have stochastic properties that depend on pheromone concentration, sex, and species, are related to the level of reproductive experience of the individual tested, and significantly diverge from both the Lévy and Brownian models identified in predators searching for low- and high-density prey. Our results are consistent with an adaptation to increase mate encounter rates and hence to optimize reproductive fitness and success.
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33
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Benhamou S. Of scales and stationarity in animal movements. Ecol Lett 2013; 17:261-72. [DOI: 10.1111/ele.12225] [Citation(s) in RCA: 109] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2013] [Revised: 10/11/2013] [Accepted: 10/30/2013] [Indexed: 12/19/2022]
Affiliation(s)
- Simon Benhamou
- Centre d’Écologie Fonctionnelle et Évolutive; CNRS UMR 5175 Montpellier France
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34
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Codling EA, Dumbrell AJ. Bridging the gap between theory and data in ecological models. ECOLOGICAL COMPLEXITY 2013. [DOI: 10.1016/j.ecocom.2013.09.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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35
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Shaffer CA. Spatial foraging in free ranging bearded sakis: traveling salesmen or Lévy Walkers? Am J Primatol 2013; 76:472-84. [PMID: 24166852 DOI: 10.1002/ajp.22227] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2013] [Revised: 09/26/2013] [Accepted: 09/26/2013] [Indexed: 11/05/2022]
Abstract
According to optimal foraging theory and most current models of primate socioecology, primate foraging involves a series of decisions concerning when is the most optimal time to leave a food patch, how to travel to the next patch in an efficient manner, and how to minimize the time and distance traveled to all patches throughout the course of the day. In this study, I assess how bearded sakis solve these challenges by presenting data on their patch use, distance minimization, and by comparing their movements with non-deterministic foraging patterns. The study group, composed of 38 ± 15 individuals, fed significantly longer in higher quality patches (quality defined by patch size and productivity) and in those that contained ripe fruit pulp. However, group size was not a significant predictor of patch occupancy. Bearded sakis traveled relatively directly between food patches, sometimes over distances > 300 m. In addition, they chose the optimal daily path among all patches visited on 9 of 17 occasions, and on average traveled only 21% more than the least distance route. Bearded saki step lengths were consistent with a Brownian rather than a Lévy Walk pattern while waiting times were consistent with a Lévy pattern. However, the distribution of their turning angles indicated a high degree of directional persistence between patches. These results suggest that bearded sakis exploit food patches that are randomly distributed spatially but heterogenous in patch quality. They appear to encode the locations of high quality food patches and minimize travel between them, despite opportunistically feeding from more abundant and randomly distributed, lower quality patches en route.
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Affiliation(s)
- Christopher A Shaffer
- Department of Anthropology, Sociology and Languages, University of Missouri-St. Louis, St. Louis, Missouri
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36
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Humphries NE, Weimerskirch H, Sims DW. A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling. Methods Ecol Evol 2013. [DOI: 10.1111/2041-210x.12096] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - Henri Weimerskirch
- Centre d'Études Biologiques de Chizé; Centre National de la Recherche Scientifique; 79360; Villiers en Bois; France
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37
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Vandercone R, Premachandra K, Wijethunga GP, Dinadh C, Ranawana K, Bahar S. Random walk analysis of ranging patterns of sympatric langurs in a complex resource landscape. Am J Primatol 2013; 75:1209-19. [DOI: 10.1002/ajp.22183] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2012] [Revised: 06/24/2013] [Accepted: 06/25/2013] [Indexed: 11/10/2022]
Affiliation(s)
| | - Kaushalya Premachandra
- Department of Physics & Astronomy and Center for Neurodynamics; University of Missouri at St. Louis; St. Louis; Missouri
| | | | - Chameera Dinadh
- Faculty of Natural Sciences; Open University of Sri Lanka; Nawala; Sri Lanka
| | | | - Sonya Bahar
- Department of Physics & Astronomy and Center for Neurodynamics; University of Missouri at St. Louis; St. Louis; Missouri
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38
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Rosser G, Fletcher AG, Maini PK, Baker RE. The effect of sampling rate on observed statistics in a correlated random walk. J R Soc Interface 2013; 10:20130273. [PMID: 23740484 DOI: 10.1098/rsif.2013.0273] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Tracking the movement of individual cells or animals can provide important information about their motile behaviour, with key examples including migrating birds, foraging mammals and bacterial chemotaxis. In many experimental protocols, observations are recorded with a fixed sampling interval and the continuous underlying motion is approximated as a series of discrete steps. The size of the sampling interval significantly affects the tracking measurements, the statistics computed from observed trajectories, and the inferences drawn. Despite the widespread use of tracking data to investigate motile behaviour, many open questions remain about these effects. We use a correlated random walk model to study the variation with sampling interval of two key quantities of interest: apparent speed and angle change. Two variants of the model are considered, in which reorientations occur instantaneously and with a stationary pause, respectively. We employ stochastic simulations to study the effect of sampling on the distributions of apparent speeds and angle changes, and present novel mathematical analysis in the case of rapid sampling. Our investigation elucidates the complex nature of sampling effects for sampling intervals ranging over many orders of magnitude. Results show that inclusion of a stationary phase significantly alters the observed distributions of both quantities.
