Transition model for the hermaphroditism-dioecy continuum in higher plants

Dioecy, characterized by the presence of distinct male and female individuals in the breeding population, has evolved independently numerous times, suggesting that a simple common mechanism may prevail behind the evolution of dioecy from hermaphroditism. In the present study, a floral sex allocation model is demonstrated for the presence of a hermaphroditism-dioecy continuum in higher plants using an N-player game model. In the continuum, we pay attention to the emergence of gynodioecy in which both hermaphroditic and female individuals coexist in the breeding population, and trioecy which includes hermaphroditic, male and female individuals in the breeding population, as these have often been considered as an intermediate step in the evolution of dioecy from hermaphroditism and vice versa. In the N-player game model, we assumed a local breeding population containing N players with different reproductive investment, and there is a trade-off between the reproductive investment to male function and female function at individual level. Furthermore, we focused on the uncertainty of pollen transportation, as dioecy is often linked to both the unreliable pollen vectors and harsh environment for pollinators. The pollen transport efficiency was explained by the probability of the pollen hitting ovules or stigmata. In the model, setting hypothetical populations with different population sizes, we showed the Nash solutions for dioecy appeared at a smaller pollen transport efficiency than for hermaphroditism in all hypothetical populations. Since the low pollen transport efficiency equals the low reliability of pollen vectors, the result is comparable with the pollinators of real dioecy such as water, wind and generalist species. The Nash solution for gynodioecy and trioecy was obtained at the transition zone between dioecy and hermaphroditism in the continuum. The number of male and female individuals in dioecy were almost stable in the range of low pollen transport efficiency. If the number of males decreased with increasing pollen transport efficiency, hermaphroditic individuals emerged in the population (establishment of trioecy). Gynodioecy established as soon as no males were left in the population. Finally, hermaphroditism established at the time no females were left in the population. These results imply that pollen transport efficiency played an important role of obtaining a variety of Nash solutions in the model. Though the Darwinian paradigm in evolutionary ecology of dioecy is based on the various aspects of the interaction between environment and species-specific characters, our model is composed of numerical interactions between and within individuals. In this paper, we argue that the association between the continuum and the pollen transport efficiency is reflected in the real world.