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How close is a complex movement model to reality?
Jonathan Potts, Marie Auger-Méthé, Karl Morkoss, Mark Lewis
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Some history
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Some history
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One outcome:
• Often conclusions are made based on relative fit between models
• How about absolute fit?
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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
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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
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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
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e.g. food distribution
e.g. topography
Actual move
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Earth mover`s distance: a generalised residual
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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
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Standardised earth mover`s distance
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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”
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Power test on simulated data
C(x) T(x)
Researcher knows about
layer 1
Researcher doesn’t know about layer 2
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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
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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
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Where is my model failing? Patterns in EMD
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Acknowledgements
Mark Lewis (Alberta)
Marie Auger-Méthé (Dalhousie)
Karl Mokross (Louisiana State)
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Conclusion
• Want to know how good your model is in an absolute rather than relative sense?
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Conclusion
• Want to know how good your model is in an absolute rather than relative sense?
• Use EMD for the best results.
EMD