acta ethologica

, Volume 16, Issue 1, pp 21–30 | Cite as

Unraveling complexity in interspecies interaction through nonlinear dynamical models

  • Graciano Dieck Kattas
  • F. Javier Pérez-BarberíaEmail author
  • Michael Small
  • Xiao-Ke Xu
  • David M. Walker
Original Paper


Unraveling complex interactions between animal species is of paramount importance to understand competition, facilitation, and community assembly processes. Using data from GPS positions of sheep (Ovis aries) and red deer (Cervus elaphus) grazing a moorland plot, we modeled the animal movement of each species as a function of the distance between individuals, with the aim to assess the role of animal interactions (i.e., attraction and repulsion) in their spatial movement. We used black box-based models. These models do not require making assumptions about the biological meaning of their parameters. They are data-driven and use embedding complex algorithms that create nonlinear functions that estimate the behavior of the system, in our case the movement of our animals, and its errors. We used an algorithm based on radial basis functions to build models of time series data, using minimum description length as the criteria for model optimization. Included in the model is a factor that captures the collective behavior of the animals based on the distance between individuals. The model emphasizes the spatial relationship between animals from the absolute navigational directions by attenuating the latter. Our simulations showed that animals of the same specie tend to group together, with sheep having a stronger grouping behavior than deer. The dynamics of the model are density dependent, that is, the number of animals within range affects the strength of the interactions and their grouping behavior. A strong swarm behavior was detected by the model, the longer the distance between species, the stronger the attraction between them; and the shorter the separation between species, the stronger their repulsion, which suggests inter- and intra-competition for food and space resources. Our modeling approach is useful to interpret animal movement interactions between animals of the same or different species, in order to unravel complex cooperative or competitive behaviors, or to make predictions of animal movement under different population scenarios.


Animal behavior Computational modeling Social dynamics Ovis aries Cervus elaphus 



In memory of our colleague and friend Chano (Graciano Dieck Kattas) who might be watching this work from greener pastures. The field work was funded by the Scottish Government's Rural and Environment Science and Analytical Services Division (RESAS), and the Leonardo da Vinci programme (European Commission) provided grant-holders that assisted this study. We thank Russell Hooper for his support with the GPS collars and the personnel from Glensaugh Experimental Field Station for looking after the animals. GDK was supported by the Hong Kong PHD Fellowship Scheme (HKPFS) from the Research Grants Council (RGC) of Hong Kong. XKX is currently supported by the PolyU Postdoctoral Fellowships Scheme (G-YX4A) and the Research Grants Council of Hong Kong (BQ19H). XKX also acknowledges the Natural Science Foundation of China (61004104, 61104143). DMW acknowledges the Australian Research Council Discovery Projects 2012 (DP120104759) and the Melbourne Energy Institute for support.

