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



Author: Michael Baake Bielefeld

Source: https://arxiv.org/



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