State-space modelling in marine science

State-space models provide a natural framework for analysing time series that cannot be observed without error. This is the case for fisheries stock assessments and movement data from marine animals. In fisheries stock assessments, the aim is to estimate the stock size; however, the only data available is the number of fish removed from the population and samples on a small fraction of the population.

In marine animal movement, accurate position systems such as GPS cannot be used. Instead, inaccurate alternative must be used yielding observations with large errors. Both assessment and individual animal movement models are important for management and conservation of marine animals. Consequently, models should be developed to be operational in a management context while adequately evaluating uncertainties in the models.

This thesis develops state-space models using the Laplace approximation within fisheries stock assessment and individual animal movement. In a fisheries stock assessment context, several observational likelihoods are implemented and evaluated using the Laplace approximation. Further, a model for multiple fish stocks is proposed.

The model connects single stocks through correlation in the survival process, without requiring any data not used in the individual assessments. Both studies show improvements in evaluating the status of a stock for management. In an individual animal movement context, the use of a normal distribution for Argos data is compared to the use of t-distributions, both implemented in a state-space model and estimated using the Laplace approximation.

Using the heavy tailed t-distribution for the uncertain Argos data improves reconstruction of the true movement trajectories. Further, the commonly used first-Difference Correlated Random Walk is generalized to allow irregular time steps and drift in the movement. Finally, an approximate filter and smoother based on sequential Laplace approximations are introduced for state-space models with Markov switching.

The method can potentially be used in both animal movement and stock assessment models to account for structural changes in behaviour or environmental effects