Application of continuous time Markov chains to modelling animal movement: estimation of movement rates and retention times for Patagonian toothfish

The study of animal movement and distribution has been a central focus in ecology since the inception of the science. However, continuous-time, discrete state models have received relatively little application in data analyses or prediction in studies movement. Here we develop a continuous time, discrete state stochastic model, a continuous time Markov chain (CTMC), for analyzing movement data, including an inferential framework which can accommodate heterogeneous sampling effort. We explore the accuracy of estimates arising from this model using simulated data with known movement rates. Finally, we apply the model to estimate the equilibrium distribution of Patagonian toothfish in the region around Heard and MacDonald Islands in the Australian Antarctic zone using to mark-recapture data from the Australian Patagonian toothfish fishery.