Local sex-ratio dynamics: a model for the dioecious liverwort Marchantia inflexa

In many dioecious bryophyte species, population sex ratios range from all female to all male. The focal species of the present study, the liverwort Marchantia inflexa, forms patches on rock and bark surfaces, and these differ widely in sex ratio at a rainforest field site in Trinidad. This analysis – to our knowledge the first modeling study of sex-ratio dynamics in a dioecious clonal organism – addresses abundances of male and female M. inflexa through time within an individual patch. We represent the life history of this species using seven different stages (non-reproductive, asexually reproductive, sexually reproductive males, non-reproductive, asexually reproductive, unfertilized and fertilized sexual females) and express their dynamics using ordinary differential equations. Some of the stages become more abundant as thalli extend over the substrate and may overgrow each other to capture space. Our simple representation of dynamics within the patch failed to stabilize the sex ratio: females gradually eliminated males at low to moderate disturbance frequency and males eliminated females at high disturbance frequency. This pattern did not hinge on whether sexual propagules could germinate within the patch, but asexual reproduction (via gemmae dispersed within the patch) played an important role. This suggests that the maintenance of sex in these populations may hinge on metapopulation structure and dynamics. Though sexual reproduction appears to be unimportant within patches, spores provide the primary means of recolonizing patches eliminated by large-scale disturbances. We found that shortly after the patch was fully occupied, the production of these wind-dispersed spores was maximized, but spore production declined thereafter as the sex ratio became increasingly biased toward one sex or the other. Much additional modeling and empirical work is needed to link within-patch dynamics across patches and account for dynamics at the metapopulation level.