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Uncovering animal movement decisions from positional data Jonathan Potts, Postdoctoral Fellow, University of Alberta, September 2013

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From decision to data

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Movement

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From decision to data Direct interactions

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From decision to data Mediated interactions

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From decision to data Environmental interactions

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From decision to data

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

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The step selection function 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.

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Example : Amazonian bird flocks Potts JR, Mokross K, Stouffer PC, Lewis MA (in revision) Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds. Ecology

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Hypotheses

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Maximum likelihood technique

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Resulting model Step length distribution Turning angle distribution Canopy height at end of step Topographical height at end of step

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Coupled step selection functions Potts JR, Mokross K, Lewis MA (in revision) A unifying framework for quantifying the nature of animal interactions Ecol Lett

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Unifying collective behaviour and resource selection Potts JR, Mokross K, Lewis MA (in revision) A unifying framework for quantifying the nature of animal interactions, Ecol Lett

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Collective/territorial models: from process to pattern Giuggioli L, Potts JR, Harris S (2011) Animal interactions and the emergence of territoriality, Plos Comput Biol, 7(3):e1002008

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Collective/territorial models: from process to pattern Deneubourg JL, Goss S, Franks N, Pasteels JM (1989) The blind leading the blind: Modeling chemically mediated army ant raid patterns. J Insect Behav, 2, 719-725 Giuggioli L, Potts JR, Harris S (2011) Animal interactions and the emergence of territoriality. Plos Comput Biol, 7(3):e1002008 Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O (1995) Novel Type of Phase Transition in a System of Self-Driven Particles. Phys Rev Lett, 75, 1226-1229

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Coupled step selection functions Resource/step-selection models: Detecting the mechanisms Model 1 Model 2Model 3Model 4 Positional data

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Detecting the territorial mechanism: the example of Amazonian birds

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Amazon birds: space use patterns

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Interaction vs. no interaction

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Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B

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Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B

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Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B Conclude process A is causing B

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Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B Conclude process A is causing B Logical fallacy: A=>B does not mean B=>A

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Classical mechanistic modelling Use maths/simulations to show: Process A => Pattern B Observe pattern B Conclude process A is causing B Logical fallacy: A=>B does not mean B=>A Guilty! Potts JR, Harris S, Giuggioli L (2013) American Naturalist

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New approach Use maths/simulations to show: Process A => Pattern B

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New approach Use maths/simulations to show: Process A => Pattern B Observe process A

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New approach Use maths/simulations to show: Process A => Pattern B Observe process A See if pattern B follows

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New approach Use maths/simulations to show: Process A => Pattern B Observe process A See if pattern B follows If not, process A is insufficient for describing data: i.e. need better model

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New approach Use maths/simulations to show: Process A => Pattern B Observe process A See if pattern B follows If not, process A is insufficient for describing data: i.e. need better model Contrapositive: A=>B means not-B=>not-A Correct logic

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Amazon birds: space use patterns

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How close is a movement model to reality?

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How close is a movement model to data?

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Try to mimic regression approaches

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

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More complicated than regression

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Earth mover`s distance: a generalised residual

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How to use the Earth Mover`s distance Simulated movement in artificial landscape with two layers:

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Earth mover`s distance and direction

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Wagon wheels

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Wagon wheels of Earth Mover`s distance: include direction

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Dharma wheel

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Dharma wheels of Earth Mover`s Distance

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Using simulated data with a = 1.5, b = 0 x-axis: value of layer 1 y-axis: earth mover`s distance (EMD) Left: EMD from model with a = b = 0 Right: EMD from model with a = 1.5, b = 0

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A scheme for testing how close your model is to “reality” (i.e. data) Suppose you have N data points

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A scheme for testing how close your model is to “reality” (i.e. data) Suppose you have N data points Simulate your model for N steps and repeat M times, where M is nice and big

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A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels

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A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels Each spoke of the dharma wheel then has a mean and standard deviation (SD)

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A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels Each spoke of the dharma wheel then has a mean and standard deviation (SD) Generate a dharma wheel for the data

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A scheme for testing how close your model is to “reality” (i.e. 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 distances to give M dharma wheels Each spoke of the dharma wheel then has a mean and standard deviation (SD) Generate a dharma wheel for the data If any spoke of the data dharma wheel is not of length mean plus/minus 1.96*SD from the simulated dharma wheel then reject null hypothesis that model describes the data well

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Normalised earth mover`s distance

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Acknowledgements Mark Lewis (University of Alberta) Karl Mokross (Louisiana State) Marie Auger-Méthé (UofA) Phillip Stouffer (Louisiana State) Members of the Lewis Lab

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

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