1. Deriving space use patterns from animal interaction mechanisms Jonathan Potts, Postdoctoral Fellow, University of Alberta, May 2013

2. From mechanism to pattern Movement

3. From mechanism to pattern Direct interactions

4. From mechanism to pattern Mediated interactions

5. From mechanism to pattern Environmental interactions

6. From mechanism to pattern

7. Outline

8. Modelling animal movement: the “correlated random walk” framework

9. Outline Modelling animal movement: the “correlated random walk” framework Adding in environmental interactions: step selection functions

10. Outline Modelling animal movement: the “correlated random walk” framework Adding in environmental interactions: step selection functions Including animal-animal interactions: coupled step selection functions

11. Outline Modelling animal movement: the “correlated random walk” framework Adding in environmental interactions: step selection functions Including animal-animal interactions: coupled step selection functions Throughout: how do these models help us understand space use phenomena?

12. Movement: correlated random walk

13. Example step length distribution:

14. Movement: correlated random walk Example step length distribution: Example turning angle distribution:

15. Mathematical formulation

16. Adding environmental interactions A, B, C different habitats. B = worse, A = better, C = best.

17. The step selection function Fortin D, Beyer HL, Boyce MS, Smith DW, Duchesne T, Mao JS (2005) Wolves influence elk movements: Behavior shapes a trophic cascade in Yellowstone National Park. Ecology 86:1320-1330.

18. Example 1: Amazonian bird flocks Potts JR, Mokross K, Stouffer PC, Lewis MA (in review) Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds. Ecology

19. Example 1: Amazonian bird flocks Potts JR, Mokross K, Stouffer PC, Lewis MA (in review) Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds. Ecology

20. Example 1: Amazonian bird flocks Potts JR, Mokross K, Stouffer PC, Lewis MA (in review) Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds. Ecology

21. Hypotheses

23. Maximum likelihood technique

25. Deriving space use patterns: stochastic simulations Potts JR, Mokross K, Stouffer PC, Lewis MA (in review) Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds. Ecology

26. Deriving space use patterns: master equations and PDEs Potts JR, Bastille-Rousseau G, Murray DL, Schaefer JA, Lewis MA (in prep) Predicting local and non-local effects of resources on animal space use using a mechanistic step-selection model

27. Deriving space use patterns: master equations and PDEs Moorcroft and Barnett (2008) Mechanistic home range models and resource selection analysis: a reconciliation and unification. Ecology 89(4), 1112–1119 Potts JR, Bastille-Rousseau G, Murray DL, Schaefer JA, Lewis MA (in prep) Predicting local and non-local effects of resources on animal space use using a mechanistic step-selection model

28. Movement data Mathematical analysis Simulations Step selection functions Statistical tests, e.g. MLE Master equations, PDEs

29. Coupled step selection functions Potts JR, Mokross K, Stouffer PC, Lewis MA (in prep) A unifying framework for quantifying the nature of animal interactions

30. Amazon birds: testing hypotheses

33. Amazon birds: space use patterns

34. Acknowledgements Mark Lewis (UofA) Karl Mokross (Louisiana State) Guillaume Bastille-Rousseau (Trent) Philip Stouffer (Louisiana State) Dennis Murray (Trent) James Schaefer (Trent) Members of the Lewis Lab (UofA)

35. Movement and interaction data Mathematical analysis Simulations Coupled step selection functions Statistical tests The final frontier! Conclusion “The challenge is to develop a statistical mechanics for ecological systems” Simon Levin Spatial patterns

36. Thanks for listening!