Precision and Reliability in Animal Navigation

Abstract

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.

Multiple cue use and integration in pigeons (Columba livia)

“…Conversely, when the amount of 373 cue conflict was large (far-shift tests), pigeons treated the conflicting cues as independent 374 sources of information. This pattern of results is consistent with the Bayesian optimal use of 375 sensory information, when that information can come from single or multiple sources (e.g., model explicitly predicts that animals will change their strategy for coping with cue conflict as 380 the amount of conflict increases (Pfuhl et al 2011). Specifically, the model predicts that when 381 the amount of cue conflict is small, animals will attempt to integrate the information from all 382 cues to identify a single goal location, as observed in the near-shift tests.…”

“…For example, it is an open question whether animals might use 423 hierarchical strategies for goal localization when they have a very short window of time to 424 search, or when trying to escape a predator. In these situations, the computational simplicity of 425 hierarchical strategies may allow animals to make a decision more quickly than more 426 computationally complex strategies (e.g., an integrative strategy) and thus provide a survival 427 advantage when a delay may be deadly (Pfuhl et al 2011). Thus, though hierarchical strategies 428 did not control pigeons' search behaviour in this study, they may be used by pigeons or other 429 animals in circumstances where a quick response provides a large survival advantage.…”

Do adjustments in search behavior depend on the precision of spatial memory?

“…Therefore, the total travel distance (search and backtracking) until finding the target should be less when using the error compensation strategy (Pfuhl et al, 2011). The reduced cost of backtracking means that the error compensation strategy should search a greater proportion of the original probability distribution before reaching the point where it is best to abandon search.…”

“…Many decision processes benefit from taking into account the variance inherent in a representation (Pfuhl, Tjelmeland, & Biegler, 2011;Pfuhl, Tjelmeland, Molden, & Biegler, 2009). However, theoretical benefits do not guarantee widespread use of estimates of precision.…”

“…This error compensation strategy is more efficient than the alternative, the target-centered strategy of starting search at the most likely target location (Pfuhl et al, 2011). Assume that a normal distribution describes your knowledge of the target location.…”