Deriving space use patterns from animal interaction mechanisms

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

2. From mechanism to pattern

3. From mechanism to pattern Movement

4. From mechanism to pattern Directinteractions

5. From mechanism to pattern Mediated interactions

6. From mechanism to pattern Environmental interactions

7. From mechanism to pattern

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

10. Mathematical formulation Probability of moving to position x given that the animal was previously at position y and arrived there on a trajectory is: where is the step length distribution and the turning angle distribution.

12. Adding environmental interactions

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

14. The step selection function • is the step length distribution, • is the turning angle distribution • is a weighting function • E is information about the environment 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 One step selection function for each agent and include an interaction term : where represents both the population positions and any traces of their past positions left either in the environment or in the memoryof agent . Potts JR, Mokross K, Lewis MA (submitted) A unifying framework for quantifying the nature of animal interactions

17. Unifying collective behaviour and resource selection Potts JR, Mokross K, Lewis MA (submitted) A unifying framework for quantifying the nature of animal interactions

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

19. Detecting the interaction mechanism Maximum likelihood: Find the that maximises: • and are, respectively, the sequence of positions and trajectories from the data • is the number of animals • is a vector of parameters in the model • Test for different models ,,,… to find best

20. Detecting the interaction mechanism: the example of Amazonian birds Territorial marking (vocalisations): if any flock is at position at time t otherwise. Hypothesis 1 (tendency not to go into another’s territory): Hypothesis 2 (tendency to retreat after visiting another’s territory): where is a von Mises distribution, is the bearing from to and is the bearing from to a central point within the territory and if X is true and 0 otherwise.

21. Amazon birds: space use patterns between competing models

22. Acknowledgements Mark Lewis (University of Alberta) Karl Mokross (Louisiana State) Members of the Lewis Lab (UofA)

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

24. Conclusion Movement and interaction data Coupled step selection functions Mathematical analysis Simulations The final frontier! Spatial patterns

25. Thanks for listening!