Thesis Project: State-Space Analysis of Animal Movement

Over the past 10 years, the Department of Fisheries and Oceans (DFO) Canada has been deploying satellite tags on grey seals breeding on Sable Island, NS.  They have accumulated a large sample of over 130 satelitte tracks sampled across sex and age classes.  As with other telemetry studies, the data provided insight into how and where the animals moved. However, the rich behavioural record embedded in the data was, for the most part, beyond the reach of statistical analyses available at the time.  During this same 10 year period, computing advances improved both satellite telemetry technology and made Markov Chain Monte Carlo (MCMC)  techniques increasingly available to fit complex models with Bayesian state-space approaches.  A number of biomathematicians began using the techniques to fit stochastic populations models in the 1990’s, and then to fit animal movement models first in one dimension and more recently in two dimensions.  So far, two dimensional state-space model fitting to animal tracks has been limited largely to demonstration studies.  The work currently underway using the DFO grey seal data will be the first practical application of state-space methods to a large set of satellite tracked animal movement data.

There are three basic goals for this work.  The first is to continue developing state-space techniques as an analytical tool for animal movement.  The second is to develop general movement models that can be implemented in a state-space framework that provide real insight into the behaviour and decision making processes of a wide range of free ranging animals in their natural habitat.  The third is to apply the developmental steps of goals 1 and 2 to the grey seal data set and answer specific questions about their behaviour and biology.  Specifically, we are currently using the models to discriminate between foraging and migrating behaviour.  I will add additional behavioural states as our ability to discriminate between them increases, and a nascent 3-state model has recently been successfully implemented.  Assuming foraging behaviour occurs in areas of foraging preference and consequently greater biological importance to grey seals, we can use state-space models to identify preferred foraging areas and differences between non-foraging areas that the seals also use.  I will also be using these techniques to assess behavioural differences between sex and age groups in order to better understand how search and foraging behaviours change as animals age and gain more experience.  The greater contribution will be successfully bridging the gap between the statisticians developing these often complex and abstruse models and the biologists deploying satellite tags, so the rich behavioral records can be more easily analyzed and interpreted by those with a greater knowledge of the animal’s biology and ecology.

Some example model fits:

The example tracks below were fit using the freely availble software WinBUGS executed through R, results were plotted using the M-Map toolbox for Matlab.  I will be posting the code, models, and graphing scripts used to produce the plots below as the work is published.  In the mean time, check out Ian Jonsen's website, where some animal movement WinBUGS code is currently available.  If you would like to see the code before the these results are formally published, please contact me.  I'm not making them available yet because they are still under development and need further refinement, documentation, and organization, but if that’s ok with you, I'll send you a copy (though there may be some conditions).

The Plots:  The square points coloured blue and red are estimated locations.  Unlike the satellite data, state-space estimated locations are equally spaced in time, in this case points are 480 minutes apart, or 3 points per day.  Colour indicates the estimated behavioural state.  Blue points are migration, with a high degree of first order autocorrelation in movement speed and direction from step to step.  Red points are estimated foraging locations, with negative first order autocorrelation from step to step.  Lighter intensity colours indicate a lower certainty in the estimated behavioural state, with white points being completely uncertain.   Green points are haulout, which are 100% certain because they are indicated by the tag.

Underneath the estimated points in light grey is the observed track.  Observations were made with the ARGOS system, which has a high degree of error, especially when tracking diving animals.  Location class 3 points, the highest confidence point delivered by ARGOS satellite system, are shown in yellow in order to truth the model fit.


Seal 6124                                              Seal 5685                                    Seal 5114                                   

                                       Seal 6122

Currently, I am developing a three state model that can identify 2 types of foraging, a mode in which the animal concentrates foraging effort in a very small area, forage on a particular resource, and another where it remains in an area limited search mode while feeding covering larger areas.  In total, the model will have 4 behavioural states: 2 foraging, 1 migratory, and 1 rest/haulout state.

Here are some .avi movies of model fits.  They are encoded with newer codecs and may not play on some computers.  I recommend downloading the free VLC movie player if Windows Media Player does not play them.  There are 2 male and 2 female tracks.  These fits are from the 2-state model.  3 of the 4 videos show the month as a number as the track is played forward.  Also note that in the animations, the colours for foraging and transiting are reversed from the example fits shown above.

Male 1
Male 2

Female 1
Female 2