Professor Jonathan Potts
School of Mathematical and Physical Sciences
Head of Mathematical and Statistical Modelling Research Cluster
Professor of Mathematical Biology
j.potts@sheffield.ac.uk
Hicks Building
Full contact details
Professor Jonathan Potts
School of Mathematical and Physical Sciences
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
School of Mathematical and Physical Sciences
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
-
I graduated in September 2012 with a PhD from the University of Bristol, before taking up a postdoctoral fellowship at the University of Alberta under the supervision of Prof. Mark Lewis FRS. In September 2014, I joined the University of Sheffield as a Lecturer, where I have remained (from January 2024 as Professor of Mathematical Biology).
- Research interests
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Mathematical biology, biological movement, statistical ecology, nonlinear partial differential equations, movement ecology, nonlocal advection
Summary of Research Project(s)
My research focuses on biological movement. Most of it so far has been on understanding animal movement and space use, using mathematical models to understand what drives animals to move and how they ultimately locate themselves in space.
This has led in various directions. Mathematically, I have made contributions to applied partial differential equations (PDEs), particularly those involving non-local advection: i.e. movement triggered by non-local sensing (animals looking around them to decide where to go; cells using protrusions to sense the environment). My interest in emergent patterns has led to a particular interest in bifurcations and stable steady states of these PDEs. Biologically, I have been involved in developing techniques for analysing data with mathematical models, such as iSSA and deepSSF, as well as applying these techniques to a variety of specific ecological questions.
From time to time, my work also has veered into related areas of biology, such as biological invasions, optimal foraging, and life-history trade-offs. Recently, I have been increasingly interested in other aspects of biological movement, such as neuron morphology and collective cell movement. Papers on these will be forthcoming, I hope!
- Publications
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Show: Featured publications All publications
Featured publications
Journal articles
- Understanding mammal avoidance of human settlements. Journal of Animal Ecology. View this article in WRRO
- High resolution data reveal fundamental steps and turns in animal movements. Ecological Monographs, 96(2). View this article in WRRO
- Environmental variability shapes life‐history trade‐offs within and between populations of a long‐lived seabird. Ecology Letters, 29(4). View this article in WRRO
- Efficient statistical inference of turning points in animal movement data. Methods in Ecology and Evolution, 17(3), 889-902. View this article in WRRO
- Predicting animal movement with deepSSF : A deep learning step selection framework. Methods in Ecology and Evolution, 17(2), 371-391. View this article in WRRO
- Positivity and global existence for nonlocal advection-diffusion models of interacting populations. Aims Mathematics, 10(9), 21254-21272. View this article in WRRO
- Aggregation–diffusion in heterogeneous environments. Journal of Mathematical Biology, 90(6). View this article in WRRO
- Biological aggregations from spatial memory and nonlocal advection. Physica D: Nonlinear Phenomena, 476. View this article in WRRO
- Variations in non-local interaction range lead to emergent chase-and-run in heterogeneous populations. Journal of The Royal Society Interface, 21(219). View this article in WRRO
- Weakly nonlinear analysis of a two-species non-local advection–diffusion system. Nonlinear Analysis: Real World Applications, 78. View this article in WRRO
- Distinguishing between long-transient and asymptotic states in a biological aggregation model. Bulletin of Mathematical Biology, 86(3). View this article in WRRO
- Understanding step selection analysis through numerical integration. Methods in Ecology and Evolution, 15(1), 24-35. View this article in WRRO
- Biological modeling with nonlocal advection–diffusion equations. Mathematical Models and Methods in Applied Sciences, 34(1), 57-107. View this article in WRRO
- How to scale up from animal movement decisions to spatiotemporal patterns: An approach via step selection. Journal of Animal Ecology.
- Detecting minimum energy states and multi-stability in nonlocal advection–diffusion models for interacting species. Journal of Mathematical Biology, 85(5).
- Local and global existence for nonlocal multispecies advection-diffusion models. SIAM Journal on Applied Dynamical Systems, 21(3), 1686-1708. View this article in WRRO
All publications
Books
- The Mathematics Behind Biological Invasions. Springer.
