Mathematics Colloquium
Zachary Kilpatrick
University of Colorado Boulder
Title: Leaderless Decisions and Resource Exchange in Collective Foraging
Date: Friday, March 6th
Place and Time: Love 101, 3:05-3:55 pm
Abstract. Social insects routinely make effective collective decisions and distribute resources without leaders or centralized control, even in uncertain and time-varying environments. This raises a fundamental mathematical question: how can simple, local interaction rules give rise to efficient group-level behavior, and what trade-offs constrain such efficiency? In this talk, I present two complementary models of collective foraging and resource exchange in honeybees. At the decision-making level, I describe a decentralized foraging model in which individuals choose whether to explore or wait under uncertainty while sharing rewards across the group. Stochastic and decision-theoretic analysis shows that efficient collective performance emerges through a division of labor: a small, heterogeneous minority explores, while a synchronized majority commits only when conditions are favorable. At the level of within-hive dynamics, nectar exchange is modeled as a velocity-jump search process coupled to queueing at resource sites, where first-passage and asymptotic analysis reveal how search, congestion, and partial absorption determine scaling laws for resource-exchange cycle times. Together, these results show how leaderless collectives self-organize across scales, balancing efficiency and cost through simple stochastic rules.