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Potts JR, Painter KJ. Distinguishing Between Long-Transient and Asymptotic States in a Biological Aggregation Model. Bull Math Biol 2024; 86:28. [PMID: 38341397 PMCID: PMC10858835 DOI: 10.1007/s11538-023-01254-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 12/30/2023] [Indexed: 02/12/2024]
Abstract
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the aggregation-diffusion equation with linear diffusion in one spatial dimension. This equation is known to support solutions that involve both single and multiple aggregations. However, numerical evidence suggests that the latter, which we term 'multi-peaked solutions' may often be long-transient solutions rather than asymptotic steady states. We develop a novel technique for distinguishing between long transients and asymptotic steady states via an energy minimisation approach. The technique involves first approximating our study equation using a limiting process and a moment closure procedure. We then analyse local minimum energy states of this approximate system, hypothesising that these will correspond to asymptotic patterns in the aggregation-diffusion equation. Finally, we verify our hypotheses through numerical investigation, showing that our approximate analytic technique gives good predictions as to whether a state is asymptotic or transient. Overall, we find that almost all twin-peaked, and by extension multi-peaked, solutions are transient, except for some very special cases. We demonstrate numerically that these transients can be arbitrarily long-lived, depending on the parameters of the system.
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Affiliation(s)
- Jonathan R Potts
- School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Sheffield, S3 7RH, UK.
| | - Kevin J Painter
- Dipartimento Interateneo di Scienze, Progetto e Politiche del Territorio (DIST), Politecnico di Torino, Turin, Italy
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2
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Eisaguirre JM, Williams PJ, Hooten MB. Rayleigh step-selection functions and connections to continuous-time mechanistic movement models. MOVEMENT ECOLOGY 2024; 12:14. [PMID: 38331810 PMCID: PMC10854073 DOI: 10.1186/s40462-023-00442-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 12/11/2023] [Indexed: 02/10/2024]
Abstract
BACKGROUND The process known as ecological diffusion emerges from a first principles view of animal movement, but ecological diffusion and other partial differential equation models can be difficult to fit to data. Step-selection functions (SSFs), on the other hand, have emerged as powerful practical tools for ecologists studying the movement and habitat selection of animals. METHODS SSFs typically involve comparing resources between a set of used and available points at each step in a sequence of observed positions. We use change of variables to show that ecological diffusion implies certain distributions for available steps that are more flexible than others commonly used. We then demonstrate advantages of these distributions with SSF models fit to data collected for a mountain lion in Colorado, USA. RESULTS We show that connections between ecological diffusion and SSFs imply a Rayleigh step-length distribution and uniform turning angle distribution, which can accommodate data collected at irregular time intervals. The results of fitting an SSF model with these distributions compared to a set of commonly used distributions revealed how precision and inference can vary between the two approaches. CONCLUSIONS Our new continuous-time step-length distribution can be integrated into various forms of SSFs, making them applicable to data sets with irregular time intervals between successive animal locations.
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Affiliation(s)
| | - Perry J Williams
- Department of Natural Resources & Environmental Science, University of Nevada, Reno, NV, USA
| | - Mevin B Hooten
- Department of Statistics and Data Sciences, The University of Texas at Austin, Austin, TX, USA
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3
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Henley L, Jones O, Mathews F, Woolley TE. Bat Motion can be Described by Leap Frogging. Bull Math Biol 2024; 86:16. [PMID: 38197980 PMCID: PMC10781826 DOI: 10.1007/s11538-023-01233-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Accepted: 11/01/2023] [Indexed: 01/11/2024]
Abstract
We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our model to include non-autonomous parameters, or a leap frogging form of motion, where bats on the exterior move back first, we find we are able to accurately capture the bat's motion. We discuss ways of distinguishing between the two movement descriptions and, finally, consider how the different motion descriptions would impact a bat's hunting strategy.
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Affiliation(s)
- Lucy Henley
- Cardiff School of Mathematics Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK
| | - Owen Jones
- Cardiff School of Mathematics Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK
| | - Fiona Mathews
- University of Sussex, John Maynard Smith Building, Falmer, Brighton, BN1 9RH, UK
| | - Thomas E Woolley
- Cardiff School of Mathematics Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK.
