Planktonic encounter rates with non-spherical encounter zones

We present general formulae for planktonic predator-prey encounter rates with encounter zones of convex shape and randomly moving point-like prey with ballistic motion. When the predator is not moving, we show that the encounter rate is independent of the shape of the encounter zone around it and proportional to the product of the surface area of the encounter zone and the prey speed. By contrast, the shape of the encounter zone plays a role when both the predator and the prey are moving. Slow predator motion results in only a weak increase of the encounter rate relative to the non-motile predator situation, but it may lead to a significant shift in where prey impact the surface of the encounter zone. By analysing disc-like and rod-like encounter zones with lengthwise and sideways motion, respectively, we show that fast predator motion may significantly influence the encounter rate, depending on the shape and the direction of motion of the encounter zone.