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Generalizing residual analysis for complex, stochastic animal movement models

Generalizing residual analysis for complex, stochastic animal movement models. Jonathan Potts , Marie Auger- Méthé , Mark Lewis. How good is our best model?.

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Generalizing residual analysis for complex, stochastic animal movement models

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  1. Generalizing residual analysis for complex, stochastic animal movement models Jonathan Potts, Marie Auger-Méthé, Mark Lewis

  2. How good is our best model? Potts JR, Harris S & Giuggioli L. (2013) Quantifying behavioural changes in territorial animals caused by sudden population declines. Am Nat 182:E73-E82

  3. A hypothetical data set

  4. High-school data analysis: best fit line

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

  6. Try again: best fit quadratic

  7. How do we extend these ideas to movement models? Generic movement model: probability of moving to x at a time τ in the future given that the agent is currently at y and arrived there on a bearing θand is travelling through environment E is

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

  9. Earth mover`s distance: a generalised residual

  10. Earth mover`s distance: a generalised residual • is the actual place the animal moves to

  11. Standardised earth mover`s distance

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

  13. 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

  14. 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)

  15. 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

  16. 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 ED

  17. 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 ED • If ED is not within 95% confidence intervals of the distribution of simulation EMDs then reject null hypothesis that model describes the data well

  18. Power test on simulated data F(x) T(x)

  19. 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. In review for Methods EcolEvol arxiv:1402.1805

  20. Acknowledgements Mark Lewis (University of Alberta) Marie Auger-Méthé (UofA) Members of the Lewis Lab

  21. Conclusion • Want to know how good your model is in an absolute rather than relative sense?

  22. Conclusion • Got a mathematical model and want to know how good it is? • Use EMD for the best results. EMD

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