The impact of population heterogeneity on the redundancy principle

Abstract

Biological signaling is often governed by extreme value statistics, where a rapid response relies on the fastest few out of a large redundant group of searchers. While extreme first passage time (FPT) theory is well established for homogeneous ensembles, its sensitivity to population heterogeneity remains open. We show that averaging over a heterogeneous population of memoryless random walkers gives rise to ensemble self-reinforcement. This heterogeneity drastically changes both the FPT and minimum FPT densities relative to a homogeneous ensemble with identical mean rates. The modal and minimum FPTs are an order of magnitude smaller for heterogeneous populations relative to homogeneous ones. Our exact analytical predictions establish that population heterogeneity is a parameter that biology can exploit and not merely noise to be averaged away.