Professor Jonathan Potts
School of Mathematical and Physical Sciences
Mathematics and Statistics Subject Group Head and Head of Mathematical and Statistical Modelling Research Cluster
Professor of Mathematical Biology
j.potts@sheffield.ac.uk
G27c, Hicks Building
Full contact details
Professor Jonathan Potts
School of Mathematical and Physical Sciences
G27c
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
School of Mathematical and Physical Sciences
G27c
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Research interests
-
Most of my research uses mathematical tools to shed light on a few fundamental questions in ecology:
- Can we construct techniques to help predict the effects of future environmental change on the ability of animal populations to survive?
- How can we infer the nature of animal interaction mechanisms, both with each other and their environment, from movement data?
- How do complex systems of animal movements and interactions give rise to emergent population-level patterns?
- Publications
-
Show: Featured publications All publications
Featured publications
Journal articles
- Weakly nonlinear analysis of a two-species non-local advection–diffusion system. Nonlinear Analysis: Real World Applications, 78. 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
- Understanding step selection analysis through numerical integration. Methods in Ecology and Evolution. 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
- Beyond resource selection : emergent spatio–temporal distributions from animal movements and stigmergent interactions. Oikos, 2022(6).
- Solving the sample size problem for resource selection functions. Methods in Ecology and Evolution, 12(12), 2421-2431.
- 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. View this article in WRRO
- Parametrising diffusion‐taxis equations from animal movement trajectories using step selection analysis. Methods in Ecology and Evolution. View this article in WRRO
- Spatial memory and taxis-driven pattern formation in model ecosystems. Bulletin of Mathematical Biology, 1-23. 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
- 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
- Flexible characterization of animal movement pattern using net squared displacement and a latent state model. Movement Ecology, 4(1). 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
- How memory of direct animal interactions can lead to territorial pattern formation. Journal of the Royal Society Interface, 13(118). 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
- A unifying framework for quantifying the nature of animal interactions. Journal of The Royal Society Interface, 11(96). 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
All publications
Books
- The Mathematics Behind Biological Invasions. Springer.
Journal articles
- Biological aggregations from spatial memory and nonlocal advection. Physica D: Nonlinear Phenomena, 134682-134682.
- Variations in non-local interaction range lead to emergent chase-and-run in heterogeneous populations. Journal of The Royal Society Interface, 21(219).
- 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).
- Biological modeling with nonlocal advection–diffusion equations. Mathematical Models and Methods in Applied Sciences, 34(1), 57-107. View this article in WRRO
- Understanding step selection analysis through numerical integration. Methods in Ecology and Evolution. 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.
- 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.
- Differences in the temporal scale of reproductive investment across the slow‐fast continuum in a passerine. Ecology Letters.
- 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.
- 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. View this article in WRRO
- Parametrising diffusion‐taxis equations from animal movement trajectories using step selection analysis. Methods in Ecology and Evolution. View this article in WRRO
- An “orientation sphere” visualization for examining animal head movements. Ecology and Evolution. View this article in WRRO
- Optimising the use of bio-loggers for movement ecology research. Journal of Animal Ecology. View this article in WRRO
- Directionally correlated movement can drive qualitative changes in emergent population distribution patterns. Mathematics, 7(7). View this article in WRRO
- Continuous time resource selection analysis for moving animals. Methods in Ecology and Evolution. View this article in WRRO
- Spatial memory and taxis-driven pattern formation in model ecosystems. Bulletin of Mathematical Biology, 1-23. View this article in WRRO
- Making sense of ultrahigh‐resolution movement data: A new algorithm for inferring sites of interest. Ecology and Evolution. View this article in WRRO
- Deciding when to intrude on a neighbour: quantifying behavioural mechanisms for temporary territory expansion. Theoretical Ecology. 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. View this article in WRRO
- Spatial scales of habitat selection decisions: implications for telemetry-based movement modelling. Ecography. 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), 185-196. View this article in WRRO
- Partial differential equation techniques for analysing animal movement: a comparison of different methods. Journal of Theoretical Biology. View this article in WRRO
- Flexible characterization of animal movement pattern using net squared displacement and a latent state model. Movement Ecology, 4(1). 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
- How memory of direct animal interactions can lead to territorial pattern formation. Journal of the Royal Society Interface, 13(118). View this article in WRRO
- Spatial patterning of prey at reproduction to reduce predation risk: what drives dispersion from groups?. American Naturalist(187). 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
- The “edge effect” phenomenon: deriving population abundance patterns from individual animal movement decisions. Theoretical Ecology, 9(2), 233-247. 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. View this article in WRRO
- A unifying framework for quantifying the nature of animal interactions. Journal of The Royal Society 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), 20140231-20140231. 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
- 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
- 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.
- Understanding and predicting animal movements and distributions in the Anthropocene. Journal of Animal Ecology.
- Predicting fine‐scale distributions and emergent spatiotemporal patterns from temporally dynamic step selection simulations. Ecography.
- Social interactions and habitat structure in understanding the dynamic space use of invasive wild pigs. Wildlife Biology.
- Combining animal interactions and habitat selection into models of space use: a case study with white‐tailed deer. Wildlife Biology.
- 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.
- Stable steady-state solutions of some biological aggregation models. SIAM Journal on Applied Mathematics.
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
- Predicting animal movement with deepSSF: a deep learning step selection framework, Cold Spring Harbor Laboratory.
- Variations in nonlocal interaction range lead to emergent chase-and-run in heterogeneous populations, Cold Spring Harbor Laboratory.
- Simulating animal movement trajectories from temporally dynamic step selection functions, Cold Spring Harbor Laboratory.
- Local and Global Existence for Non-local Multi-Species
Advection-Diffusion Models.
- Behaviourally-mediated interactions of landscape pattern shape predator-prey dynamics in highly altered landscapes, PeerJ Preprints.
- 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, Authorea, Inc..
- Beyond resource selection: emergent spatio-temporal distributions from animal movements and stigmergent interactions, Cold Spring Harbor Laboratory.
- Energy selection functions: modelling the energetic drivers of animal movement and habitat use, Authorea, Inc..
- 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, Authorea, Inc..
- 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.
- Weakly nonlinear analysis of a two-species non-local advection–diffusion system. Nonlinear Analysis: Real World Applications, 78. View this article in WRRO
- Research group
- Grants
-
Current:
Measuring resource acquisition to reveal life-history trade-offs over different temporal scales NERC Previous grants, as Coinvestigator
Dispersal through fitness landscapes in a social bird: from individuals to populations NERC Previous grants, as Sole Investigator
Multi-species aggregation equations: a bridge between movement ecology and spatial population dynamics EPSRC
- Teaching activities
-
MAS108 Mathematical Modelling