Positional entropy during pigeon homing I: application of Bayesian latent state modelling

In these two companion papers, we introduce a new approach to the analysis of bird navigation which brings together several novel mathematical and technical applications. Miniaturized GPS logging devices provide track data of sufficiently high spatial and temporal resolution that considerable variation in flight behaviour can be observed remotely from the form of the track alone. We analyse a fundamental measure of bird flight track complexity, spatio-temporal entropy, and explore its state-like structure using a probabilistic hidden Markov model. The emergence of a robust three-state structure proves that the technique has analytical power, since this structure was not obvious in the tracks alone. We propose the hypothesis that positional entropy is indicative of underlying navigational uncertainty, and that familiar area navigation may break down into three states of navigational confidence. By interpreting the relationship between these putative states and features on the map, we are able to propose a number of hypothetical navigational strategies feeding into these states. The first of these two papers details the novel technical developments associated with this work and the second paper contains a navigational interpretation of the results particularly with respect to visual features of the landscape.