Journal articles
- Understanding mammal avoidance of human settlements. Journal of Animal Ecology. View this article in WRRO
- High resolution data reveal fundamental steps and turns in animal movements. Ecological Monographs, 96(2). View this article in WRRO
- Environmental variability shapes life‐history trade‐offs within and between populations of a long‐lived seabird. Ecology Letters, 29(4). View this article in WRRO
- Efficient statistical inference of turning points in animal movement data. Methods in Ecology and Evolution, 17(3), 889-902. View this article in WRRO
- Predicting animal movement with deepSSF : A deep learning step selection framework. Methods in Ecology and Evolution, 17(2), 371-391. View this article in WRRO
- Positivity and global existence for nonlocal advection-diffusion models of interacting populations. Aims Mathematics, 10(9), 21254-21272. View this article in WRRO
- Aggregation–diffusion in heterogeneous environments. Journal of Mathematical Biology, 90(6). View this article in WRRO
- Biological aggregations from spatial memory and nonlocal advection. Physica D: Nonlinear Phenomena, 476. View this article in WRRO
- Understanding and predicting animal movements and distributions in the Anthropocene. Journal of Animal Ecology, 94(6), 1146-1164. View this article in WRRO
- Predicting fine‐scale distributions and emergent spatiotemporal patterns from temporally dynamic step selection simulations. Ecography, 2025(2). View this article in WRRO
- Variations in non-local interaction range lead to emergent chase-and-run in heterogeneous populations. Journal of The Royal Society Interface, 21(219). View this article in WRRO
- Social interactions and habitat structure in understanding the dynamic space use of invasive wild pigs. Wildlife Biology: A journal for wildlife science, 2024(5). View this article in WRRO
- Weakly nonlinear analysis of a two-species non-local advection–diffusion system. Nonlinear Analysis: Real World Applications, 78. View this article in WRRO
- Distinguishing between long-transient and asymptotic states in a biological aggregation model. Bulletin of Mathematical Biology, 86(3). View this article in WRRO
- Combining animal interactions and habitat selection into models of space use: a case study with white‐tailed deer. Wildlife Biology, 2024(3). View this article in WRRO
- Understanding step selection analysis through numerical integration. Methods in Ecology and Evolution, 15(1), 24-35. View this article in WRRO
- Biological modeling with nonlocal advection–diffusion equations. Mathematical Models and Methods in Applied Sciences, 34(1), 57-107. View this article in WRRO
- How to scale up from animal movement decisions to spatiotemporal patterns: An approach via step selection. Journal of Animal Ecology.
- Detecting minimum energy states and multi-stability in nonlocal advection–diffusion models for interacting species. Journal of Mathematical Biology, 85(5).
- Highlighting when animals expend excessive energy for travel using dynamic body acceleration. iScience, 25(9).
- Local and global existence for nonlocal multispecies advection-diffusion models. SIAM Journal on Applied Dynamical Systems, 21(3), 1686-1708. View this article in WRRO
- Assessing the predictive power of step selection functions: how social and environmental interactions affect animal space use. Methods in Ecology and Evolution, 13(8), 1805-1818.
- Beyond resource selection : emergent spatio–temporal distributions from animal movements and stigmergent interactions. Oikos, 2022(6).
- Energy‐based step selection analysis : modelling the energetic drivers of animal movement and habitat use. Journal of Animal Ecology, 91(5), 946-957.
- Differences in the temporal scale of reproductive investment across the slow‐fast continuum in a passerine. Ecology Letters, 25(5), 1139-1151.
- Solving the sample size problem for resource selection functions. Methods in Ecology and Evolution, 12(12), 2421-2431.
- Be different to be better: the effect of personality on optimal foraging with incomplete knowledge. Theoretical Ecology, 14(4), 575-587.
- Stable steady-state solutions of some biological aggregation models. SIAM Journal on Applied Mathematics, 81(3), 1248-1263. View this article in WRRO
- Why did the animal turn? Time‐varying step selection analysis for inference between observed turning‐points in high frequency data. Methods in Ecology and Evolution, 12(5), 921-932.
- Mechanistic home range analysis reveals drivers of space use patterns for a non-territorial passerine. Journal of Animal Ecology, 89(12), 2763-2776. View this article in WRRO
- Parametrising diffusion‐taxis equations from animal movement trajectories using step selection analysis. Methods in Ecology and Evolution, 11(9), 1092-1105.
