Efficient strategy to track a planktonic target from its hydrodynamic signature

Copepods are one of the most successful organisms in the marine ecosystem. Yet, these millimetric planktonic crustaceans are blind. To perceive their neighborhood, they use hydrodynamic signals. Flow velocities are measured with sensitive hairs, called setae, located along a pair of antennae. Experimental evidence show that copepods respond to hydrodynamic signals to escape predators, attack preys or catch passive food particles. Thus, they seem able to track a target in a turbulent environment through its hydrodynamic signature measured along two segments (the antennae). How they process this information is still unknown.

To tackle this problem, we model the flow disturbance generated by a target in the Stokes limit assuming the target is an essential singularity of the Stokes equations (a stokeslet, a stressless, etc.). We suppose the copepod measures this flow, its gradient or the symmetric part of the gradient (the strain) along the direction of the antennae. The question is whether the copepod is able to locate the target from this information only. We show that an algorithm based on a triangulation from two measures, one on each antenna, is a robust strategy to track the target. This strategy is robust since the flow singularity is always the point where the field lines of the vector field converge. This vector field being the flow velocity itself, its gradient or its symmetric part projected along the antennae direction. The triangulation algorithm is applicable to any target, whatever the hydrodynamic signature of the target, which can be always modeled through a combination of flow singularities. Moreover, it allows to overcome one of the fundamental difficulties of tracking: the intrinsic symmetries of the measured flow field.