title: A model for the evolution of paralog families in genomes.
abstract: We introduce and analyse a simple probabilistic model of genome evolution. It is based on three fundamental evolutionary events: gene loss, duplication and accumulated change. This is motivated by previous works which consisted in fitting the available genomic data into, what is called paralog distributions. This formalism is described by a system of infinite number of linear equations. We show that this system generates a semigroup of linear operators on the space l (1). We prove that size distribution of paralogous gene families in a genome converges to the equilibrium as time goes to infinity. Moreover we show that when probabilities of gene removal and duplication are close to each other, then the resulting distribution is close to logarithmic distribution. Some empirical results for yeast genomes are presented.
authors.affiliation: Institute of Mathematics, Polish Academy of Sciences and Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland. rudnicki@us.edu.pl
authors.forename: Ryszard
authors.initials: R
authors.lastname: Rudnicki
authors.forename: Jerzy
authors.initials: J
authors.lastname: Tiuryn
authors.forename: Damian
authors.initials: D
authors.lastname: Wójtowicz
mesh_terms: D019143:Evolution, Molecular; D017353:Gene Deletion; D020440:Gene Duplication; D051456:Gene Flow; D014644:Genetic Variation; D016681:Genome, Fungal / Q000235:genetics*; D008957:Models, Genetic; D015003:Yeasts / Q000235:genetics