Modelling migration patterns of fish using depth and temperature preferences
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Time series of depth and temperature derived from electronic tagging of fish have been used to construct a stochastic model that aims at capturing main characteristics of the observations. Mixed Ornstein-Uhlenbeck process models are used to model attraction towards different concentration points in the depth/temperature plane, and a methodology to determine model parameters is presented. Simulations of the model displays very similar dynamics to the original data. Further, an optimization problem for finding a path expressing the geographical location of the tagged fish is formulated. An interpolation procedure using thin-plate splines for interpolating an atlas over temperature in the ocean is introduced. As general-purpose optimization solvers fail to find optimal solutions to the problem, a special-purpose algorithm, based on an ensemble search, is developed. The algorithm solves the problem to optimality, both for test instances and for real data, but demonstrates that there may be many radically different paths through the ocean that match the temperature and depth time series. The algorithm has a potential of making good estimates on the geolocation of fish provided external information is used to guide the algorithm and to select the most likely solutions.