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Generalizing residual analysis for complex, stochastic animal movement modelsPowerPoint Presentation

Generalizing residual analysis for complex, stochastic animal movement models

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### Generalizing residual analysis for complex, stochastic animal movement models

Jonathan Potts, Marie Auger-Méthé, Mark Lewis

How good is our best model? animal movement models

Potts JR, Harris S & Giuggioli L. (2013) Quantifying behavioural changes in territorial animals caused by sudden population declines. Am Nat 182:E73-E82

A hypothetical data set animal movement models

High-school data analysis: best fit line animal movement models

Check: look at the residuals animal movement models

“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

Try again: best fit quadratic animal movement models

How do we extend these ideas to movement models? animal 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

Earth mover`s distance: a generalised residual animal movement models

Earth mover`s distance: a generalised residual animal movement models

- is the actual place the animal moves to

Standardised earth mover`s distance animal movement models

A scheme for testing how close your model is to data animal movement models

- Suppose you have N data points

A scheme for testing how close your model is to data animal movement models

- Suppose you have N data points
- Simulate your model for N steps and repeat M times, where M is nice and big

A scheme for testing how close your model is to data animal movement models

- 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)

A scheme for testing how close your model is to data animal movement models

- 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

A scheme for testing how close your model is to data animal movement models

- 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

A scheme for testing how close your model is to data animal movement models

- 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

Power test on simulated data animal movement models

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

Acknowledgements animal movement models

Mark Lewis (University of Alberta)

Marie Auger-Méthé (UofA)

Members of the Lewis Lab

Conclusion animal movement models

- Want to know how good your model is in an absolute rather than relative sense?

Conclusion animal movement models

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

EMD

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