Most of the phenotypic traits commonly used in introductory genetics are qualitative, meaning that the phenotype exists in only two (or possibly a few more) alternative forms, such as either purple or white flowers, or red or white eyes. These qualitative traits are therefore said to exhibit discrete variation. On the other hand, many interesting and important traits exhibit continuous variation; these exhibit a continuous range of phenotypes that are usually measured quantitatively, such as intelligence, body mass, blood pressure in animals including humans, and yield, water use, or vitamin content in crops. Traits with continuous variation are often complex, and do not show the simple Mendelian segregation ratios (e.g. 3:1) observed with some qualitative traits. Many complex traits are also influenced heavily by the environment. Nevertheless, complex traits can often be shown to have a component that is heritable, and which must therefore involve one or more genes.
How can genes, which are inherited (in the case of a diploid) as at most two variants each, explain the wide range of continuous variation observed for many traits? The lack of an immediately obvious explanation to this question was one of the early objections to Mendel's explanation of the mechanisms of heredity. However, upon further consideration, it becomes clear that the more loci that contribute to trait, the more phenotypic classes may be observed for that trait (Figure 10.6). If the number of phenotypic classes is sufficiently large, individual classes may become indistinguishable from each other (particularly when environmental effects are included), and the result is continuous variation (Figure 10.7). Thus, quantitative traits are sometimes called polygenic traits, because it is assumed that their phenotypes are controlled by the combined activity of many genes. Note that this does not imply that each of the individual genes has an equal influence on a polygenic trait. Furthermore, any give gene may influence more than one trait, whether these traits are quantitative or qualitative traits.
We can use molecular markers to identify at least some of the genes that affect a given quantitative trait. This is essentially an extension of the mapping techniques we have already considered for discrete traits. A QTL mapping experiment will ideally start with two purebreeding lines that differ greatly from each other in respect to one or more quantitative traits (Figure 10.8). The parents and all of their progeny should be raised in under similar environmental conditions, to ensure that observed variation is due to genetic rather than external factors. These parental lines must also be polymorphic for a large number of molecular loci, meaning that they must have different alleles from each other at hundreds of loci. The parental lines are crossed, and then this F_{1} individual, in which recombination between parental chromosomes has occurred is selffertilized (or backcrossed). Because of recombination, each of the F_{2} individuals will contain a different combination of molecular markers, and also a different combination of alleles for the genes that control the quantitative trait of interest (Table 10.1). By comparing the molecular marker genotypes of several hundred F_{2} individuals with their quantitative phenotypes, a researcher can identify molecular markers for which the presence of particular alleles is always associated with extreme values of the trait. In this way, regions of chromosomes that contain genes that contribute to quantitative traits can be identified. (Figure 10.9) It then takes much more work (further mapping and other experimentation) to identify the individual genes in each of the regions that control the quantitative trait.
