Olfactory navigation: how to make decisions using a sparse signal

All living organisms are surrounded by fluids, either air or water, which create unique sensory landscapes. For example, chemical signals disperse in the flow by diffusion and advection and, when the flow is turbulent, odor breaks up in filaments and discrete patches of varying intensity. In my thesis I focused on olfactory navigation in turbulent environments and I aimed at understanding how organisms overcome uncertainties to make decisions. I developed three-dimensional direct numerical simulations of a turbulent channel flow to recreate a realistic environment for olfactory searches. I realized these state of the art simulations by customizing an open software called Nek5000, which solves the Navier-Stokes equations for the velocity field and the advection-diffusion equation, which regulates the evolution of the odor (passive scalar) in a fluid. After generating large fluid dynamics datasets of odorant evolution in a channel, I analyzed which features of the olfactory signal are more relevant to locate the odor source. Surprisingly, not only the signal, but also its absence can be informative to infer the distance from the odor source. Using supervised learning algorithms I showed that the intensity of odor concentration is an informative measure, but that when it is coupled to the temporal dynamics of the signal, it allows robust predictions in different conditions and at different ranges from the source. These theoretical results suggest that it is computationally advantageous to measure both odor intensity and timing. I analyzed a set of neural recording from awake mice, demonstrating that they are indeed able to store both quantities, and that the neural representation depends on the underlying flow. I then considered the problem of navigating to the source of the turbulent odor. Although animals (for example moths and crustaceans) robustly perform this task, the algorithms they use are not understood. I modeled olfactory navigation using the framework of Partially Observable Markov Decision Processes (POMDP) and I proposed a normative theory to explain the alternation between sniffing in the air and sniffing the ground, typical of mammals like rodents and dogs. Alternation stems from the physics of fluids, prescribing that odor near the ground is more continuous than up in the air, but remains relatively close to the source. In contrast, at nose level the odor is transported quickly away from the source, but is more noisy and intermittent. An agent searching for the odor source should thus sniff in the air when it is far from the source to increase its chances of detecting the odor. Once the agent localizes the odor plume, it should continue the search sniffing the ground where the trail is less intermittent. The exact timing for alternation stems from marginal value theory. Finally, the commonly observed behavior of searchers proceeding in casts and surges emerges from this computational framework, and alternation naturally complements this dynamics to ensure optimal exploration.