Repeat distributions from unequal crossovers

Volume 80 / 2008

Michael Baake Banach Center Publications 80 (2008), 53-70 MSC: Primary 92D25, 92D10; Secondary 60B10, 46B50. DOI: 10.4064/bc80-0-3

Abstract

It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibrium distributions of this type. Due to the nonlinear and infinite-dimensional nature of these models, their analysis requires some nontrivial tools from measure theory and functional analysis, which makes them interesting also from a mathematical point of view. In particular, they can be viewed as quadratic, hence nonlinear, analogues of Markov chains.

Authors

  • Michael BaakeFakultät für Mathematik
    Universität Bielefeld
    Postfach 100131
    33501 Bielefeld, Germany
    e-mail

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