Journal of Mathematical Biology

, Volume 64, Issue 1–2, pp 163–210 | Cite as

A general stochastic model for sporophytic self-incompatibility

  • Sylvain Billiard
  • Viet Chi Tran


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 can be less sensitive to extinction while they can suffer more pollen limitation.


Birth and death process ODE approximation Inhomogeneous random walk on the positive quadrant Inbreeding depression Extinction probability Mating system Distyly 

Mathematics Subject Classification (2000)

92D40 92D25 60J80 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Génétique et évolution des populations végétales, UFR de Biologie, FRE CNRS 3268Université des Sciences et Technologies de Lille 1Villeneuve d’Ascq CedexFrance
  2. 2.Laboratoire Paul Painlevé, UFR de Mathématiques, UMR CNRS 8524Université des Sciences et Technologies de Lille 1Villeneuve d’Ascq CedexFrance
  3. 3.Centre de Mathématiques Appliquées, UMR CNRS 7641Ecole PolytechniquePalaiseau cedexFrance

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