Modelling rates of random search over the transition from diffusive to ballistic movement of plankton

Abstract

The rate of search for food (i.e. maximum clearance rate), F, of a plankter is essential to the prediction of encounter rates, and is dependent on movement. Classic encounter rate models assume diffusive or ballistic movements, which represent opposing extremes of directional persistence. From the perspective of the predator, the directional persistence of prey is determined by the ratio of the persistence length (i.e. "run length" of a random walker), λ, and the radius of prey detection, r. We developed an individual-based model to (i) describe variation in F due to λ/r and time, and (ii) evaluate the utility of published corrections (that take into account the effect of λ/r on F ) to the classic models. Our results illustrate that classic models overestimate F when their assumptions of movement are invalid, and indicate that the effect of time variation in F on food consumption is most substantial near the middle of the diffusive to ballistic transition (i.e. λ/r 1). At λ/r 1, predators may exploit high clearance rates by "jumping", provided that the far-field concentration of prey is sufficiently high. We recommend a published Michaelis-Menten type correction to the classic models, and discuss the assumptions and applications of our model system.