"It's not so hard, really; the trouble is that it's all expressed in words. The same thing can be expressed in symbols and then you can see what's happening" - Donald Knuth



  1. Lewis MA, Petrovskii SV, Potts JR. (2016) The mathematics behind biological invasions. Springer, Interdisciplinary Applied Maths Series 44.


  1. Jeffries PM, Patrick SC, Potts JR. (2021) Be different to be better: the effect of personality on optimal foraging with incomplete knowledge. Theoretical Ecology
  2. Potts JR, Painter KJ (2021) Stable steady-state solutions of some biological aggregation models. SIAM J Appl Math 81(3):248-1263
  3. Giunta V, Hillen T, Lewis MA, Potts JR. (2021) Local and Global Existence for Non-local Multi-Species Advection-Diffusion Models. arXiv 2106.06383
  4. Street GM, Potts JR, Börger L, et al. (2021) Solving the sample size problem for resource selection analysis. Methods Ecol Evol doi:10.1111/2041-210X.13701
  5. (preprint)
  6. Munden R, Börger L, Wilson RP, Redcliffe J, Brown R, Garel M, Potts JR. (2021) Why did the animal turn? Time-varying step selection analysis for inference between observed turning points in high frequency data. Methods Ecol Evol 12(5):921-932, doi:10.1111/2041-210X.13574
  7. Klappstein NJ, Potts JR, Michelot T, Börger L, Pilford N, Lewis M, Derocher A. (2020) Energy selection functions: modelling the energetic drivers of animal movement and habitat use. Authorea doi:10.22541/au.160640483.30543006/v1
  8. Ellison N, Hatchwell BJ, Biddiscombe SJ, Napper CJ, Potts JR. (2020) Mechanistic home range analysis reveals drivers of space use patterns for a non-territorial passerine. J Anim Ecol 89(12):2763-2776, doi:10.1111/1365-2656.13292
  9. Potts JR, Schlägel UE. (2020) Parametrising diffusion-taxis equations from animal movement trajectories using step selection analysis. Methods Ecol Evol 11(9):1092-1105, doi:10.1111/2041-210X.13406
  10. Wilson RP, Williams H, Holton M, di Virgilio A, Börger L, Potts JR, Gunner R, Arkwright A, Fahlman A, Bennett N, Alagaili A, Cole N, Duarte C, Scantlebury DM (2020) An ‘orientation sphere’ visualisation for examining animal head movements. Ecol Evol 10:4291-4302, doi:10.1002/ece3.6197
  11. Williams HJ, Taylor LA, Benhamou S, Bijleveld AI, Clay TA, de Grissac S, Demšar U, English HM, Franconi N, Gómez-Laich A, Griffiths RC, Kay WP, Morales JM, Potts JR, Rogerson KF, Rutz C, Spelt A, Trevail AM, Wilson RP, Börger L. (2020) Optimising the use of biologgers for movement ecology research. J Anim Ecol 89:186-206, doi:10.1111/1365-2656.13094
  12. Potts JR. (2019) Directionally-correlated movement can drive qualitative changes in emergent population distribution patterns. Mathematics 7:640, doi:10.3390/math7070640
  13. Wang Y, Blackwell PG, Merkle JA, Potts JR (2019) Continuous time resource selection analysis for moving animals. Methods Ecol Evol 10:1664-1678, doi:10.1111/2041-210X.13259
  14. Potts JR, Lewis MA. (2019) Spatial memory and taxis-driven pattern formation for model ecosystems. Bull Math Biol 81(7):2725-2747, doi:10.1007/s11538-019-00626-9
  15. Munden R, Börger L, Wilson RP, Redcliffe J, Loison A, Garel M, Potts JR. (2019) Making sense of ultra-high resolution animal movement data: an algorithm for inferring sites of interest. Ecol Evol doi:10.1002/ece3.4
  16. Potts JR, Fagan WF, Mourão G. (2018) Deciding when to intrude on a neighbour: Quantifying behavioural mechanisms for temporary territory expansion. Theor Ecol doi:10.1007/s12080-018-0396-x
  17. Potts JR, Börger L, Scantlebury DM, Bennett NC, Alagaili A, Wilson RP. (2018) Finding turning-points in ultra-high-resolution animal movement data. Methods Ecol Evol 9:2091–2101, doi: 10.1111/2041-210X.13056
  18. Mokross K, Potts JR, Rutt C, Stouffer PC, Schaefer JA, Lewis MA, Mahoney S. (2018) What can mixed-species flock movement tell us about the value of Amazonian secondary forests? Insights from spatial behavior. Biotropica 50:664-673, doi: 10.1111/btp.12557
  19. Bastille-Rousseau G, Murray DL, Schaefer JA, Lewis MA, Mahoney S, Potts JR. (2018) Spatial scales of habitat selection decisions: implications for telemetry-based movement modelling. Ecography 40:001–007, doi:10.1111/ecog.02655 Editor's Choice
  20. Potts JR, Petrovskii SV. (2017) Fortune favours the brave: movement responses shape demographic dynamics in strongly competing populations. J Theor Biol 420:190–199, doi:10.1016/j.jtbi.2017.03.011
