The extinction problem for a class of distylous plant populations with sporophytic self-incompatibility

Gerold Alsmeyer (1) , Kilian Raschel (2)

1 Institut für Mathematische Stochastik [Münster]
2 IDP - Institut Denis Poisson

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.

Mots clés: Markov jump process; Extinction probability; Random walk; Sub- and superharmonic function; Random environment; Branching process; Potential theory

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Gerold Alsmeyer, Kilian Raschel. The extinction problem for a class of distylous plant populations with sporophytic self-incompatibility. Journal of Mathematical Biology, 2019, 78 (6), pp.1841-1874. ⟨10.1007/s00285-019-01328-5⟩. ⟨hal-01895778v2⟩