Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant - Centre de mathématiques appliquées (CMAP) Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant

Résumé

In this paper, we study a distylous flower population in which self-reproduction is not permitted. Individuals are diploid, and two alleles, A and a, can be found at the considered locus S. Pollen and ovules of flowers with the same genotype at locus S cannot mate. This prevents the pollen of a given flower to fecundate its stigmates. Only genotypes AA and Aa can be maintained in the population, so that the latter can be described by a random walk in the positive quadrant whose components are the number of individuals of each genotype. This random walk is not homogeneous and its transitions depend on the location of the process. We are interested in the computation of the extinction probabilities, where extinction happens when one of the axis is reached by the process. These extinction probabilities, which depend on the initial condition, satisfy a doubly-indexed recurrence equation that cannot be solved directly. We consider the associated generating function and show that it satisfies a partial differential equation that is solved but whose solution is explicit, though hardly tractable. Numerical results comparing stochastic and deterministic approximations of the extinction probabilities are studied.
Fichier principal
Vignette du fichier
marche_aleatoire_plan_v11.pdf (2.45 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00664536 , version 1 (30-01-2012)
hal-00664536 , version 2 (26-09-2012)

Identifiants

Citer

Pauline Lafitte-Godillon, Kilian Raschel, Viet Chi Tran. Extinction probabilities for a distylous plant population modeled by an inhomogeneous random walk on the positive quadrant. 2012. ⟨hal-00664536v1⟩
478 Consultations
157 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More