The Prior Distribution of the Minimum and Maximum Distance between Several Marker Loci and Quantitative Trait Loci

In order to control linkage experiments, exact formulas and approximations are derived for the minimum distance between quantitative trait loci and the nearest marker locus. The locations of the loci are assumed to be uniformly distributed over the genome. The locations of the marker loci may be known or unknown. The number and length of the chromosomes are arbitrary and therefore the results are applicable for all kinds of species. Analogous formulas are derived for the maximum distance between the quantitative trait loci and the nearest marker loci. For the probability of linkage more simple expressions are derived. The accuracy of the approximations is checked by a simulation.