Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species

With the advent of new molecular marker technologies, it is now feasible to initiate genome projects for outcrossing plant species, which have not received much attention in genetic research, despite their great agricultural and environmental value. Because outcrossing species typically have heterogeneous genomes, data structure for molecular markers representing an entire genome is complex: some markers may have more alleles than others, some markers are codominant whereas others are dominant, and some markers are heterozygous in one parent but fixed in the other parent whereas the opposite can be true for other markers. A major difficulty in analyzing these different types of marker at the same time arises from uncertainty about parental linkage phases over markers. In this paper, we present a general maximum-likelihood-based algorithm for simultaneously estimating linkage and linkage phases for a mixed set of different marker types containing fully informative markers (segregating 1:1:1:1) and partially informative markers (or missing markers, segregating 1:2:1, 3:1, and 1:1) in a full-sib family derived from two outbred parent plants. The characterization of linkage phases is based on the posterior probability distribution of the assignment of alternative alleles at given markers to two homologous chromosomes of each parent, conditional on the observed phenotypes of the markers. Two- and multi-point analyses are performed to estimate the recombination fraction and determine the most likely linkage phase between different types of markers. A numerical example is presented to demonstrate the statistical properties of the model for characterizing the linkage phase between markers.