On the Detection and Estimation of Linkage between a Locus Influencing a Quantitative Character and a Marker Locus

Most methods so far used for locating genes for a quantitative character have been dependent on selection experiments or on making special crosses. For example, Cavalli [1952] crossed lines of Drosophila melanogaster selected for high and low abdominal bristle number, and found evidence for linkage between polygenes. Harrison and MIather [1950] and Gibson and Thoday [1962], by selection experiments in Drosophila melanogaster, were able to locate polygenes for bristle number on a particular chromosome. Thoday [1961] made a further advance by developing methods for detecting linkage of polygenes with marker loci. By mak-ing special crosses in wheat, Wehrhahn and Allard [1965] and Law [1966] located genes influencing time of development of the plant. However, there have been attempts to detect linkage betweeni a marker locus determining a qualitative character and another locus which affects either a meristic (graded) character (Penrose [1938; 1946]), or one which affects a metric character (Lowry and Schultz [1959]; Neimann-Sorensen and Robertson [1961]). The technique consists of looking for interaction between the marker genotype and the metric character in offspring fromi particular matings. The rationale behind this method is explained by Thoday [1966]. The present analysis is an attempt to work out these techniques mathematically in order to develop general methods for the detection and the estimation of linkage from the offspring of given crosses. The notation used is that of Mather [1949]. These methods should be useful for any population of diploid organisms under certain restrictions, and do not require making specific crosses. They should therefore be applicable also in human genetics. Various difficulties which arise in practice will be considered later in the discussion.