The impact of rheotaxis and flow on the aggregation of organisms

Dispersed populations often need to organize into groups. Chemical attractants provide one means of directing individuals into an aggregate, but whether these structures emerge can depend on various factors, such as there being a sufficiently large population or the response to the attractant being sufficiently sensitive. In an aquatic environment, fluid flow may heavily impact on population distribution and many aquatic organisms adopt a rheotaxis response when exposed to a current, orienting and swimming according to the flow field. Consequently, flow-induced transport could be substantially different for the population members and any aggregating signal they secrete. With the aim of investigating how flows and rheotaxis responses impact on an aquatic population's ability to form and maintain an aggregated profile, we develop and analyse a mathematical model that incorporates these factors. Through a systematic analysis into the effect of introducing rheotactic behaviour under various forms of environmental flow, we demonstrate that each of flow and rheotaxis can act beneficially or detrimentally on the ability to form and maintain a cluster. Synthesizing these findings, we test a hypothesis that density-dependent rheotaxis may be optimal for group formation and maintenance, in which individuals increase their rheotactic effort as they approach an aggregated state.