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4
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McClintock BT, Lander ME. A multistate Langevin diffusion for inferring behavior-specific habitat selection and utilization distributions. Ecology 2024; 105:e4186. [PMID: 37794831 DOI: 10.1002/ecy.4186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Revised: 06/29/2023] [Accepted: 09/07/2023] [Indexed: 10/06/2023]
Abstract
The identification of important habitat and the behavior(s) associated with it is critical to conservation and place-based management decisions. Behavior also links life-history requirements and habitat use, which are key to understanding why animals use certain habitats. Animal population studies often use tracking data to quantify space use and habitat selection, but they typically either ignore movement behavior (e.g., foraging, migrating, nesting) or adopt a two-stage approach that can induce bias and fail to propagate uncertainty. We develop a habitat-driven Langevin diffusion for animals that exhibit distinct movement behavior states, thereby providing a novel single-stage statistical method for inferring behavior-specific habitat selection and utilization distributions in continuous time. Practitioners can customize, fit, assess, and simulate our integrated model using the provided R package. Simulation experiments demonstrated that the model worked well under a range of sampling scenarios as long as observations were of sufficient temporal resolution. Our simulations also demonstrated the importance of accounting for different behaviors and the misleading inferences that can result when these are ignored. We provide case studies using plains zebra (Equus quagga) and Steller sea lion (Eumetopias jubatus) telemetry data. In the zebra example, our model identified distinct "encamped" and "exploratory" states, where the encamped state was characterized by strong selection for grassland and avoidance of other vegetation types, which may represent selection for foraging resources. In the sea lion example, our model identified distinct movement behavior modes typically associated with this marine central-place forager and, unlike previous analyses, found foraging-type movements to be associated with steeper offshore slopes characteristic of the continental shelf, submarine canyons, and seamounts that are believed to enhance prey concentrations. This is the first single-stage approach for inferring behavior-specific habitat selection and utilization distributions from tracking data that can be readily implemented with user-friendly software. As certain behaviors are often more relevant to specific conservation or management objectives, practitioners can use our model to help inform the identification and prioritization of important habitats. Moreover, by linking individual-level movement behaviors to population-level spatial processes, the multistate Langevin diffusion can advance inferences at the intersection of population, movement, and landscape ecology.
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Affiliation(s)
- Brett T McClintock
- Marine Mammal Laboratory, Alaska Fisheries Science Center, NOAA, National Marine Fisheries Service, Seattle, Washington, USA
| | - Michelle E Lander
- Marine Mammal Laboratory, Alaska Fisheries Science Center, NOAA, National Marine Fisheries Service, Seattle, Washington, USA
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5
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Wang H, Salmaniw Y. Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping. J Math Biol 2023; 86:71. [PMID: 37029822 DOI: 10.1007/s00285-023-01905-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Revised: 03/12/2023] [Accepted: 03/16/2023] [Indexed: 04/09/2023]
Abstract
The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in chemistry or physics. Hence, it is essential to incorporate such knowledge-based processes into animal movement models. Here, we summarize popular deterministic mathematical models derived from first principles that begin to incorporate such influences on movement behaviour mechanisms. Most generally, these models take the form of nonlocal reaction-diffusion-advection equations, where the nonlocality may appear in the spatial domain, the temporal domain, or both. Mathematical rules of thumb are provided to judge the model rationality, to aid in model development or interpretation, and to streamline an understanding of the range of difficulty in possible model conceptions. To emphasize the importance of biological conclusions drawn from these models, we briefly present available mathematical techniques and introduce some existing "measures of success" to compare and contrast the possible predictions and outcomes. Throughout the review, we propose a large number of open problems relevant to this relatively new area, ranging from precise technical mathematical challenges, to more broad conceptual challenges at the cross-section between mathematics and ecology. This review paper is expected to act as a synthesis of existing efforts while also pushing the boundaries of current modelling perspectives to better understand the influence of cognitive movement mechanisms on movement behaviours and space use outcomes.
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Affiliation(s)
- Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
| | - Yurij Salmaniw
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
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Potts JR, Börger L. How to scale up from animal movement decisions to spatiotemporal patterns: An approach via step selection. J Anim Ecol 2023; 92:16-29. [PMID: 36321473 PMCID: PMC10099581 DOI: 10.1111/1365-2656.13832] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Accepted: 10/16/2022] [Indexed: 11/17/2022]
Abstract
Uncovering the mechanisms behind animal space use patterns is of vital importance for predictive ecology, thus conservation and management of ecosystems. Movement is a core driver of those patterns so understanding how movement mechanisms give rise to space use patterns has become an increasingly active area of research. This study focuses on a particular strand of research in this area, based around step selection analysis (SSA). SSA is a popular way of inferring drivers of movement decisions, but, perhaps less well appreciated, it also parametrises a model of animal movement. Of key interest is that this model can be propagated forwards in time to predict the space use patterns over broader spatial and temporal scales than those that pertain to the proximate movement decisions of animals. Here, we provide a guide for understanding and using the various existing techniques for scaling up step selection models to predict broad-scale space use patterns. We give practical guidance on when to use which technique, as well as specific examples together with code in R and Python. By pulling together various disparate techniques into one place, and providing code and instructions in simple examples, we hope to highlight the importance of these techniques and make them accessible to a wider range of ecologists, ultimately helping expand the usefulness of SSA.