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Affiliation(s)
- G Rosser
- Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK
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39
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Nams VO. Sampling animal movement paths causes turn autocorrelation. Acta Biotheor 2013; 61:269-84. [PMID: 23463145 DOI: 10.1007/s10441-013-9182-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2012] [Accepted: 02/27/2013] [Indexed: 10/27/2022]
Abstract
Animal movement models allow ecologists to study processes that operate over a wide range of scales. In order to study them, continuous movements of animals are translated into discrete data points, and then modelled as discrete models. This discretization can bias the representation of the movement path. This paper shows that discretizing correlated random movement paths creates a biased path by creating correlations between successive turning angles. The discretization also biases statistical tests for correlated random walks (CRW) and causes an overestimate in distances travelled; a correction is given for these biases. This effect suggests that there is a natural scale to CRWs, but that distance-discretized CRWs are in a sense, scale invariant. Perhaps a new null model for continuous movement paths is needed. Authors need to be aware of the biases caused by discretizing correlated random walks, and deal with them appropriately.
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40
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Ding Z, Feeley KJ, Wang Y, Pakeman RJ, Ding P. Patterns of bird functional diversity on land-bridge island fragments. J Anim Ecol 2013; 82:781-90. [DOI: 10.1111/1365-2656.12046] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2011] [Accepted: 12/03/2012] [Indexed: 11/30/2022]
Affiliation(s)
- Zhifeng Ding
- The Key Laboratory of Conservation Biology for Endangered Wildlife of the Ministry of Education; College of Life Sciences; Zhejiang University; Hangzhou; China
| | | | - Yanping Wang
- The Key Laboratory of Conservation Biology for Endangered Wildlife of the Ministry of Education; College of Life Sciences; Zhejiang University; Hangzhou; China
| | - Robin J. Pakeman
- The James Hutton Institute; Craigiebuckler; Aberdeen; AB15 8QH; UK
| | - Ping Ding
- The Key Laboratory of Conservation Biology for Endangered Wildlife of the Ministry of Education; College of Life Sciences; Zhejiang University; Hangzhou; China
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41
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Lenz F, Chechkin AV, Klages R. Constructing a stochastic model of bumblebee flights from experimental data. PLoS One 2013; 8:e59036. [PMID: 23520551 PMCID: PMC3592844 DOI: 10.1371/journal.pone.0059036] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2012] [Accepted: 02/11/2013] [Indexed: 11/19/2022] Open
Abstract
The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and energy constraints. As the number of factors is large, it is very hard to build comprehensive movement models. Even when movement patterns in simple environments are analysed, the organisms can display very complex behaviours. While for largely undirected motion or long observation times the dynamics can sometimes be described by isotropic random walks, usually the directional persistence due to a preference to move forward has to be accounted for, e.g., by a correlated random walk. In this paper we generalise these descriptions to a model in terms of stochastic differential equations of Langevin type, which we use to analyse experimental search flight data of foraging bumblebees. Using parameter estimates we discuss the differences and similarities to correlated random walks. From simulations we generate artificial bumblebee trajectories which we use as a validation by comparing the generated ones to the experimental data.
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Affiliation(s)
- Friedrich Lenz
- School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom.
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42
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Gautestad AO. Lévy meets poisson: a statistical artifact may lead to erroneous recategorization of Lévy walk as Brownian motion. Am Nat 2013; 181:440-50. [PMID: 23448891 DOI: 10.1086/669148] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The flow of GPS data on animal space is challenging old paradigms, such as the issue of the scale-free Lévy walk versus scale-specific Brownian motion. Since these movement classes often require different protocols with respect to ecological analyses, further theoretical development in this field is important. I describe central concepts such as scale-specific versus scale-free movement and the difference between mechanistic and statistical-mechanical levels of analysis. Next, I report how a specific sampling scheme may have produced much confusion: a Lévy walk may be wrongly categorized as Brownian motion if the duration of a move, or bout, is used as a proxy for step length and a move is subjectively defined. Hence, the categorization and recategorization of movement class compliance surrounding the Lévy walk controversy may have been based on a statistical artifact. This issue may be avoided by collecting relocations at a fixed rate at a temporal scale that minimizes over- and undersampling.
