The fluid dynamics of yellow dung fly sperm flow

The mechanisms regulating sperm transfer, storage, and use in insects are far from clear. Even in one of the most well-resolved systems for studying post-copulatory sexual selection, the yellow dung fly (Scathophaga stercoraria), the process of sperm transfer is not well understood. Our aim is to model the fluid dynamics of sperm flow in the reproductive tracts of female yellow dung flies to determine what aspects of female morphology may influence sperm movement. We model fluid flow using computational mathematics, and investigate geometric parameters suspected of influencing rates of ejaculate movement: the curvature of sperm storage ducts, the smoothness of the inner duct wall (surface area), spermathecal duct length and duct diameter. Duct length does not influence the flow rate, where duct diameter has a strong influence of up to 71% at the extremes of the natural range observed in female dung flies. Whereas duct curvature influences the flow rate only slightly (with an effect size of 1.6% over the natural range), the duct wall smoothness has a pronounced effect (50%). The increase in duct surface area also slightly increases the effect of curvature, implying that these structures might act synergistically, although the small size of this effect argues against such a synergy having evolved as an adaptation for controlling sperm flow. We discuss the implications of our model and methods for research in sperm competition and sexual selection.