Table 10.1 Genotypes and quantitative data for some individuals from the crosses shown in Figure 10.8

genotype 
fruit mass 
P 
A_{1}A_{1}B_{1}B_{1}C_{1}C_{1}D_{1}D_{1}E_{1}E_{1}F_{1}F_{1}G_{1}G_{1}H_{1}H_{1}J_{1}J_{1}K_{1}K_{1} 
10g 
P 
A_{2}A_{2}B_{2}B_{2}C_{2}C_{2}D_{2}D_{2}E_{2}E_{2}F_{2}F_{2}G_{2}G_{2}H_{2}H_{2}J_{2}J_{2}K_{2}K_{2} 
90g 
F_{1} 
A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{2}K_{1}K_{2} 
50g 
F_{2} #001 
A_{1}A_{1}B_{1}B_{2}C_{1}C_{1}D_{2}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{1}J_{1}J_{2}K_{1}K_{2} 
80g 
F_{2} #002 
A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}D_{1}D_{1}E_{1}E_{2}F_{1}F_{2}G_{2}G_{2}H_{1}H_{2}J_{2}J_{2}K_{1}K_{1} 
10g 
F_{2} #003 
A_{2}A_{2}B_{1}B_{2}C_{2}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{1}H_{1}H_{2}J_{1}J_{2}K_{1}K_{2} 
50g 
F_{2} #004 
A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{2}K_{2}K_{2} 
60g 
F_{2} #005 
A_{1}A_{2}B_{1}B_{1}C_{1}C_{2}D_{2}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{1}K_{2}K_{2} 
90g 
F_{2} #006 
A_{1}A_{2}B_{2}B_{2}C_{1}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{2}G_{2}G_{2}H_{1}H_{2}J_{1}J_{2}K_{1}K_{2} 
60g 
F_{2} #007 
A_{2}A_{2}B_{1}B_{1}C_{1}C_{2}D_{2}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{1}H_{1}H_{2}J_{1}J_{1}K_{1}K_{2} 
80g 
F_{2} #008 
A_{1}A_{1}B_{1}B_{2}C_{1}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{2}K_{1}K_{2} 
50g 
F_{2} #009 
A_{1}A_{2}B_{1}B_{2}C_{2}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{2}K_{1}K_{2} 
50g 
F_{2} #010 
A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{2}K_{2}K_{2} 
30g 
F_{2} #011 
A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}D_{2}D_{2}E_{1}E_{1}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{2}K_{1}K_{2} 
80g 
F_{2} #012 
A_{1}A_{1}B_{1}B_{2}C_{1}C_{2}D_{1}D_{1}E_{1}E_{2}F_{2}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{2}K_{2}K_{2} 
30g 
F_{2} #013 
A_{2}A_{2}B_{1}B_{1}C_{1}C_{2}D_{1}D_{1}E_{1}E_{2}F_{1}F_{1}G_{1}G_{2}H_{2}H_{2}J_{1}J_{1}K_{1}K_{1} 
10g 
F_{2} #014 
A_{2}A_{2}B_{1}B_{1}C_{1}C_{1}D_{2}D_{2}E_{1}E_{2}F_{1}F_{2}G_{1}G_{2}H_{1}H_{2}J_{1}J_{1}K_{1}K_{1} 
70g 
F_{2} #015 
A_{2}A_{2}B_{2}B_{2}C_{1}C_{2}D_{1}D_{2}E_{1}E_{2}F_{2}F_{2}G_{1}G_{2}H_{1}H_{1}J_{2}J_{2}K_{1}K_{2} 
40g 
F_{2} #016 
A_{1}A_{2}B_{2}B_{2}C_{1}C_{2}D_{1}D_{1}E_{1}E_{2}F_{1}F_{1}G_{2}G_{2}H_{1}H_{1}J_{1}J_{2}K_{1}K_{1} 
10g 
F_{2} #017 
A_{1}A_{2}B_{2}B_{2}C_{1}C_{2}D_{2}D_{2}E_{2}E_{2}F_{1}F_{1}G_{2}G_{2}H_{1}H_{2}J_{1}J_{2}K_{2}K_{2} 
90g 
F_{2} #018 
A_{1}A_{2}B_{2}B_{2}C_{1}C_{2}D_{1}D_{2}E_{1}E_{2}F_{1}F_{1}G_{2}G_{2}H_{1}H_{2}J_{1}J_{2}K_{1}K_{1} 
40g 
F_{2} #019 
A_{1}A_{1}B_{1}B_{2}C_{1}C_{2}D_{1}D_{1}E_{1}E_{2}F_{2}F_{2}G_{1}G_{1}H_{1}H_{1}J_{1}J_{2}K_{1}K_{2} 
20g 
F_{2} #100 
A_{1}A_{1}B_{1}B_{2}C_{1}C_{2}D_{2}D_{2}E_{1}E_{2}F_{1}F_{2}G_{2}G_{2}H_{1}H_{2}J_{2}J_{2}K_{1}K_{2} 
80g 