  Disentangling the processes leading populations to extinction is a major
topic in ecology and conservation biology. The difficulty to find a mate in
many species is one of these processes. Here, we investigate the impact of
self-incompatibility in flowering plants, where several inter-compatible
classes of individuals exist but individuals of the same class cannot mate. We
model pollen limitation through different relationships between mate
availability and fertilization success. After deriving a general stochastic
model, we focus on the simple case of distylous plant species where only two
classes of individuals exist. We first study the dynamics of such a species in
a large population limit and then, we look for an approximation of the
extinction probability in small populations. This leads us to consider
inhomogeneous random walks on the positive quadrant. We compare the dynamics of
distylous species to self-fertile species with and without inbreeding
depression, to obtain the conditions under which self-incompatible species
could be less sensitive to extinction while they can suffer more pollen
limitation.