  21. Wang Y, Potts JR. (2017) Partial differential equation techniques for analysing animal movement: a comparison of different methods. J Theor Biol 416:52-67, doi:10.1016/j.jtbi.2017.01.002
  22. Merkle JA, Potts JR, Fortin D. (2017) Energy benefits and emergent space use patterns of an empirically parameterized model of memory-based patch selection. Oikos 126:185-196, doi:10.1111/oik.03356
  23. Bastille-Rousseau G, Potts JR, Yackulic C, Frair J, Ellington EH, Gibbs J, Blake S. (2016) Flexible characterization of animal movement pattern using net squared displacement and a latent state model. Move Ecol 4:15, doi:10.1186/s40462-016-0080-y
  24. Potts JR, Lewis MA. (2016) How memory of direct animal interactions can lead to territorial pattern formation. J Roy Soc Interface 13:20160059, doi:10.1098/rsif.2016.0059 (preprint)
  25. Demars CA, Breed GA, Potts JR, Boutin S. (2016) Spatial patterning of prey at reproduction to reduce predation risk: what drives dispersion from groups? Am Nat 187:678-687, doi:10.1086/685856
  26. Potts JR, Lewis MA. (2016) Territorial pattern formation in the absence of an attractive potential. J Math Biol 72:25-46, doi:10.1007/s00285-015-0881-4 (preprint)
  27. Avgar T, Potts JR, Boyce MS, Lewis MA. (2016) Integrated step selection analysis: bridging the gap between resource selection and animal movement. Methods Ecol Evol 7:619-630, doi:10.1111/2041-210X.12528
  28. Potts JR, Hillen T, Lewis MA. (2016) The `edge effect' phenomenon: deriving population abundance patterns from individual movement decisions. Theor Ecol 9:233-247, doi:10.1007/s12080-015-0283-7
  29. Bastille-Rousseau G, Potts JR, Schaefer JA, Lewis MA, Ellington H, Rayl ND, Mahoney SP, Murray DL. (2015) Unveiling tradeoffs in resource selection of migratory caribou using a mechanistic movement model of availability. Ecography 38:1049–1059, doi:10.1111/ecog.01305
  30. Potts JR, Mokross K, Stouffer PC, Lewis MA. (2014) Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds. Ecol Evol 4:4578–4588, doi:10.1002/ece3.1306
  31. Potts JR, Auger-Méthé M, Mokross K, Lewis MA. (2014) A generalized residual technique for analyzing complex movement models using earth mover's distance. Methods Ecol Evol 5:1012-1022 (preprint)
  32. Potts JR, Lewis MA. (2014) A mathematical approach to territorial pattern formation. Am Math Mon 121(9):754-770
  33. Potts JR, Mokross K, Lewis MA. (2014) A unifying framework for quantifying the nature of animal interactions. J Roy Soc Interface 11:20140333 (preprint)
  34. Potts JR, Lewis MA. (2014) How do animal territories form and change? Lessons from 20 years of mechanistic modelling. Proc Roy Soc B 281:20140231
  35. Potts JR, Bastille-Rousseau G, Murray DL, Schaefer JA, Lewis MA. (2014) Predicting local and non-local effects of resources on animal space use using a mechanistic step-selection model. Methods Ecol Evol 5:253–262.
  36. Giuggioli L, Potts JR, Rubenstein DI, Levin SA. (2013) Stigmergy, collective actions and social spacing. Proc Nat Acad Sci 110(42):16904-9
  37. Potts JR, Harris S, Giuggioli L. (2013) Quantifying behavioural changes in territorial animals caused by sudden population declines. Am Nat 182:E73-E82
  38. Potts JR, Harris S, Giuggioli L. (2012) Territorial dynamics and stable home range formation for central place foragers. PLoS One 7(3):e0034033
  39. Giuggioli L, Potts JR, Harris S. (2012) Predicting oscillatory dynamics in the movement of territorial animals. J Roy Soc Interface 9:1529-1543
  40. Potts JR, Harris S, Giuggioli L. (2011) An anti-symmetric exclusion process for two particles on an infinite 1D lattice. J Phys A: Math Theor 44:485003
  41. Giuggioli L, Potts JR, Harris S. (2011) Brownian walkers within subdiffusing territorial boundaries. Phys Rev E 83:061138
  42. Giuggioli L, Potts JR, Harris S. (2011) Animal interactions and the emergence of territoriality. PLoS Comput Biol 7(3):e1002008

Please feel free to email me about any of the above writings. Names in bold are past or present members of my Research Group.


  1. Potts JR. (2012) A complex systems approach to the emergence of animal territoriality. PhD, Bristol University.
  2. Potts JR. (2006) Algebraic structures on singular (co)chains. PhD, Warwick University.