Uncovering animal movement decisions from positional data Jonathan Potts, Postdoctoral Fellow,...
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Transcript of Uncovering animal movement decisions from positional data Jonathan Potts, Postdoctoral Fellow,...
Uncovering animal movement decisions from positional data
Jonathan Potts, Postdoctoral Fellow, University of Alberta, September 2013
From decision to data
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 walkExample step length distribution:
Example turning angle distribution:
The step selection function
• is the step length distribution,• is the turning angle distribution• is a weighting function• E is information about the environment
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.
Example : Amazonian bird flocks 𝑓 (𝒙|𝒚 ,𝜃0 )∝ 𝜌 (|𝒙−𝒚|)𝑉 (𝒙 , 𝒚 , 𝜃0 )𝑊 (𝒙 , 𝒚 ,𝐸)
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
1. Birds are more likely to move to higher canopies:
𝑓 (𝒙|𝒚 ,𝜃0 )∝ 𝜌 (|𝒙−𝒚|)𝑉 (𝒙 , 𝒚 , 𝜃0 )𝑊 (𝒙 , 𝒚 ,𝐸)
Hypotheses
1. Birds are more likely to move to higher canopies:
2. In addition, birds are more likely to move to lower ground:
(
𝑓 (𝒙|𝒚 ,𝜃0 )∝ 𝜌 (|𝒙−𝒚|)𝑉 (𝒙 , 𝒚 , 𝜃0 )𝑊 (𝒙 , 𝒚 ,𝐸)
Maximum likelihood technique
1. Find the that maximises:
where and are, respectively, the sequence of positions and trajectories from the data, and
Maximum likelihood technique
2. Find the that maximises:
where is the value of that maximises the likelihood function on the previous page, and
Resulting model
Step length distribution
Turning angle distribution
Canopy height at end of step
Topographical height at end of step
Coupled step selection functionsOne step selection function for each agent and include an interaction term :
where represents both the population positions and any traces of their past positions left either in the environment or in the memory of agent .
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):e1002008
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, 719-725Giuggioli L, Potts JR, Harris S (2011) Animal interactions and the emergence of territoriality. Plos Comput Biol, 7(3):e1002008Vicsek 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
Coupled step selection functions
Resource/step-selection models: Detecting the mechanisms
Model 1 Model 2 Model 3 Model 4
Positional data
Detecting the territorial mechanism: the example of Amazonian birds
Territorial marking (vocalisations): if any flock is at position at time totherwise.
Hypothesis 1 (tendency not to go into another’s territory):
Hypothesis 2 (tendency to retreat after visiting another’s territory):
where is a von Mises distribution, is the bearing from to and is the bearing from to a central point within the territory and if X is true and 0 otherwise.
Detecting the territorial mechanism: the example of Amazonian birds
Territorial marking (vocalisations): if any flock is at position at time totherwise.
Hypothesis 1 (tendency not to go into another’s territory):
Hypothesis 2 (tendency to retreat after visiting another’s territory):
where is a von Mises distribution, is the bearing from to and is the bearing from to a central point within the territory and if X is true and 0 otherwise.
Amazon birds: space use patterns
Interaction vs. no interaction
between competing models
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
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
• predicted positions given by the contours• is the actual place the animal moves to
More complicated than regression
• predicted positions given by the contours• is the actual place the animal moves to
Earth mover`s distance: a generalised residual
Earth mover`s distance: a generalised residual
• is the actual place the animal moves to
Earth mover`s distance: a generalised residual
• is the actual place the animal moves to
∫Ω
❑
𝑓 (𝑥|𝑦 ,𝜃 ,𝐸 )∨𝑥−𝑥0∨𝑑𝑥
How to use the Earth Mover`s distance
Simulated movement in artificial landscape with two layers:
Earth mover`s distance and direction
Earth mover’s distance:
is the actual place the animal moves to
Direction where:
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 = 0x-axis: value of layer 1y-axis: earth mover`s distance (EMD)Left: EMD from model with a = b = 0Right: 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 statisticalmechanics for ecological systems” Simon Levin, 2011
Spatial patterns
Thanks for listening!