Title :

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

Author(s) :

Lafitte-Godillon, Pauline [Auteur correspondant]
Mathématiques Appliquées aux Systèmes - EA 4037 [MAS]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Raschel, Kilian [Auteur correspondant]
Laboratoire de Mathématiques et Physique Théorique [LMPT]
Tran, Chi [Auteur correspondant]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

SIAM Journal on Applied Mathematics

Pages :

700-722

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2013

ISSN :

0036-1399

English keyword(s) :

Inhomogeneous random walk on the positive quadrant
boundary absorption
transport equation
method of characteristics
self-incompatibility in flower populations
extinction in diploid population with sexual reproduction

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Sciences de l'environnement/Biodiversité et Ecologie

English abstract : [en]

In this paper, we study a flower population in which self-reproduction is not permitted. Individuals are diploid, {that is, each cell contains two sets of chromosomes}, and {distylous, that is, two alleles, A and a, can ...
Show more >In this paper, we study a flower population in which self-reproduction is not permitted. Individuals are diploid, {that is, each cell contains two sets of chromosomes}, and {distylous, that is, 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 {own} stigmata. 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, {as} 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. {Our contribution is twofold : on the one hand, we obtain an explicit, though intricate, solution through the study of the PDE solved by the associated generating function. On the other hand, we provide numerical results comparing stochastic and deterministic approximations of the extinction probabilities.Show less >

Language :

Anglais

Popular science :

Non

Comment :

23 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL