  Many processes in biology involve both reactions and chemotaxis. However, to
the best of our knowledge, the question of interaction between chemotaxis and
reactions has not yet been addressed either analytically or numerically. We
consider a model with a single density function involving diffusion, advection,
chemotaxis, and absorbing reaction. The model is motivated, in particular, by
studies of coral broadcast spawning, where experimental observations of the
efficiency of fertilization rates significantly exceed the data obtained from
numerical models that do not take chemotaxis (attraction of sperm gametes by a
chemical secreted by egg gametes) into account. We prove that in the framework
of our model, chemotaxis plays a crucial role. There is a rigid limit to how
much the fertilization efficiency can be enhanced if there is no chemotaxis but
only advection and diffusion. On the other hand, when chemotaxis is present,
the fertilization rate can be arbitrarily close to being complete provided that
the chemotactic attraction is sufficiently strong. Moreover, an interesting
feature of the estimates on fertilization rate and timescales in the
chemotactic case is that they do not depend on the amplitude of the reaction
term.
