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

From decision to data

Movement

From decision to data Direct interactions

From decision to data Mediated interactions

From decision to data Environmental interactions

From decision to data

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

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:

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

Hypotheses

Maximum likelihood technique

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

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

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

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):e

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, Giuggioli L, Potts JR, Harris S (2011) Animal interactions and the emergence of territoriality. Plos Comput Biol, 7(3):e 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,

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

Detecting the territorial mechanism: the example of Amazonian birds

Amazon birds: space use patterns

Interaction vs. no interaction

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

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

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

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

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

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

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

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

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

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

Amazon birds: space use patterns

How close is a movement model to reality?

How close is a movement model to data?

Try to mimic regression approaches

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

More complicated than regression

Earth mover`s distance: a generalised residual

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

Earth mover`s distance and direction

Wagon wheels

Wagon wheels of Earth Mover`s distance: include direction

Dharma wheel

Dharma wheels of Earth Mover`s Distance

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

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

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

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

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)

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

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

Normalised earth mover`s distance

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

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

Thanks for listening!