The extinction problem for a class of distylous plant populations

TL;DR

This paper investigates the extinction probabilities of certain distylous plant populations modeled as nonhomogeneous nearest-neighbor random walks, developing potential-theoretic tools to improve bounds on absorption probabilities.

Contribution

It introduces new potential-theoretic methods and constructs sub- and super-harmonic functions to better estimate extinction probabilities for these plant populations.

Findings

Derived bounds for extinction probabilities that improve previous estimates

Developed potential-theoretic tools applicable to nonhomogeneous random walks

Connected extinction analysis with classical probabilistic models

Abstract

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.