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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc80-0-3,
author = {Michael Baake},
title = {Repeat distributions from unequal crossovers},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {53-70},
zbl = {1146.92024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc80-0-3}
}
Michael Baake. Repeat distributions from unequal crossovers. Banach Center Publications, Tome 83 (2008) pp. 53-70. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc80-0-3/