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Many phenomena in biology involve both reactions and chemotaxis. Theseprocesses can clearly influence each other, and chemotaxis can play animportant role in sustaining and speeding up the reaction. In continuation ofour earlier work, we consider a model with a single density function involvingdiffusion, advection, chemotaxis, and absorbing reaction. The model ismotivated, in particular, by the studies of coral broadcast spawning, whereexperimental observations of the efficiency of fertilization ratessignificantly exceed the data obtained from numerical models that do not takechemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes)into account. We consider the case of the weakly coupled quadratic reactionterm, which is the most natural from the biological point of view and was leftopen. The result is that similarly to higher power coupling, the chemotaxisplays a crucial role in ensuring efficiency of reaction. However,mathematically, the picture is quite different in the quadratic reaction caseand is more subtle. The reaction is now complete even in the absence ofchemotaxis, but the timescales are very different. Without chemotaxis, thereaction is very slow, especially for the weak reaction coupling coefficient.With chemotaxis, the timescale and efficiency of reaction are independent ofthe coupling parameter.

Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case