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Affiliation(s)
- Jonathan R Potts
- School of Mathematics and Statistics, University of Sheffield, Sheffield, UK
| | - Luca Börger
- Department of Biosciences, College of Science, Swansea University, Swansea, UK.,Centre for Biomathematics, College of Science, Swansea University, Swansea, UK
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7
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Picardi S, Abrahms B, Gelzer E, Morrison TA, Verzuh T, Merkle JA. Defining null expectations for animal site fidelity. Ecol Lett 2023; 26:157-169. [PMID: 36453059 DOI: 10.1111/ele.14148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Revised: 10/31/2022] [Accepted: 11/02/2022] [Indexed: 12/03/2022]
Abstract
Site fidelity-the tendency to return to previously visited locations-is widespread across taxa. Returns may be driven by several mechanisms, including memory, habitat selection, or chance; however, pattern-based definitions group different generating mechanisms under the same label of 'site fidelity', often assuming memory as the main driver. We propose an operational definition of site fidelity as patterns of return that deviate from a null expectation derived from a memory-free movement model. First, using agent-based simulations, we show that without memory, intrinsic movement characteristics and extrinsic landscape characteristics are key determinants of return patterns and that even random movements may generate substantial probabilities of return. Second, we illustrate how to implement our framework empirically to establish ecologically meaningful, system-specific null expectations for site fidelity. Our approach provides a conceptual and operational framework to test hypotheses on site fidelity across systems and scales.
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Affiliation(s)
- Simona Picardi
- Department of Wildland Resources, Jack H. Berryman Institute, Utah State University, Logan, Utah, USA
| | - Briana Abrahms
- Center for Ecosystem Sentinels, Department of Biology, University of Washington, Seattle, Washington, USA
| | - Emily Gelzer
- Department of Zoology and Physiology, University of Wyoming, Laramie, Wyoming, USA
| | - Thomas A Morrison
- Institute of Biodiversity, Animal Health and Comparative Medicine, University of Glasgow, Glasgow, UK
| | - Tana Verzuh
- Department of Zoology and Physiology, University of Wyoming, Laramie, Wyoming, USA
| | - Jerod A Merkle
- Department of Zoology and Physiology, University of Wyoming, Laramie, Wyoming, USA
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8
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McClintock BT, Abrahms B, Chandler RB, Conn PB, Converse SJ, Emmet RL, Gardner B, Hostetter NJ, Johnson DS. An integrated path for spatial capture-recapture and animal movement modeling. Ecology 2022; 103:e3473. [PMID: 34270790 PMCID: PMC9786756 DOI: 10.1002/ecy.3473] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Revised: 01/25/2021] [Accepted: 03/15/2021] [Indexed: 12/30/2022]
Abstract
Ecologists and conservation biologists increasingly rely on spatial capture-recapture (SCR) and movement modeling to study animal populations. Historically, SCR has focused on population-level processes (e.g., vital rates, abundance, density, and distribution), whereas animal movement modeling has focused on the behavior of individuals (e.g., activity budgets, resource selection, migration). Even though animal movement is clearly a driver of population-level patterns and dynamics, technical and conceptual developments to date have not forged a firm link between the two fields. Instead, movement modeling has typically focused on the individual level without providing a coherent scaling from individual- to population-level processes, whereas SCR has typically focused on the population level while greatly simplifying the movement processes that give rise to the observations underlying these models. In our view, the integration of SCR and animal movement modeling has tremendous potential for allowing ecologists to scale up from individuals to populations and advancing the types of inferences that can be made at the intersection of population, movement, and landscape ecology. Properly accounting for complex animal movement processes can also potentially reduce bias in estimators of population-level parameters, thereby improving inferences that are critical for species conservation and management. This introductory article to the Special Feature reviews recent advances in SCR and animal movement modeling, establishes a common notation, highlights potential advantages of linking individual-level (Lagrangian) movements to population-level (Eulerian) processes, and outlines a general conceptual framework for the integration of movement and SCR models. We then identify important avenues for future research, including key challenges and potential pitfalls in the developments and applications that lie ahead.
