Modelling animal movement in complex environments Jonathan Potts, University of Leicester, 24 th September 2014.

What complex environment? Resources Topography Predators Conspecifics Stigmergent cues Human constructions

Roadmap

1.Model construction

Roadmap 1.Model construction 2.Inference

Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

Movement: correlated random walk Example step length distribution: Example turning angle distribution: Turchin P. (1998) Quantitative analysis of movement:measuring and modeling population redistribution in animals and plants. Sunderland, MA: SinauerAssociates.

Mathematical formulation

Adding environmental interactions

A, B, C different habitats. B = worse, A = better, C = best.

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:

Coupled step selection functions Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11, Scent marks Mate Competitor

An example CSSF Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11,

Unifying collective behaviour and resource selection Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11,

Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

Coupled step selection functions Detecting the interaction mechanism Model 1 Model 2Model 3Model 4 Positional data

Detecting the interaction mechanism

Coupled step selection functions Potts, J.R., Mokross,K.,&Lewis, M.A. (2014) A unifying framework for quantifying the nature of animal interactions. Journal of the Royal Society Interface, 11,

Detecting the interaction mechanism: the example of Amazonian birds

Amazon birds: space use patterns

Roadmap 1.Model construction 2.Inference 3.Goodness-of-fit

High-school data analysis: best fit line

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

Try again: best fit quadratic

How do we extend these ideas to movement models?

e.g. food distribution e.g. topography Start

e.g. food distribution e.g. topography Actual move

Earth mover`s distance: a generalised residual

Standardised earth mover`s distance

How close is your model to the data? Test the following null hypothesis: H0: “The data is a stochastic realisation of the model”

A scheme for testing how close your model is to data Suppose you have N data points

A scheme for testing how close your model is to 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 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 distance (EMD)

A scheme for testing how close your model is to 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 distance (EMD) This gives a distribution of simulation EMDs

A scheme for testing how close your model is to 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 distance (EMD) This gives a distribution of simulation EMDs Also calculate EMD between data and model E D

A scheme for testing how close your model is to 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 distance (EMD) This gives a distribution of simulation EMDs Also calculate EMD between data and model E D If E D 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 F(x) T(x) Researcher knows about layer 1 Researcher doesn’t know about layer 2

Power test on simulated data F(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: / X.12253A generalized residual technique for analyzing complex movement models using earth mover's distance

Application to Amazonian birds: patterns in EMD

Acknowledgements Mark Lewis (Alberta) Marie Auger-Méthé (Dalhousie) Karl Mokross (Louisiana State) Thomas Hillen (Alberta)