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Affiliation(s)
- Arild O Gautestad
- Centre for Ecological and Evolutionary Synthesis, Department of Biology, University of Oslo, P.O. Box 1066 Blindern, NO-0316 Oslo, Norway.
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43
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Costa DP, Breed GA, Robinson PW. New Insights into Pelagic Migrations: Implications for Ecology and Conservation. ANNUAL REVIEW OF ECOLOGY EVOLUTION AND SYSTEMATICS 2012. [DOI: 10.1146/annurev-ecolsys-102710-145045] [Citation(s) in RCA: 154] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Highly pelagic large marine vertebrates have evolved the capability of moving across large expanses of the marine environment; some species routinely move across entire ocean basins. Our understanding of these movements has been enhanced by new technologies that now allow us to follow their movements over great distances and long time periods in great detail. This technology provides not only detailed information on the movements of a wide variety of marine species, but also detailed characteristics of the habitats they use and clues to their navigation abilities. Advances in electronic tracking technologies have been coupled with rapid development of statistical and analytical techniques. With these developments, conservation of highly migratory species has been aided by providing new information on where uncommon or endangered species go, what behaviors they perform and why, which habitats are critical, and where they range, as well as, in many cases, better estimates of their population size and the interconnectedness of subpopulations. Together these tools are providing critical insights into the ecology of highly pelagic marine vertebrates that are key for their conservation and management.
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Affiliation(s)
- Daniel P. Costa
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, California 95060
| | - Greg A. Breed
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, California 95060
| | - Patrick W. Robinson
- Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, California 95060
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44
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Lundy MG, Harrison A, Buckley DJ, Boston ES, Scott DD, Teeling EC, Montgomery WI, Houghton JDR. Prey field switching based on preferential behaviour can induce Lévy flights. J R Soc Interface 2012; 10:20120489. [PMID: 23054951 DOI: 10.1098/rsif.2012.0489] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Using the foraging movements of an insectivorous bat, Myotis mystacinus, we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit different functional responses, which are considered to be central in the development of stable predator–prey communities. Recognizing how the foraging movements of an animal relate to environmental conditions also elucidates the evolution of optimized search and the prevalence of discrete strategies in natural systems. Applying techniques that use changes in the frequency distribution of movements facilitates exploration of the processes that underpin behavioural changes.
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Affiliation(s)
- Mathieu G Lundy
- Centre for Irish Bat Research, Queen’s University Belfast and University College Dublin, Dublin, Ireland
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45
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Edwards AM, Freeman MP, Breed GA, Jonsen ID. Incorrect likelihood methods were used to infer scaling laws of marine predator search behaviour. PLoS One 2012; 7:e45174. [PMID: 23071508 PMCID: PMC3465316 DOI: 10.1371/journal.pone.0045174] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2011] [Accepted: 08/17/2012] [Indexed: 11/24/2022] Open
Abstract
Background Ecologists are collecting extensive data concerning movements of animals in marine ecosystems. Such data need to be analysed with valid statistical methods to yield meaningful conclusions. Principal Findings We demonstrate methodological issues in two recent studies that reached similar conclusions concerning movements of marine animals (Nature 451∶1098; Science 332∶1551). The first study analysed vertical movement data to conclude that diverse marine predators (Atlantic cod, basking sharks, bigeye tuna, leatherback turtles and Magellanic penguins) exhibited “Lévy-walk-like behaviour”, close to a hypothesised optimal foraging strategy. By reproducing the original results for the bigeye tuna data, we show that the likelihood of tested models was calculated from residuals of regression fits (an incorrect method), rather than from the likelihood equations of the actual probability distributions being tested. This resulted in erroneous Akaike Information Criteria, and the testing of models that do not correspond to valid probability distributions. We demonstrate how this led to overwhelming support for a model that has no biological justification and that is statistically spurious because its probability density function goes negative. Re-analysis of the bigeye tuna data, using standard likelihood methods, overturns the original result and conclusion for that data set. The second study observed Lévy walk movement patterns by mussels. We demonstrate several issues concerning the likelihood calculations (including the aforementioned residuals issue). Re-analysis of the data rejects the original Lévy walk conclusion. Conclusions We consequently question the claimed existence of scaling laws of the search behaviour of marine predators and mussels, since such conclusions were reached using incorrect methods. We discourage the suggested potential use of “Lévy-like walks” when modelling consequences of fishing and climate change, and caution that any resulting advice to managers of marine ecosystems would be problematic. For reproducibility and future work we provide R source code for all calculations.
