Mallory Gaspard: When is Camouflage Useful? A Case Study in Hover Fly Pursuit-Evasion Interactions

Camouflaging is a widely used concealment tactic across the animal kingdom, but when is it actually beneficial for an organism to use? In this talk, we focus on analyzing when it is worthwhile for a pursuer to utilize motion camouflage (MC) amidst uncertainty in when an evader will feel threatened and attempt to escape. Using MC movement techniques to trick an evader's visual system into believing that a pursuer is less threatening than they actually are has been observed in hover flies during mating rituals and in dragonflies during territorial disputes. To ground our discussion in a concrete example, I will focus on mathematically modeling biologically observed MC behaviors exhibited in hover fly pursuit-evasion interactions. In this model, the evader's escape attempt time occurs as the result of a non-homogeneous Poisson point process governed by a rate function that is dependent on the pursuer’s state and the evader’s position. I will then present a general mathematical framework to determine when MC tactics may be worthwhile for an energy-optimizing pursuer, and I will highlight the resulting sequence of Hamilton-Jacobi-Bellman (HJB) partial differential equations which encode the pursuer's optimal trajectories. After presenting the model and mathematical approach, I will show a selection of numerical simulations and statistics that reveal the existence of a specific parameter regime for the rate function in which MC tactics are useful. Finally, I will wrap up our discussion with some suggestions for future expansions of the framework.