How close is a complex movement model to reality?

Jonathan Potts, Marie Auger-Méthé, Karl Morkoss, Mark Lewis

Some history

Some history

One outcome:

• Often conclusions are made based on relative fit between models

• How about absolute fit?

One outcome:

• Often conclusions are made based on relative fit between models

• How about absolute fit?• Suggestion: look at the residuals in step-length

and turning angle distributions

How do we extend the idea of a residual to more complex movement models?

Generic movement kernel: 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 θ and is travelling through environment E is

How do we extend the idea of a residual to more complex movement models?

Generic movement kernel: 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 θ and is travelling through environment E is

Study species

e.g. food distribution

e.g. topography

Actual move

Earth mover`s distance: a generalised residual

Earth mover`s distance: a generalised residual

• is the actual place the animal moves to

∫Ω

❑

𝑓 (𝑥|𝑦 ,𝜃 ,𝐸 )∨𝑥−𝑥0∨𝑑𝑥

𝑓 (𝑥)

𝑥

Standardised earth mover`s distance

How close is your model to the data?

Test the following null hypothesis:

H0: “The data is indistinguishable from a stochastic realisation of the model”

Power test on simulated data

C(x) T(x)

Researcher knows about

layer 1

Researcher doesn’t know about layer 2

Power test on simulated data

“Real” process: Best model:

C(x) T(x)

Researcher knows about

layer 1

Researcher doesn’t know about layer 2

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.12253

Where is my model failing? Patterns in EMD

Acknowledgements

Mark Lewis (Alberta)

Marie Auger-Méthé (Dalhousie)

Karl Mokross (Louisiana State)

Conclusion

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

Conclusion

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

• Use EMD for the best results.

EMD