Inference procedures to estimate potential based movement models in ecology

This paper proposes a statistical analysis of movement data in ecology using partially observed stochastic differential equations. Usually, in movement ecology, parameters of these models are estimated using approximate maximum likelihood procedures based on the Euler-Maruyama discretization.However, GPS sampling rate in ecology might not be large enough to ensure the stability and convergence of the Euler based estimates. To our best knowledge, there is no practical study to assess the performance of the Euler Maruyama method to estimate movement ecology models compared to other inference procedures for stochastic differential equations. In this paper, we propose such a practical study by comparing the Euler method with the Ozaki linearization method, an adaptive high order Gaussian approximation method and a Monte Carlo Expectation Maximization approach based on the Exact Algorithm. The performance of these methods are assessed using a new potential based stochastic differential equation where the drift is given as the gradient of a mixture of attractive zones, which are of main interest in ecology and fisheries science. It is shown both on simulated data and actual fishing vessels data that the Euler method performs worse than the other procedures for non high frequency sampling schemes. We also show, on this model, that the other discretization based methods are quite robust and perform in a similar way as the exact method.