Distribution of the quasispecies for a Galton–Watson process on the sharp peak landscape
Résumé
Abstract We study a classical multitype Galton–Watson process with mutation and selection. The individuals are sequences of fixed length over a finite alphabet. On the sharp peak fitness landscape together with independent mutations per locus, we show that, as the length of the sequences goes to ∞ and the mutation probability goes to 0, the asymptotic relative frequency of the sequences differing on k digits from the master sequence approaches (σe - a - 1)( a k / k !)∑ i ≥ 1 i k /σ i , where σ is the selective advantage of the master sequence and a is the product of the length of the chains with the mutation probability. The probability distribution Q (σ, a ) on the nonnegative integers given by the above equation is the quasispecies distribution with parameters σ and a .
Domaines
Mathématiques [math]
Fichier principal
distribution_quasispecies_gw_sharp_peak_landscape.pdf (227.59 Ko)
Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)