A new perspective to fish trajectory imputation: a spatiotemporal probability model for simulating acoustically tagged fish movement

This paper develops a probability model for understanding, interpolating, and predicting fish movement patterns based on spatiotemporal data recorded by spatially static acoustic receivers. Unlike tracking technology with continuous or regular spatial coverage while emitting signals from the animal's location at regular time intervals, acoustic receivers are irregularly spaced stationary sensors that record signals only when the animal is nearby a sensor and sets it off. Thus, for periods of time, the fish can evade detection but still be within the spatial domain of interest, resulting in the absence of location data. This poses challenges to the understanding of fish movement patterns, and hence, the identification of existing statistical inference frameworks for modeling trajectories that must not cross land barriers or the detection range of any receiver that did not record fish signals. As the foundation for an inferential methodology, in this paper, we derive and implement a model-based simulation strategy that relies on both Markov chain and random-walk principles to enhance our dataset over time. This methodology will be generalizable and applicable to all fish species with similar migration patterns or data with similar structures due to the use of static acoustic receivers.