- An “orientation sphere” visualization for examining animal head movements. Ecology and Evolution, 10(10), 4291-4302. View this article in WRRO
- Optimising the use of bio-loggers for movement ecology research. Journal of Animal Ecology, 89(1), 186-206. View this article in WRRO
- Continuous time resource selection analysis for moving animals. Methods in Ecology and Evolution, 10(10), 1664-1678.
- Directionally correlated movement can drive qualitative changes in emergent population distribution patterns. Mathematics, 7(7).
- Spatial memory and taxis-driven pattern formation in model ecosystems. Bulletin of Mathematical Biology, 81(7), 2725-2747. View this article in WRRO
- Making sense of ultrahigh‐resolution movement data: A new algorithm for inferring sites of interest. Ecology and Evolution, 9(1), 265-274. View this article in WRRO
- Deciding when to intrude on a neighbour: quantifying behavioural mechanisms for temporary territory expansion.. Theoretical Ecology, 12(3), 307-318. View this article in WRRO
- Finding turning-points in ultra-high-resolution animal movement data. Methods in Ecology and Evolution, 9(10), 2091-2101. View this article in WRRO
- What can mixed-species flock movement tell us about the value of Amazonian secondary forests? Insights from spatial behavior. Biotropica, 50(4), 654-673. View this article in WRRO
- Spatial scales of habitat selection decisions: implications for telemetry-based movement modelling. Ecography, 41(3), 437-443. View this article in WRRO
- Fortune favours the brave: movement responses shape demographic dynamics in strongly competing populations. Journal of Theoretical Biology, 420, 190-199. View this article in WRRO
- Energy benefits and emergent space use patterns of an empirically parameterized model of memory-based patch selection. Oikos, 126(2). View this article in WRRO
- Partial differential equation techniques for analysing animal movement: a comparison of different methods. Journal of Theoretical Biology, 416, 52-67. View this article in WRRO
- Flexible characterization of animal movement pattern using net squared displacement and a latent state model. Movement Ecology, 4. View this article in WRRO
- How memory of direct animal interactions can lead to territorial pattern formation. Interface, 13(118). View this article in WRRO
- Integrated step selection analysis: Bridging the gap between resource selection and animal movement. Methods in Ecology and Evolution, 7(5), 619-630. View this article in WRRO
- Spatial patterning of prey at reproduction to reduce predation risk: what drives dispersion from groups?. American Naturalist, 187(5), 678-687. View this article in WRRO
- The “edge effect” phenomenon: deriving population abundance patterns from individual animal movement decisions. Theoretical Ecology, 9(2), 233-247. View this article in WRRO
- Territorial pattern formation in the absence of an attractive potential. Journal of Mathematical Biology, 72(1-2), 25-46. View this article in WRRO
- Unveiling trade-offs in resource selection of migratory caribou using a mechanistic movement model of availability. Ecography, 38(10), 1049-1059. View this article in WRRO
- Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds. Ecology and Evolution, 4(24), 4578-4588. View this article in WRRO
- A Mathematical Approach to Territorial Pattern Formation. The American Mathematical Monthly, 121(9), 754-770.
- A generalized residual technique for analysing complex movement models using earth mover's distance. Methods in Ecology and Evolution, 5(10), 1012-1022. View this article in WRRO
- A unifying framework for quantifying the nature of animal interactions. Interface, 11(96). View this article in WRRO
- How do animal territories form and change? Lessons from 20 years of mechanistic modelling. Proceedings of the Royal Society B: Biological Sciences, 281(1784). View this article in WRRO
- Predicting local and non-local effects of resources on animal space use using a mechanistic step selection model. Methods in Ecology and Evolution, 5(3), 253-262. View this article in WRRO
- Stigmergy, collective actions, and animal social spacing. Proceedings of the National Academy of Sciences, 110(42), 16904-16909.
- Predicting oscillatory dynamics in the movement of territorial animals. Journal of The Royal Society Interface, 9(72), 1529-1543.
- An anti-symmetric exclusion process for two particles on an infinite 1D lattice. Journal of Physics A: Mathematical and Theoretical, 44(48), 485003-485003.
- Impacts of Harvest Removal on Mesocarnivore Territorial Dynamics Captured by Mechanistic Home Range Analysis. The American Naturalist, 000-000.
- Quantifying behavioral changes in territorial animals caused by sudden population declines. The American Naturalist, 182(3), E73-E82. View this article in WRRO
- Territorial Dynamics and Stable Home Range Formation for Central Place Foragers. PLoS ONE, 7(3), e34033-e34033.
