Hyunjoong Kim
University of Cincinnati
Title
The Redundancy Principle Revisited: What If Searchers Are Not Independent?
Abstract
Many biological events are triggered by the first of many searchers to reach a target: the first ion to reach a receptor cluster, or the first fish in a shoal whose evidence of a predator crosses a threshold. According to the redundancy principle, such events are fast and reliable because the extremes of many independent searchers are sharp. But searchers in a common environment are rarely independent. Part of their noise is shared, and shared noise cannot be averaged away by adding more searchers. Using extreme first-passage theory, I will ask how much independence redundancy really needs. For many diffusing searchers with correlated noise, redundancy succeeds or fails depending on whether the independent part of the noise vanishes more slowly or faster than 1/ ln N. On the boundary between the two, search can be fast on average yet have infinite variance. I will then apply these ideas to collective alarms in fish shoals,where each fish flees when its evidence of a predator crosses a threshold and departures spread to others. Because the fish share part of their sensory noise, false alarms become all-or-none and independent of shoal size. They also occur far more often than they would if the fish were independent, so a shoal needs a much higher escape threshold than independent-searcher theory suggests. Together, these results suggest that what makes a group fast and reliable is not its size alone, but how independent its members are. The first part of this talk is joint work withSeanD. Lawley(University of Utah), together with students Josh Satter (University of Cincinnati) and Alexander Krol (Duke University).
