Subekshya Bidari, Department of Applied Mathematics, University of Colorado Boulder
Mathematical Biology Seminar for 16 November 2020
Honey bees make decisions regarding foraging and nest-site selection in groups ranging from hundreds to thousands of individuals. To effectively make these decisions bees need to communicate within a spatially distributed group. However, the spatial aspects of honey bee communication have been mostly overlooked in models of collective decisions, focusing primarily on mean field models of opinion dynamics. We analyze how the spatial properties of the nest or hive, and the movement of individuals with different belief states(uncommitted or committed) therein affect the rate of information transmission using spatially extended models of collective decision-making. Honeybees waggle-dance to recruit conspecifics with an intensity that is a threshold nonlinear function of the waggler concentration. Our models range from treating the hive as a chain of discrete patches to a continuous line (long narrow hive). The combination of population-thresholded recruitment and compartmentalized populations generates tradeoffs between rapid information propagation with strong population dispersal and recruitment failures resulting from excessive population diffusion and also creates an effective colony-level signal-detection mechanism whereby recruitment to low quality objectives is blocked. We exploit a separation of timescales in the limit of slow/fast movement dynamics, and piecewise linearity of simple threshold functions to analyze our models in several tractable scenarios.