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Affiliation(s)
- Brett T. McClintock
- Marine Mammal LaboratoryNOAA‐NMFS Alaska Fisheries Science CenterSeattleWashingtonUSA
| | - Briana Abrahms
- Department of BiologyUniversity of WashingtonLife Sciences Building, Box 351800SeattleWashingtonUSA
| | - Richard B. Chandler
- Warnell School of Forestry and Natural ResourcesUniversity of Georgia180 E. Green St.AthensGeorgiaUSA
| | - Paul B. Conn
- Marine Mammal LaboratoryNOAA‐NMFS Alaska Fisheries Science CenterSeattleWashingtonUSA
| | - Sarah J. Converse
- U.S. Geological SurveyWashington Cooperative Fish and Wildlife Research UnitSchool of Environmental and Forest Sciences & School of Aquatic and Fishery SciencesUniversity of WashingtonBox 355020SeattleWashingtonUSA
| | - Robert L. Emmet
- Quantitative Ecology and Resource ManagementUniversity of WashingtonSeattleWashingtonUSA
| | - Beth Gardner
- School of Environmental and Forest SciencesUniversity of WashingtonSeattleWashingtonUSA
| | - Nathan J. Hostetter
- Washington Cooperative Fish and Wildlife Research UnitSchool of Aquatic and Fishery SciencesUniversity of WashingtonSeattleWashingtonUSA
| | - Devin S. Johnson
- Marine Mammal LaboratoryNOAA‐NMFS Alaska Fisheries Science CenterSeattleWashingtonUSA
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9
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Dominant motion identification of multi-particle system using deep learning from video. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07421-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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10
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Potts JR, Börger L, Strickland BK, Street GM. Assessing the predictive power of step selection functions: how social and environmental interactions affect animal space use. Methods Ecol Evol 2022. [DOI: 10.1111/2041-210x.13904] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jonathan R. Potts
- School of Mathematics and Statistics University of Sheffield, Hicks Building, Hounsfield Road Sheffield UK
| | - Luca Börger
- Department of Biosciences College of Science Swansea University, Singleton Park Swansea Wales UK
- Centre for Biomathematics College of Science Swansea University, Singleton Park Swansea Wales UK
| | - Bronson K. Strickland
- Department of Wildlife, Fisheries, and Aquaculture Mississippi State University Mississippi State MS USA
| | - Garrett M. Street
- Department of Wildlife, Fisheries, and Aquaculture Mississippi State University Mississippi State MS USA
- Quantitative Ecology and Spatial Technologies Laboratory Mississippi State University Mississippi State MS USA
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11
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Potts JR, Giunta V, Lewis MA. Beyond resource selection: emergent spatio–temporal distributions from animal movements and stigmergent interactions. OIKOS 2022. [DOI: 10.1111/oik.09188] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Jonathan R. Potts
- School of Mathematics and Statistics, Univ. of Sheffield, Hicks Building Sheffield UK
| | - Valeria Giunta
- School of Mathematics and Statistics, Univ. of Sheffield, Hicks Building Sheffield UK
| | - Mark A. Lewis
- Depts of Mathematical and Statistical Sciences and Biological Sciences, Univ. of Alberta Edmonton Alberta Canada
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12
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Alfaro M, Giletti T, Kim YJ, Peltier G, Seo H. On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals. J Math Biol 2022; 84:38. [PMID: 35419762 DOI: 10.1007/s00285-022-01738-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 03/20/2022] [Accepted: 03/21/2022] [Indexed: 11/30/2022]
Abstract
We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which include both spatial heterogeneity and anisotropy. In particular, we introduce the notion of deciding factors which single out a nonlocal diffusion model and typically consist of the total jump rate and the average jump length. In this framework, we also discuss the dependence of the profile of the steady state solutions on these deciding factors, thus shedding light on the preferential position of individuals.
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Affiliation(s)
- Matthieu Alfaro
- Laboratoire de Mathématiques Raphaël Salem, CNRS, Université de Rouen Normandie, Saint-Etienne-du-Rouvray, France. .,BioSP, INRAE, 84914, Avignon, France.
