Mathematical Modelling of Animal Navigation

Abstract

Animals navigate all over the world at many different scales. Among their navigation abilities is an intriguing skill which allows them to navigate in the absence of familiar landmarks or outward journey information. This skill is hypothesised to be an ability to use a map and compass. Animals are known to use a variety of compasses, such as the sun and the magnetic field vector, however, the map mechanism is still poorly understood. This thesis focuses on grid map hypotheses and how they might be experimentally tested. The hypotheses propose that the animal uses two predictably varying environmental fields as coordinates. The animal is assumed to know the field values at their target and current location, but may either hold information on the coordinate field gradients based on the fields about the target or about the current location. The hypotheses also differ in how they incorporate field gradient magnitudes and directions. Certain combinations of assumptions give different navigation models, which we term: Correct Bicoordinate (Target or Release based), Approximate Bicoordinate, and Directional Navigation. Differences in model predictions can be exploited to test the model assumptions. In particular, this thesis presents methods for model comparison to: initial bearings such as might be obtained when an animal is released after displacement, bearings from virtual displacement experiments, and animal trajectories recorded by tracking devices. The methods are trialled using homing pigeons as a model species utilising historical data. We test the additional hypothesis that features of the geomagnetic field are used as coordinates. No evidence is found to support the hypothesis that pigeons are using the magnetic field as part of a bicoordinate map over distances of a few hundred kilometres. We suggest that using the magnetic field as a coordinate would be more efficient over greater distances where it would be robust to variation. As tracking devices improve, more data are being collected from long distance travellers. This in combination with the grid map navigation models will enable testing of the navigation hypothesis of the use of the magnetic field, or alternative environmental fields, as a map coordinate in multiple species.