When a colony of honeybees outgrows a hive, it will swarm for the purpose of selecting a new home. The swarm engages in a fascinating process (taking place in the late spring and early summer), during which the swarm’s scout bees examine the surrounding environment for new homes and report back on quality and location. This "house-hunting" process continues until a sufficient number of scouts agree on a site. Swarms will very often choose the best site when many are available . In this talk I will describe a discrete-time model for this process. In the most basic version, a single bee finds one of a number of potential sites, and either recruits another bee to it or switches to another site. Recruitment or switching occurs according to fixed site-dependent probabilities, meant to encode the relative quality of the sites. The number of bees grows until a quorum threshold is reached, and the process terminates in a decision for the site with the most bees. Urn schemes with appropriate replacement rules provide a natural and well-studied framework for investigation of certain simplified versions of this model. Natural questions
for such a model include whether or not the process locates the best site, the rate at which decisions are reached, and to what extent the speed of the decision impacts the quality of the site ultimately selected. Preliminary results on these questions will be presented. This is based on work from my Ph.D. thesis and continuing work-in-progress with my thesis adviser, Edward Waymire.