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Affiliation(s)
- Andrew M Edwards
- Marine Ecosystems and Aquaculture Division, Pacific Biological Station, Fisheries and Oceans, Canada, Nanaimo, British Columbia, Canada.
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46
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Gautestad AO. Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion. J R Soc Interface 2012; 9:2332-40. [PMID: 22456456 PMCID: PMC3405745 DOI: 10.1098/rsif.2012.0059] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2012] [Accepted: 03/02/2012] [Indexed: 11/12/2022] Open
Abstract
Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.
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Affiliation(s)
- Arild O Gautestad
- Department of Biology, Centre for Ecological and Evolutionary Synthesis, University of Oslo, , PO Box 1066, Blindern, 0316 Oslo, Norway.
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47
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Abstract
Lévy walks are a widely used but contentious model of animal movement patterns. They are contentious because they have been wrongly ascribed to some animal species through use of incorrect statistical methods and because they have not been adequately compared against strong alternative models, such as composite correlated random walks. This lack of comparison has been partly because the strong alternative models do not have simple likelihood functions. Here I show that power-spectra and the distribution of the first significant digits (the leading non-zero digits) of the step lengths can distinguish between Lévy walks and composite correlated random walks. Using these diagnostic tools, I bolster previous claims that honey bees use a movement strategy that can be approximated by Lévy walks when searching for their hive or for a food source.
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Affiliation(s)
- A M Reynolds
- Rothamsted Research, Harpenden, Hertfordshire AL5 2JQ, United Kingdom.
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48
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Kawai R, Petrovskii S. Multi-scale properties of random walk models of animal movement: lessons from statistical inference. Proc Math Phys Eng Sci 2012. [DOI: 10.1098/rspa.2011.0665] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
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 systems and human motion. In this paper, we address the issue of statistical inference for ordinary Gaussian, Pareto, tempered Pareto and fractional Gaussian random walk models, which are among the most studied random walk models proposed as the best strategy in the random search problem. Based on rigorous analysis of the local asymptotic normality property and the Fisher information, we discuss some issues in unbiased joint estimation of the model parameters, in particular, the maximum-likelihood estimation. We present that there exist both theoretical and practical difficulties in more realistic tempered Pareto and fractional Gaussian random walk models from a statistical standpoint. We discuss our findings in the context of individual animal movement and show how our results may be used to facilitate the analysis of movement data and to improve the understanding of the underlying stochastic process.
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Affiliation(s)
- Reiichiro Kawai
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
| | - Sergei Petrovskii
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
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49
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Kawai R. Sampling rate of spatial stochastic processes with independent components in modeling random search paths. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021907. [PMID: 22463244 DOI: 10.1103/physreve.85.021907] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2011] [Revised: 01/05/2012] [Indexed: 05/31/2023]
Abstract
Continuous-time modeling of random searches is designed to be robust to the sampling rate while the spatial model is required to be of rotation-invariant type, which is often computationally prohibitive. Such computational difficulty may be circumvented by employing a model with independent components. We demonstrate that its disadvantages in statistical properties are blurred under lower frequency. We propose a quantitative criterion for choice of the sampling rate at which a spatial model with independent components resembles a rotation-invariant model. Our findings have the potential to assist the observer to employ simpler models in the continuous-time framework to avoid expensive computation required for statistical inference.
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Affiliation(s)
- Reiichiro Kawai
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom.
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50
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Giuggioli L, Potts JR, Harris S. Predicting oscillatory dynamics in the movement of territorial animals. J R Soc Interface 2012; 9:1529-43. [PMID: 22262814 DOI: 10.1098/rsif.2011.0797] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Understanding ecological processes relies upon the knowledge of the dynamics of each individual component. In the context of animal population ecology, the way animals move and interact is of fundamental importance in explaining a variety of observed patterns. Here, we present a theoretical investigation on the movement dynamics of interacting scent-marking animals. We study how the movement statistics of territorial animals is responsible for the appearance of damped oscillations in the mean square displacement (MSD) of the animals. This non-monotonicity is shown to depend on one dimensionless parameter, given by the ratio of the correlation distance between successive steps to the size of the territory. As that parameter increases, the time dependence of the animal's MSD displays a transition from monotonic, characteristic of Brownian walks, to non-monotonic, characteristic of highly correlated walks. The results presented here represent a novel way of determining the degree of persistence in animal movement processes within confined regions.
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Affiliation(s)
- L Giuggioli
- Bristol Centre for Complexity Sciences, University of Bristol, Bristol, UK.
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