Male penile propulsion into spiraled spermathecal ducts of female chrysomelid beetles: A numerical simulation approach

• Penial propulsion velocity and energy depend on female ducts shapes.
• The velocity dependence on the female duct spirals radius has a sigmoidal shape.
• The smaller the radius of the spiral, the lower the penile propulsion velocity.
• Reversal turns of the female duct results in higher penial propulsion velocity.
• But propagation on the reversals requires higher energy expenditure by males.

Genital diversification in animals is an interesting evolutionary phenomenon. Sexual selection is the main driving force behind the diversification. However, evolutionary mechanisms that have established and maintained variations in genitalia shape parameters observed in related species are not well understood. Here, for the first time, we used numerical simulations to test the hypothesis that variations in female spermathecal duct shapes among related beetle species mechanically interfere with penile propulsion in varying ways. Our numerical simulations showed that high curvature of the spiraled spermathecal ducts of the female have effects with a threshold-based interaction on male penile insertion. The relative size of spirals observed in the beetle, Cassida rubiginosa, studied here is not small enough to interfere with penile propulsion. But the model revealed that propulsion is impeded by the presence of reverse turns in spermathecal ducts. This type of morphology leads to an increase in the velocity of the propulsion but also to an increase in the propulsion energy cost for males. Our results showed that quantitative differences in spermathecal duct shape can mediate qualitative differences in penile motion. This explains, in part, the mechanism behind origin and maintenance of genital divergence among closely related species in general.