Predator-prey encounter rates in turbulent water: Analytical models and numerical tests

In aquatic environments the encounter rates between small predators and their prey are increased by turbulence. We present an expression for the flux of prey into the detective sphere of a small self-propelled predator. We then test this model by direct comparison of theoretical encounter rates with predictions from a numerical experiment where the Navier-Stokes equation is solved explicitly. This allows us to estimate encounter rates numerically under realistic small-scale flow environments, and to explore the accuracy of a simple theoretical formulation of this process. Our analysis includes results for cruising and spiralling motions, as well as pause-travel search behaviour. We find that the analytical model yield surprisingly accurate predictions for models including also the shape of the predator's perceptive sphere and turbulence conditions. This adds confidence to such simple approximations in applied models of predator-prey encounter rates for a wide range of scale sizes of the predator's reactive volumes, their motility patterns and turbulence levels.