1. Uncovering animal movement decisions from positional data Jonathan Potts, Postdoctoral Fellow, University of Alberta, September 2013

2. From decision to data

3. Movement

4. From decision to data Direct interactions

5. From decision to data Mediated interactions

6. From decision to data Environmental interactions

7. From decision to data

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

11. 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.

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

13. Hypotheses

15. Maximum likelihood technique

17. Resulting model Step length distribution Turning angle distribution Canopy height at end of step Topographical height at end of step

19. Coupled step selection functions Potts JR, Mokross K, Lewis MA (in revision) A unifying framework for quantifying the nature of animal interactions Ecol Lett

20. Unifying collective behaviour and resource selection Potts JR, Mokross K, Lewis MA (in revision) A unifying framework for quantifying the nature of animal interactions, Ecol Lett

21. Collective/territorial models: from process to pattern Giuggioli L, Potts JR, Harris S (2011) Animal interactions and the emergence of territoriality, Plos Comput Biol, 7(3):e1002008

22. Collective/territorial models: from process to pattern Deneubourg JL, Goss S, Franks N, Pasteels JM (1989) The blind leading the blind: Modeling chemically mediated army ant raid patterns. J Insect Behav, 2, 719-725 Giuggioli L, Potts JR, Harris S (2011) Animal interactions and the emergence of territoriality. Plos Comput Biol, 7(3):e1002008 Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O (1995) Novel Type of Phase Transition in a System of Self-Driven Particles. Phys Rev Lett, 75, 1226-1229

23. Coupled step selection functions Resource/step-selection models: Detecting the mechanisms Model 1 Model 2Model 3Model 4 Positional data

24. Detecting the territorial mechanism: the example of Amazonian birds

26. Amazon birds: space use patterns

27. Interaction vs. no interaction

28. Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B

29. Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B

30. Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B Conclude process A is causing B

31. Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B Conclude process A is causing B Logical fallacy: A=>B does not mean B=>A

32. Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B Conclude process A is causing B Logical fallacy: A=>B does not mean B=>A Guilty! Potts JR, Harris S, Giuggioli L (2013) American Naturalist

33. New approach Use maths/simulations to show: Process A => Pattern B

34. New approach Use maths/simulations to show: Process A => Pattern B Observe process A

35. New approach Use maths/simulations to show: Process A => Pattern B Observe process A See if pattern B follows

36. New approach Use maths/simulations to show: Process A => Pattern B Observe process A See if pattern B follows If not, process A is insufficient for describing data: i.e. need better model

37. New approach Use maths/simulations to show: Process A => Pattern B Observe process A See if pattern B follows If not, process A is insufficient for describing data: i.e. need better model Contrapositive: A=>B means not-B=>not-A Correct logic

38. Amazon birds: space use patterns

39. How close is a movement model to reality?

40. How close is a movement model to data?

41. Try to mimic regression approaches

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

44. More complicated than regression

46. Earth mover`s distance: a generalised residual

49. How to use the Earth Mover`s distance Simulated movement in artificial landscape with two layers:

50. Earth mover`s distance and direction

51. Wagon wheels

52. Wagon wheels of Earth Mover`s distance: include direction

53. Dharma wheel

54. Dharma wheels of Earth Mover`s Distance

55. Using simulated data with a = 1.5, b = 0 x-axis: value of layer 1 y-axis: earth mover`s distance (EMD) Left: EMD from model with a = b = 0 Right: EMD from model with a = 1.5, b = 0

56. A scheme for testing how close your model is to “reality” (i.e. data) Suppose you have N data points

57. A scheme for testing how close your model is to “reality” (i.e. data) Suppose you have N data points Simulate your model for N steps and repeat M times, where M is nice and big

58. A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels

59. A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels Each spoke of the dharma wheel then has a mean and standard deviation (SD)

60. A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels Each spoke of the dharma wheel then has a mean and standard deviation (SD) Generate a dharma wheel for the data

61. A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels Each spoke of the dharma wheel then has a mean and standard deviation (SD) Generate a dharma wheel for the data If any spoke of the data dharma wheel is not of length mean plus/minus 1.96*SD from the simulated dharma wheel then reject null hypothesis that model describes the data well

62. Normalised earth mover`s distance

64. Acknowledgements Mark Lewis (University of Alberta) Karl Mokross (Louisiana State) Marie Auger-Méthé (UofA) Phillip Stouffer (Louisiana State) Members of the Lewis Lab

65. Movement and interaction data Mathematical analysis Simulations/IBMs Coupled step selection functions Conclusion “To develop a statistical mechanics for ecological systems” Simon Levin, 2011 Spatial patterns

66. Thanks for listening!