Random motility of plankton: diffusive and aggregative contributions

Abstract

We examine the spatial distribution of motile zooplankton moving with a variety of idealized random motility modes. The aggregation of organisms is examined for situations where the parameters governing random motility are cued to a heterogeneous environment and vary spatially. While spatial variation in swimming speed v, always leads to aggregation, spatial variations in the duration of swimming bouts T, only leads to aggregation for some motility modes. At steady state, the concentration of organisms is proportional to 1/v and independent of τ for an organism that continually adjusts its motility in response to local conditions (random cruise motility). In comparison, an organism that sets its motility only at the start of a run (random jump motility) reaches a steady state concentration proportional to 1/(τυ 2 ). For an encounter-pause random motility, steady state concentration is proportional to [1 + (pause interval)(encounter rate)]. The latter incorporates the sensory ability and swimming behaviour exhibited by many pelagic copepods. Biodffusion is a poor descriptor of random motility as it does not distinguish between the behavioural components that bring about accumulation of organisms. Mathematical formalism is provided to link individual-based random motility to macroscale phenomenology as encapsulated in appropriate advection diffusion equations.