Scaling and fractal behaviour underlying meiotic recombination.
In this paper we investigate some of the mathematical properties of meiotic recombination. Working within the framework of a genetic model with n loci, where alpha alleles are possible at each locus, we find that the proportion of all possible diploid parental genotypes that can produce a particular haploid gamete is exp[-n log(alpha(2)/[2alpha-1])]. We show that this proportion connects recombination with a fractal geometry of dimension log(2alpha-1)/log(alpha). The fractal dimension of a geometric object manifests itself when it is measured at increasingly smaller length scales. Decreasing the length scale of a geometric object is found to be directly analogous, in a genetics problem, to specifying a multilocus haplotype at a larger number of loci, and it is here that the fractal dimension reveals itself.
Waxman
D
D
Centre for the Study of Evolution, School of Life Sciences, University of Sussex, Brighton BN1 9QG, Sussex, UK. D.Waxman@sussex.ac.uk
Stoletzki
N
N
D000818:Animals; D002467:Cell Nucleus / Q000235:genetics*; D003198:Computer Simulation; D017709:Fractals; D006801:Humans; D008540:Meiosis / Q000235:genetics*; D008957:Models, Genetic; D011995:Recombination, Genetic / Q000235:genetics*