Estimating fertilization success in marine benthic invertebrates: A case study with the tropical sea star Oreaster reticulatus

Abstract

Several factors can influence fertilization success, and for marine broadcast spawners, the main constraint is rapid dilution of gametes. Because the measurement of fertilization success in the field is logistically difficult, theoretical models have been used as an alternative method of estimation. We tested the predictive ability of the existing models (time-averaged diffusion model in conjunction with a fertilization kinetics model) by making direct comparisons between empirical and corresponding predicted rates of fertilization in the tropical sea star Oreaster reticulatus. Using induced spawnings, we measured in situ fertilization in field experiments at 4 sites on sand bottoms and seagrass beds in the Bahamas. Rate of fertilization decreased exponentially with increasing distance downstream (x) from a spawning male for all experimental runs at all sites, and when averaged across all sites, it ranged from 74% at x = 1 m to 31% at x = 32 m. For each experimental run, we parameterized the 2 models by quantifying the flow field, and thus obtained predicted estimates of fertilization success. The shape of the fitted exponentially-decaying curves was similar between the observed and predicted data for sites on sand bottoms, but not in seagrass beds. There was a highly significant correlation between the observed and predicted data at each distance directly downstream for each run, but the predicted values were 1 to 10 orders of magnitude lower than the observed values for distances off the main axis of advection. We also used dye dilution runs to test the validity of the diffusion model and, in agreement with the observed values, the predicted concentrations of dye decreased as a power function of distance downstream from the point of release. Turbulent diffusivity was quantified in 2 ways: by measuring the standard deviation of dye concentration across-stream and vertically (sigmay and sigmaz), and by calculating coefficients of diffusivity (alphay and alphaz). Using alphay and alphaz, the values predicted with the model of diffusion were up to 24 orders of magnitude lower than the observed values at heights >0.2 m above the bottom, but this inconsistency was alleviated when sigmay and sigmaz were used. Thus, the combination of the 2 models currently used can predict fertilization rate reliably for a particular parameter space, which can be increased by quantifying turbulent diffusivity more accurately. These modified models can substitute field experiments to estimate fertilization success in species of marine benthic invertebrates that are fragile, such as O. reticulatus, or are relatively inaccessible, such as inhabitants of the deep sea.