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 nonhomogeneous 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.
About the speaker:
Mallory Gaspard is a Postdoctoral Research Associate in the Leonard Lab and Levin Lab at Princeton University, mentored by Professor Naomi Ehrich Leonard, and Professor Simon Levin. She is broadly inspired by developing mathematical approaches to decision making and optimal control under uncertainty, particularly to solve problems arising in technological, ecological, and sociological contexts. As an applied mathematician, she aims to use these approaches to reveal insights into the “why” behind physical phenomena and provide recommendations for the design or improvement of such systems. Mallory completed her B.S. in Mathematics and Applied Physics at Rensselaer Polytechnic Institute (RPI) in December 2018, followed by her Ph.D. in Applied Mathematics at Cornell University in summer 2025. At Cornell, Mallory’s doctoral research focused on developing dynamic programming based frameworks for optimal control under uncertainty to determine driving strategies in the face of limited traffic signal timing information, to compute enhanced driving directions that also provide lane change timing and effort information, and to better understand when predators in the animal kingdom might decide to utilize motion camouflage tactics while pursuing prey. At Princeton, Mallory is both extending and broadening these mathematical approaches to enhance our understanding of collective behavior in large scale systems of interconnected individuals (e.g., living organisms, technological devices) to investigate the roles that social connections play in shaping outcomes and to deepen our intuition about life-event timing in ecological contexts.
