Precision and reliability in animal navigation

Uncertainty plays an important role in several navigational computations. Navigation typically depends on multiple sources of information, and different navigational systems may operate both in parallel and in combination. The optimal combination of information from different sources must take into account the uncertainty of that information. We distinguish between two types of spatial uncertainty, precision, and reliability. Precision is the inverse variance of the probability distribution that describes the information a cue contributes to an organism's knowledge of its location. Reliability is the probability of the cue being correctly identified, or the probability of a cue being related to a target location. We argue that in most environments, precision and reliability are negatively correlated. In case of cue conflict, precision and reliability must be traded off against each other. We offer a quantitative description of optimal behaviour. Knowledge of uncertainty is also needed to optimally determine the point where a search should start when an organism has more precise spatial information in one of the spatial dimensions. We show that if there is any cost to travel, it is advantageous to head off to one side of the most likely target location and head toward the target. The magnitude of the optimal offset depends on both travel cost and search cost.