1. Modelling animal movement in complex environments Jonathan Potts, University of Leicester, 24 th September 2014.

2. What complex environment? Resources Topography Predators Conspecifics Stigmergent cues Human constructions

3. Roadmap

4. 1.Model construction

5. Roadmap 1.Model construction 2.Inference

6. Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

7. Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

9. Movement: correlated random walk Example step length distribution: Example turning angle distribution: Turchin P. (1998) Quantitative analysis of movement:measuring and modeling population redistribution in animals and plants. Sunderland, MA: SinauerAssociates.

10. Mathematical formulation

12. Adding environmental interactions

13. A, B, C different habitats. B = worse, A = better, C = best.

14. 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.

16. Coupled step selection functions Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11, 20140333. Scent marks Mate Competitor

17. An example CSSF Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11, 20140333.

18. Unifying collective behaviour and resource selection Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11, 20140333.

19. Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

20. Coupled step selection functions Detecting the interaction mechanism Model 1 Model 2Model 3Model 4 Positional data

21. Detecting the interaction mechanism

22. Coupled step selection functions Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11, 20140333.

23. Detecting the interaction mechanism: the example of Amazonian birds

25. Amazon birds: space use patterns

26. Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

27. High-school data analysis: best fit line

28. Check: look at the residuals Zuur et al. (2009) Mixed effects models and extensions in ecology with R. Springer Verlag “Residual”: the distance between the model prediction and the data

29. Try again: best fit quadratic

30. How do we extend these ideas to movement models?

31. e.g. food distribution e.g. topography Start

32. e.g. food distribution e.g. topography Actual move

33. Earth mover`s distance: a generalised residual

36. Standardised earth mover`s distance

37. How close is your model to the data? Test the following null hypothesis: H0: “The data is a stochastic realisation of the model”

38. A scheme for testing how close your model is to data Suppose you have N data points

39. A scheme for testing how close your model is to data Suppose you have N data points Simulate your model for N steps and repeat M times, where M is nice and big

40. A scheme for testing how close your model is to data Suppose you have N data points Simulate your model for N steps and repeat M times, where M is nice and big For each simulation, generate the Earth Movers distance (EMD)

41. A scheme for testing how close your model is to data Suppose you have N data points Simulate your model for N steps and repeat M times, where M is nice and big For each simulation, generate the Earth Movers distance (EMD) This gives a distribution of simulation EMDs

42. A scheme for testing how close your model is to data Suppose you have N data points Simulate your model for N steps and repeat M times, where M is nice and big For each simulation, generate the Earth Movers distance (EMD) This gives a distribution of simulation EMDs Also calculate EMD between data and model E D

43. A scheme for testing how close your model is to data Suppose you have N data points Simulate your model for N steps and repeat M times, where M is nice and big For each simulation, generate the Earth Movers distance (EMD) This gives a distribution of simulation EMDs Also calculate EMD between data and model E D If E D is not within 95% confidence intervals of the distribution of simulation EMDs then reject null hypothesis that model describes the data well

44. Power test on simulated data F(x) T(x) Researcher knows about layer 1 Researcher doesn’t know about layer 2

45. Power test on simulated data F(x) T(x) Researcher knows about layer 1 Researcher doesn’t know about layer 2

46. Power test on simulated data Potts JR, Auger-Méthé M, Mokross K, Lewis MA. A generalized residual technique for analyzing complex movement models using earth mover's distance. Methods Ecol Evol DOI: 10.1111/2041-210X.12253A generalized residual technique for analyzing complex movement models using earth mover's distance

47. Application to Amazonian birds: patterns in EMD

48. Acknowledgements Mark Lewis (Alberta) Marie Auger-Méthé (Dalhousie) Karl Mokross (Louisiana State) Thomas Hillen (Alberta)