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Modern Genetic Analysis Chapter 18. Quantitative Genetics
Introduction

Ultimately, the goal of genetics is the analysis of the genotype of organisms. But the genotype can be identifiedand therefore studiedonly through its phenotypic effect. We recognize two genotypes as different from each other because the phenotypes of their carriers are different. Basic genetic experiments, then, depend on the existence of a simple relation between genotype and phenotype. That is why studies of DNA sequences are so important, because we can read off the genotype directly from this most basic of all phenotypes. In general, we hope to find a uniquely distinguishable phenotype for each genotype and only a simple genotype for each phenotype. At worst, when one allele is completely dominant, it may be necessary to perform a simple genetic cross to distinguish the heterozygote from the homozygote. Where possible, geneticists avoid studying genes that have only partial penetrance and incomplete expressivity (page 182) because of the difficulty of making genetic inferences from such traits. For the most part, then, the study of genetics presented in the preceding chapters has been the study of allelic substitutions that cause qualitative differences in phenotype.

However, the actual variation between organisms is usually quantitative, not qualitative. Wheat plants in a cultivated field or wild asters at the side of the road are not neatly sorted into categories of "tall" and "short," any more than humans are neatly sorted into categories of "black" and "white." Height, weight, shape, color, metabolic activity, reproductive rate, and behavior are characteristics that vary more or less continuously over a range (Figure 18-1). Even when the character is intrinsically countable (such as eye facet or bristle number in Drosophila), the number of distinguishable classes may be so large that the variation is nearly continuous. If we consider extreme individualssay, a corn plant 8 feet tall and another one 3 feet talla cross between them will not produce a Mendelian result. Such a corn cross will produce plants about 6 feet tall, with some clear variation among siblings. The F2 from selfing the F1 will not fall into two or three discrete height classes in ratios of 3:1 or 1:2:1. Instead, the F2 will be continuously distributed in height from one parental extreme to the other. This behavior of crosses is not an exception; it is the rule for most characters in most species. Mendel obtained his simple results because he worked with horticultural varieties of the garden pea that differed from one another by single allelic differences that had drastic phenotypic effects. Had Mendel conducted his experiments on the natural variation of the weeds in his garden, instead of abnormal pea varieties, he would never have discovered Mendel's laws. In general, size, shape, color, physiological activity, and behavior do not assort in a simple way in crosses.

The fact that most phenotypic characters vary continuously does not mean that their variation is the result of some genetic mechanisms different from the Mendelian genes with which we have been dealing. The continuity of phenotype is a result of two phenomena. First, each genotype does not have a single phenotypic expression but a norm of reaction (see Chapter 1) that covers a wide phenotypic range. As a result, the phenotypic differences between genotypic classes become blurred, and we are not able to assign a particular phenotype unambiguously to a particular genotype. Second, many segregating loci may have alleles that make a difference to the phenotype being observed. Suppose, for example, that five equally important loci affect the number of flowers that will develop in an annual plant and that each locus has two alleles (call them + and ). For simplicity, also suppose that there is no dominance and that a + allele adds one flower, whereas a allele adds nothing. Thus, there are 35 = 243 different possible genotypes [three possible genotypes (+ / +, + / , and / ) at each of five loci], ranging from

but there are only 11 phenotypic classes (10, 9, 8, ..., 0) because many of the genotypes will have the same numbers of + and alleles. For example, although there is only one genotype with 10 + alleles and therefore an average phenotypic value of 10, there are 51 different genotypes with 5 + alleles and 5 alleles; for example,

Thus, many different genotypes may have the same average phenotype. At the same time, because of environmental variation, two individuals of the same genotype may not have the same phenotype. This lack of a one-to-one correspondence between genotype and phenotype obscures the underlying Mendelian mechanism. If we cannot study the behavior of the Mendelian factors controlling such traits directly, then what can we learn about their genetics?

Using current experimental techniques, geneticists can answer the following questions about the genetics of a continuously varying character in a population (say, height in a human population). These questions constitute the study of quantitative geneticsthe study of the genetics of continuously varying characters:

1. Is the observed variation in the character influenced at all by genetic variation? Are there alleles segregating in the population that produce some differential effect on the character or is all the variation simply the result of environmental variation and developmental noise (pages 1417)?
2. If there is genetic variation, what are the norms of reaction of the various genotypes?
3. How important is genetic variation as a source of total phenotypic variation? Are the norms of reaction and the environments such that nearly all the variation is a consequence of environmental difference and developmental instabilities or does genetic variation predominate?
4. Do many loci (or only a few) vary with respect to the character? How are they distributed over the genome?
5. How do the different loci interact with one another to influence the character? Is there dominance, and is there any epistasis (interaction between genes at different loci)?
6. Is there any nonnuclear inheritance (for example, any maternal effect)?

In the end, the purpose of asking these questions is to be able to predict what kinds of offspring will be produced by crosses of different phenotypes.

The precision with which these questions can be framed and answered varies greatly. In experimental organisms, on the one hand, it is relatively simple to determine whether there is any genetic influence at all, but extremely laborious experiments are required to localize the genes (even approximately). In humans, on the other hand, it is extremely difficult to answer even the question of the presence of genetic influence for most traits because it is almost impossible to separate environmental from genetic effects in an organism that cannot be manipulated experimentally. As a consequence, we know a relatively large amount about the genetics of bristle number in Drosophila but virtually nothing about the genetics of complex human traits; a few (such as skin color) clearly are influenced by genes, whereas others (such as the specific language spoken) clearly are not. It is the purpose of this chapter to develop the basic statistical and genetic concepts needed to answer these questions and to provide some examples of the applications of these concepts to particular characters in particular species.

© 1999 by W. H. Freeman and Company. All rights reserved.