Mathematics of gamete diffusion and fertilization in aquatic habitats

Many aquatic invertebrates and algae sexually reproduce using external fertilization. Fertilization can occur in plumes via interception of free-floating eggs by free-floating sperm (“gamete interception”), active filtration of sperm by females who retains eggs (“gamete filtration”), or passive accumulation of gametes by sticky masses of gametes of the opposite sex (“gamete targeting”). Gaussian plume models suggest that gamete interception is unlikely to succeed in high flow-rate habitats because of rapid dilution of sperm. The predictions of revised gamete interception models are contrasted with the predictions of new gamete filtration and targeting models in unidirectional and oscillatory flows. Mathematical models for gamete filtration and targeting suggest that success rates may be high as long as many sperm are released, egg numbers are small, sperm accumulation occurs over a long time, or females seek fertilizers for only a small proportion of their eggs at once. The practice of either gamete targeting or filtration may allow reproduction to succeed despite rapid gamete dilution, and thus permit high-flow habitats, to serve as sources, not just sinks, of larvae and spores. The invasive ability of some filter-feeding organisms may be enhanced by their capacity to filter gametes from the water column and thus reproduce at low population densities. Up to this point, most gamete interception models have ignored the configuration of spawners likely to produce the highest fertilization rates. All previous predictions of high fertilization rates have been based on low flow conditions, overestimates of sperm-egg contact time or improper treatment of egg passage over sperm sources. Revised gamete interception models indicate that fertilization success rates may be high in some regions of the egg plume when females are situated upstream of males, but low when males precede females. However, generalizing these high success rates to the entire plume may not be justifiable. Since gamete interception seems less likely to succeed than either filtration or targeting in high-flow habitats, populations that rely on interception may be more sensitive to depletion than those that can actively or passively filter gametes.