A model for the evolution of paralog families in genomes

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 distr...

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Bibliographic Details
Published in:Journal of mathematical biology 2006-11, Vol.53 (5), p.759-770
Main Authors: Rudnicki, Ryszard, Tiuryn, Jerzy, Wójtowicz, Damian
Format: Article
Language:English
Subjects:
Evolution, Molecular
Gene Deletion
Gene Duplication
Gene Flow
Genetic Variation
Genome, Fungal - genetics
Models, Genetic
Studies
Yeasts - genetics
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-006-0040-z