- Brownian walkers within subdiffusing territorial boundaries. Physical Review E, 83(6).
- Animal Interactions and the Emergence of Territoriality. PLoS Computational Biology, 7(3), e1002008-e1002008.
Book chapters
- Stochastic Spread, Interdisciplinary Applied Mathematics (pp. 233-256). Springer International Publishing
- Dynamics of Biological Invasions, Interdisciplinary Applied Mathematics (pp. 19-68). Springer International Publishing
- Reaction–Diffusion Models: Single Species, Interdisciplinary Applied Mathematics (pp. 69-105). Springer International Publishing
- Invasion in a Multispecies System, Interdisciplinary Applied Mathematics (pp. 107-154). Springer International Publishing
- Assessing Invasion Risk, Interdisciplinary Applied Mathematics (pp. 257-285). Springer International Publishing
- A User’s Guide to Integrodifference Models for Invasive Spread, Interdisciplinary Applied Mathematics (pp. 195-209). Springer International Publishing
- Introduction, Interdisciplinary Applied Mathematics (pp. 1-18). Springer International Publishing
- Responding to Invasions: Detection, Control, and Adaptation, Interdisciplinary Applied Mathematics (pp. 287-305). Springer International Publishing
- Long-Distance Dispersal and Spread, Interdisciplinary Applied Mathematics (pp. 155-193). Springer International Publishing
- Stochasticity and Invasion Dynamics, Interdisciplinary Applied Mathematics (pp. 211-232). Springer International Publishing
Datasets
Preprints
- Understanding mammal avoidance of human settlements, Wiley.
- Predicting animal movement with deepSSF: a deep learning step selection framework, Cold Spring Harbor Laboratory.
- High resolution data reveal fundamental steps and turning points in animal movements, Springer Science and Business Media LLC.
- Variations in nonlocal interaction range lead to emergent chase-and-run in heterogeneous populations, Cold Spring Harbor Laboratory.
- Predicting fine-scale distributions and emergent spatiotemporal patterns from temporally dynamic step selection simulations, Cold Spring Harbor Laboratory.
- How to scale up from animal movement decisions to spatio-temporal patterns: an approach via step selection, Cold Spring Harbor Laboratory.
- Solving the Sample Size Problem for Resource Selection Analysis, Wiley.
- Beyond resource selection: emergent spatio-temporal distributions from animal movements and stigmergent interactions, Cold Spring Harbor Laboratory.
- Local and Global Existence for Non-local Multi-Species
Advection-Diffusion Models.
- Energy selection functions: modelling the energetic drivers of animal movement and habitat use, Wiley.
- Solving the Sample Size Problem for Resource Selection Analysis, Cold Spring Harbor Laboratory.
- Energy selection functions: modelling the energetic drivers of animal movement and habitat use, Wiley.
- Parametrising diffusion-taxis equations from animal movement trajectories using step selection analysis, Cold Spring Harbor Laboratory.
- Behaviourally-mediated interactions of landscape pattern shape predator-prey dynamics in highly altered landscapes, PeerJ.
- Behaviourally-mediated interactions of landscape pattern shape predator-prey dynamics in highly altered landscapes, PeerJ.
- Understanding mammal avoidance of human settlements. Journal of Animal Ecology. View this article in WRRO
- Research group
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Mathematical and Statistical Modelling
- Grants
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Impacts of Habitat Loss, Animal Movement Behaviour, and Population Persistence (Leverhulme ECF-2025-084) 06/26-04/29 £101K
Measuring resource acquisition to reveal life-history trade-offs over different temporal scales (NERC NE/X000680/1) 11/23-05/27 £735K
Multi-species aggregation equations: a bridge between movement ecology and spatial population dynamics (EPSRC EP/V002988/1) 01/21-12/23 £438K
Advancing Spatial Analysis in the High- Performance Computing Era (US Department of Agriculture) 10/20-09/22 £12K
Dispersal through fitness landscapes in a social bird: from individuals to populations (NERC NE/R001669/1) 03/18-12/21 £601K
- Teaching activities
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MAS108 Mathematical Modelling
- Professional activities and memberships
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EPSRC Peer Review College
NERC Peer Review College
British Ecological Society (BES) Peer Review College
Deputy Secretary of the BES Movement Ecology group
Member of the British Ecological Society