The calculation of recombination frequencies in crosses of allogamous plant species with applications to linkage mapping

The recombination frequency (r) between two loci defined by conventional or molecular markers can be estimated by solving proper Maximum Likelihood equations. These are based on expected and observed marker class frequencies in the progeny of a cross, and are specific for each allelic configuration of the parents((1)), In a cross between two diploid parents up to four different alleles, besides a null allele, can be detected at one locus. This defines in each parent, considering a locus A, nine basic allelic configurations based on two allelic marker fragments (A(i)/A(j)), one single marker allele and a null allele (A(i)/A0), or just null alleles (A0/A0), With respect to two loci the consideration of all possible diploid allelic configurations in the parents of a cross allows the detection of 21 different expected marker class distributions producing estimates of r in the progeny. General formulas for calculating the ML equations and the corresponding information functions have been developed for the 21 marker class distributions. Simplified formulas have been also derived and the relative efficiency of the information functions compared, As expected, in the majority of cases, allelic marker configurations give more precise estimates of linkage values than single marker configurations. A method for the construction of linkage maps based on two point estimates, linkage subgroups and allelic bridges is presented. The method is an improvement on an original proposal by Ritter et al. (1990).