A general stochastic model for sporophytic self-incompatibility

The extinction problem for a distylous plant population with sporophytic self-incompatibility

In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means absorption at one of the axes. Despite connections with some classical probabilistic models (standard two-type Galton-Watson process, two-urn model), exact formulae for the probabilities of absorption seem to be difficult to come by and one must therefore resort to good approximations. In order to meet this task, we develop potential-theoretic tools and provide various sub- and super-harmonic functions which, for large initial populations, provide bounds which in particular improve those that have appeared earlier in the literature.

A one-locus model of androdioecy with two homomorphic self-incompatibility groups: expected vs. observed male frequencies

Androdioecy, the occurrence of males and hermaphrodites in a single population, is a rare breeding system because the conditions for maintenance of males are restrictive. In the androdioecious shrub Phillyrea angustifolia, high male frequencies are observed in some populations. The species has a sporophytic self-incompatibility (SI) system with two self-incompatibility groups, which ensures that two groups of hermaphrodites can each mate only with the other group, whereas males can fertilize hermaphrodites of both groups. Here, we analyse a population genetic model to investigate the dynamics of such an androdioecious species, assuming that self-incompatibility and sex phenotypes are determined by a single locus. Our model confirms a previous prediction that a slight reproductive advantage of males relative to hermaphrodites allows the maintenance of males at high equilibrium frequencies. The model predicts different equilibria between hermaphrodites of the two SI groups and males, depending on the male advantage, the initial composition of the population and the population size, whose effect is studied through stochastic simulations. Although the model can generate high male frequencies, observed frequencies are considerably higher than the model predicts. We finally discuss how this model may help explain the large male frequency variation observed in other androdioecious species of Oleaceae: some species show only androdioecious populations, as P. angustifolia, whereas others show populations either completely hermaphrodite or androdioecious.