The previous section assumed that some markers were close to the genes controlling the trait of interest. Some studies have shown that this may not be too bad, particularly for dense linkage maps. However, in many studies, for instance with a new crop or searching for a new trait, it may be infeasible to have or use a dense map. In fact, a strong argument can be made for first using a sparse map, with markers spaced every 5-20 cM, to identify probable regions containing QTLs. Subsequent studies, with an independent sample from the genome, can fine tune gene loci.
Regardless of marker spacing, one can improve estimates of gene loci by using all the information about linkage between markers and the trait. This requires additional assumptions about the relationship between genetic linkage and physical distance, similar to those made in developing linkage maps in an earlier chapter.
This section develops the ideas of interval mapping, in which one uses flanking markers around an alleged gene, along with assumptions about recombination, to develop a probability distribution, or likelihood. Traditionally this likelihood for genome studies has been presented has been presented as the LOD score. The best estimate of gene locus, in the interval between these flanking markers, maximizes this LOD. Theory suggests an interpretation, and a way to create confidence intervals for gene loci. However, practical experience provides conflicting evidence about the utility of such intervals.