Journal of Mathematical Biology

, Volume 53, Issue 5, pp 759–770

A model for the evolution of paralog families in genomes

  • Ryszard Rudnicki
  • Jerzy Tiuryn
  • Damian Wójtowicz
Article

DOI: 10.1007/s00285-006-0040-z

Cite this article as:
Rudnicki, R., Tiuryn, J. & Wójtowicz, D. J. Math. Biol. (2006) 53: 759. doi:10.1007/s00285-006-0040-z

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 l1. 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.

Keywords

Genome evolution Paralogous genes Markov semigroups Asymptotic stability 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Ryszard Rudnicki
    • 1
  • Jerzy Tiuryn
    • 2
  • Damian Wójtowicz
    • 2
  1. 1.Institute of Mathematics, Polish Academy of Sciences and Institute of MathematicsSilesian UniversityKatowicePoland
  2. 2.Institute of InformaticsWarsaw UniversityWarsawPoland