A class of statistical models for the motion of Daphnia over small time scales

A common question in the aquatic sciences is that of how zooplankter movement can be modeled. It is well-established in the literature that there exists a randomness to this movement, but the question is how to characterize this randomness. The most common methods for doing this involve the random walk and correlated random walk (CRW) models. Here, we present a time series model that allows a better description the randomness in Daphnia motion when the amount of time that elapses between observations of their position is small. Our approach is adaptable to description of tracks of a multitude of animal species through re-estimation of model parameters. The model we propose uses information about how the animal moved during the previous two time intervals to explain how it moves currently. We demonstrate that the proposed model provides better predictive accuracy and fit than do the CRW and random walk models.