Supplementary material


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  1. Ballerini M, Calbibbo N, Candeleir R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M, Zdravkovic V (2008) Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of The National Academy of Sciences of The United States of America 105:1232–1237PubMedCrossRefGoogle Scholar
  2. Bell RHV (1970) The use of the herb layer by grazing ungulates in the Serengeti. In: Watson A (ed) Animal populations in relation to their food resources. Blackwell, Oxford, pp 111–123Google Scholar
  3. Bon R, Campan R (1996) Unexplained sexual segregation in polygamous ungulates—A defense of an ontogenic approach. Behavioural Processes 38:131–154CrossRefGoogle Scholar
  4. Clutton-Brock TH, Albon SD (1989) Red deer in the Highlands. Blackwell, OxfordGoogle Scholar
  5. Couzin ID, Krause J, James R, Ruxton GD, Franks NR (2002) Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology 218:1–11PubMedCrossRefGoogle Scholar
  6. Deer Commission for Scotland. Annual report 2001–2002. 2002. Edinburgh, Her Majesty’s Stationery OfficeGoogle Scholar
  7. Dieck Kattas G, Xu X-K, Small M. (2011) Dynamical modeling of collective behavior from pigeon flight data: Flock cohesion and dispersion. arXiv:1110.1739v1.Google Scholar
  8. Eriksson A, Jacobi MN, Nystrom J, Tunstrom K (2010) Determining interaction rules in animal swarms. Behavioral Ecology 21:1106–1111CrossRefGoogle Scholar
  9. Farnsworth KD, Focardi S, Beecham JA (2002) Grassland–herbivore interactions: How do grazers coexist? American Naturalist 159:24–39PubMedCrossRefGoogle Scholar
  10. Grant SA, Lamb WIC, Kerr CD, Bolton GR (1976) Utilization of blanket bog vegetation by grazing sheep. Journal of Applied Ecology 13:857–869CrossRefGoogle Scholar
  11. Herbert-Read JE, Perna A, Mann RP, Schaerf TM, Sumpter DJ, Ward AJ (2011) Inferring the rules of interaction of shoaling fish. Proceedings of The National Academy of Sciences of The United States of America 108:18726–18731PubMedCrossRefGoogle Scholar
  12. Judd K, Mees A (1995) On selecting models for nonlinear time-series. Physica D 82:426–444CrossRefGoogle Scholar
  13. Lukeman R, Li YX, Edelstein-Keshet L (2010) Inferring individual rules from collective behavior. Proceedings of The National Academy of Sciences of The United States of America 107:12576–12580PubMedCrossRefGoogle Scholar
  14. McLeod, D (2002) Geographical variation in the density of grazing mammals on montane sites in the Highlands of Scotland. Scottish Natural Heritage Commissioned Report F99AC402AGoogle Scholar
  15. Michelena P, Jeanson R, Deneubourg JL, Sibbald AM (2010) Personality and collective decision-making in foraging herbivores. Proceedings of the Royal Society B-Biological Sciences 277:1093–1099CrossRefGoogle Scholar
  16. Nagy M, Akos Z, Biro D, Vicsek T (2010) Hierarchical group dynamics in pigeon flocks. Nature 464:890–U99PubMedCrossRefGoogle Scholar
  17. Okubo A, Levin SA (2001) Diffusion and ecological problems: Modern perspectives. Springer, New YorkGoogle Scholar
  18. Pérez-Barbería FJ, Robertson E, Gordon IJ (2005) Are social factors sufficient to explain sexual segregation in ungulates? Animal Behaviour 69:827–834CrossRefGoogle Scholar
  19. Perez-Barberia FJ, Yearsley JM (2010) Sexual selection for fighting skills as a driver of sexual segregation in polygynous ungulates: An evolutionary model. Animal Behaviour 80:745–755CrossRefGoogle Scholar
  20. Price EO (1999) Behavioral development in animals undergoing domestication. Applied Animal Behaviour Science 65:245–271CrossRefGoogle Scholar
  21. Reynolds CW (1987) Flocks, herds and schools: A distributed behavioral model. SIGGRAPH Comput. Graph 21:25–34CrossRefGoogle Scholar
  22. Ricklefs RE (2010) Evolutionary diversification, coevolution between populations and their antagonists, and the filling of niche space. Proceedings of The National Academy of Sciences of The United States of America 107:1265–1272PubMedCrossRefGoogle Scholar
  23. Robbins CT (1993) Wildlife feeding and nutrition. Academic, San DiegoGoogle Scholar
  24. Ruckstuhl KE, Neuhaus P (2005) Sexual segregation in vertebrates: Ecology of the two sexes. Cambridge University Press, CambridgeGoogle Scholar
  25. Small M, Judd K (1998) Comparisons of new nonlinear modeling techniques with applications to infant respiration. Physica D 117:283–298CrossRefGoogle Scholar
  26. Small M, Tse CK (2002) Minimum description length neural networks for time series prediction. Physical Review 66(6 Pt 2):066701PubMedGoogle Scholar
  27. Inc TMW (2006) Matlab: the language of technical computing. The MathWorks Inc., NatickGoogle Scholar
  28. Vicsek T, Czirok A, Benjacob E, Cohen I, Shochet O (1995) Novel type of phase-transition in a system of self-driven particles. Physical Review Letters 75:1226–1229PubMedCrossRefGoogle Scholar
  29. Ward AJ, Herbert-Read JE, Sumpter DJ, Krause J (2011) Fast and accurate decisions through collective vigilance in fish shoals. Proceedings of The National Academy of Sciences of The United States of America 108:2312–2315PubMedCrossRefGoogle Scholar
  30. Whittaker RJ, Fernández-Palacios JM (2010) Island biogeography. Oxford University Press, OxfordGoogle Scholar

Copyright information

© Springer-Verlag and ISPA 2012

Authors and Affiliations

  • Graciano Dieck Kattas
    • 1
  • F. Javier Pérez-Barbería
    • 2
    Email author
  • Michael Small
    • 3
    • 1
  • Xiao-Ke Xu
    • 4
  • David M. Walker
    • 5
  1. 1.Department of Electronic and Information EngineeringThe Hong Kong Polytechnic UniversityHung HomHong Kong, China
  2. 2.The James Hutton InstituteAberdeenUK
  3. 3.School of Mathematics and StatisticsUniversity of Western AustraliaCrawleyAustralia
  4. 4.College of Information and Communication EngineeringDalian Nationalities UniversityDalianChina
  5. 5.Department of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia

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