| | - Thomas Giletti
- IECL, Université de Lorraine, B.P. 70239, 54506, Vandoeuvre-lès-Nancy Cedex, France
| | - Yong-Jung Kim
- Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Korea
| | - Gwenaël Peltier
- Laboratoire J.-L. Lions, CNRS, Inria, Université de Paris-Cité, Sorbonne Université, 75005, Paris, France
| | - Hyowon Seo
- Department of mathematics, Kunsan National University, 558 Daehak-ro, Gunsan-si, Jeollabuk-do, 54150, South Korea
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13
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Gurarie E, Potluri S, Cosner GC, Cantrell RS, Fagan WF. Memories of Migrations Past: Sociality and Cognition in Dynamic, Seasonal Environments. Front Ecol Evol 2021. [DOI: 10.3389/fevo.2021.742920] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Seasonal migrations are a widespread and broadly successful strategy for animals to exploit periodic and localized resources over large spatial scales. It remains an open and largely case-specific question whether long-distance migrations are resilient to environmental disruptions. High levels of mobility suggest an ability to shift ranges that can confer resilience. On the other hand, a conservative, hard-wired commitment to a risky behavior can be costly if conditions change. Mechanisms that contribute to migration include identification and responsiveness to resources, sociality, and cognitive processes such as spatial memory and learning. Our goal was to explore the extent to which these factors interact not only to maintain a migratory behavior but also to provide resilience against environmental changes. We develop a diffusion-advection model of animal movement in which an endogenous migratory behavior is modified by recent experiences via a memory process, and animals have a social swarming-like behavior over a range of spatial scales. We found that this relatively simple framework was able to adapt to a stable, seasonal resource dynamic under a broad range of parameter values. Furthermore, the model was able to acquire an adaptive migration behavior with time. However, the resilience of the process depended on all the parameters under consideration, with many complex trade-offs. For example, the spatial scale of sociality needed to be large enough to capture changes in the resource, but not so large that the acquired collective information was overly diluted. A long-term reference memory was important for hedging against a highly stochastic process, but a higher weighting of more recent memory was needed for adapting to directional changes in resource phenology. Our model provides a general and versatile framework for exploring the interaction of memory, movement, social and resource dynamics, even as environmental conditions globally are undergoing rapid change.
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Munden R, Börger L, Wilson RP, Redcliffe J, Brown R, Garel M, Potts JR. Why did the animal turn? Time‐varying step selection analysis for inference between observed turning‐points in high frequency data. Methods Ecol Evol 2021. [DOI: 10.1111/2041-210x.13574] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Rhys Munden
- School of Mathematics and Statistics University of Sheffield Sheffield UK
| | - Luca Börger
- Department of Biosciences College of Science Swansea University Swansea UK
- Centre for Biomathematics College of Science Swansea University Swansea UK
| | - Rory P. Wilson
- Department of Biosciences College of Science Swansea University Swansea UK
| | - James Redcliffe
- Department of Biosciences College of Science Swansea University Swansea UK
| | - Rowan Brown
- College of Engineering Swansea UniversityBay Campus Wales UK
| | - Mathieu Garel
- Office Français de la BiodiversitéUnité Ongulés Sauvages Gières France
| | - Jonathan R. Potts
- School of Mathematics and Statistics University of Sheffield Sheffield UK
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Fieberg J, Signer J, Smith B, Avgar T. A 'How to' guide for interpreting parameters in habitat-selection analyses. J Anim Ecol 2021; 90:1027-1043. [PMID: 33583036 PMCID: PMC8251592 DOI: 10.1111/1365-2656.13441] [Citation(s) in RCA: 64] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 02/02/2021] [Indexed: 11/29/2022]
Abstract
Habitat‐selection analyses allow researchers to link animals to their environment via habitat‐selection or step‐selection functions, and are commonly used to address questions related to wildlife management and conservation efforts. Habitat‐selection analyses that incorporate movement characteristics, referred to as integrated step‐selection analyses, are particularly appealing because they allow modelling of both movement and habitat‐selection processes. Despite their popularity, many users struggle with interpreting parameters in habitat‐selection and step‐selection functions. Integrated step‐selection analyses also require several additional steps to translate model parameters into a full‐fledged movement model, and the mathematics supporting this approach can be challenging for many to understand. Using simple examples, we demonstrate how weighted distribution theory and the inhomogeneous Poisson point process can facilitate parameter interpretation in habitat‐selection analyses. Furthermore, we provide a ‘how to’ guide illustrating the steps required to implement integrated step‐selection analyses using the amt package By providing clear examples with open‐source code, we hope to make habitat‐selection analyses more understandable and accessible to end users.
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Affiliation(s)
- John Fieberg
- Department of Fisheries, Wildlife, and Conservation Biology, University of Minnesota, St. Paul, MN, USA
| | - Johannes Signer
- Wildlife Science, Faculty of Forestry and Forest Ecology, University of Goettingen, Göttingen, Germany
| | - Brian Smith
- Department of Wildland Resources and Ecology Center, Utah State University, Logan, UT, USA
| | - Tal Avgar
- Department of Wildland Resources and Ecology Center, Utah State University, Logan, UT, USA
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