Mackay Review, Evolution 53: 307-309

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Lynch and Walsh's masterful treatise, Genetics and Analysis of Quantitative Traits, is thus especially timely. ... This is an exceptionally well and clearly written book, and it is beautifully produced. Accompanying the text are numerous worked examples, review/summary tables, figures and illustrations. I could not find any topic in general quantitative genetics (including some arcane favorites) that was not covered, with one glaring exception. There is little mention of response of quantitative traits to artificial and natural selection. This topic will be covered in full in the companion text, Evolution and Selection of Quantitative Traits, however, a brief introduction would have been useful because the effects of selection are alluded to throughout. One word of warning: despite the claim that the text is intended for anyone with rudimentary knowledge of genetic and statistics, it is definitely not for the statistically/algebraically challenged among us. A more gentle introduction might serve as a useful warm-up to this text. Nevertheless, 'Lynch and Walsh' is a 'must have' for graduate students and active researchers in the field; it is worth the purchase price for the list of over 2000 references alone. I recommend it most enthusiastically.


Complete Review

Quantitative Genetics

Trudy F. C. Mackay
Department of Genetics, Box 7614, North Carolina State University, Raleigh NC 27695-7614
E-mail: Trudy_Mackay@ncsu.edu

Phenotypic variation among individuals within populations is ubiquitous for morphological, behavioral, physiological, and life history characters. The genetic architecture of these characters is typically complex, with multiple interacting genetic factors that are sensitive to the environment contributing to the observed phenotypic variation. Because the phenotypes of complex traits are often continuously distributed in populations, either on the scale of the observed phenotype or an underlying scale of liability, they are referred to as quantitative traits and the underlying genetic loci are Quantitative Trait Loci, or QTLs. Most human diseases (e.g., cancer, heart disease, diabetes, arteriosclerosis), production and yield characters in agriculturally important species of animals and plants, and traits involved in adaptation of wild species to their environments, are quantitative traits. Knowledge of the genetic and molecular basis of quantitative variation in complex diseases is of major importance for public health, because of the large proportion of the population affected, and the potential for environmental modification of disease risk. Response to therapeutic drugs and resistance to infectious agents may often have a multifactorial genetic component, and knowledge of the genes involved can guide treatment regimes tailored to individual genotypes, and lead to the development of novel drugs based on the mechanism of action of resistant genotypes. Our understanding of evolution will also be advanced by the genetic dissection of quantitative traits. Currently, we know little of the nature of the forces maintaining variation for quantitative traits (including complex diseases) within populations, the genetic basis of adaptation within species, or the numbers and nature of the loci causing divergence between species. Discovery of the genes affecting quantitative traits will enable us to apply the powerful methods of molecular population genetics to infer the historical forces of mutation, natural selection and genetic drift acting on them. Further, the complete and nearly complete genome sequences of yeast, many bacteria, and Caenorhabditis elegans have revealed that much of these genomes consists of loci with no known function. Therefore, classical mutagenesis and molecular biology techniques are necessary but not sufficient to assign function to these sequences, and quantitative genetics methodology that enables the detection of mutations and segregating variants with subtle effects may prove to be an effective gene discovery tool.

The terms in which we should seek to describe the genetic architecture of quantitative traits are quite clear. We need to know (1) the loci at which mutations affecting the trait arise; (2) the subset of these loci at which alleles segregate within and between natural populations and species; (3) the homozygous, heterozygous, epistatic and pleiotropic effects of mutational and segregating alleles at these loci, in an ecologically relevant range of environments; (4) the molecular nature of the polymorphisms causing the difference in phenotype between QTL alleles; (5) the developmental and tissue-specific pattern of expression of the different QTL alleles; (6) the gene frequencies at the QTLs within and among populations; and (7) the molecular divergence at the QTLs between taxa.

Individual QTLs have, by definition, genetic effects that are small relative to the background of other segregating QTLs and superimposed environmental variation. Because the correspondence between genotype and phenotype for quantitative traits is not 1:1, the effects of individual QTLs and interactions between them cannot be inferred directly from observations on populations, and statistical analyses of phenotypes of related individuals are necessary to infer their effects. Until recently, quantitative genetic parameters have been summarized as the aggregate effects of all QTLs on the population mean, phenotypic variance, and genetic variances and covariances. The limitation in progressing from complex statistics to complex genetics has been technical, not philosophical. Early in this century, Sax (1923) showed that individual QTL effects could be inferred in crosses between lines in which QTL alleles were in linkage disequilibrium with alleles at a visible marker, whose genotype could be unambiguously ascertained (although the estimate of the effect of the QTL is confounded with its map distance from the marker). Neimann-Sorensen and Robertson (1961) examined the utility of mapping QTLs in random breeding populations by associating quantitative trait phenotype with marker alleles, and concluded that rather dense marker maps were necessary if this approach was to be used, since linkage disequilibrium between the marker and QTL alleles is likely to exist only if they are very tightly linked. Thoday (1961) described an interval mapping method whereby the map positions and effects of linked QTLs could be estimated simultaneously given pairs of flanking visible markers. The utility of introgressing single QTL alleles into an otherwise inbred background to reduce background complexity and effectively 'Mendelizing' the QTL was recognized (Wright, 1952; Breese and Mather, 1957). However, these methods required multiple linked visible markers, which until a decade ago existed only in Drosophila melanogaster, and even these markers were less than ideal since they had deleterious effects on fitness and often direct effects on the traits of interest.

Until the latter half of the 1980s, the study of quantitative traits largely remained the province of animal and plant breeders, and a dedicated cadre of evolutionary biologists and statistical geneticists. Two factors have contributed towards the current excitement about the feasibility of genetically dissecting quantitative traits. The first was the discovery of abundant, highly polymorphic molecular variation that provide neutral molecular markers that can be used to map QTLs. Beginning with Jeffrey's discovery of minisatellite, or VNTR variation (Jeffreys et al.,1985), a veritable stable of polymorphic acronyms is now at our disposal, among them SSR (microsatellite), RAPD, AFLP and SNP. The second was the landmark paper of Lander and Botstein (1989), which for the first time put QTL mapping on a solid statistical footing. Improved statistical methods for mapping QTLs in line crosses and random mating outbred populations is now a growth industry. It is possible to undertake such a study in humans and all of the common model organisms with relative ease. Advances in chip-based expression and sequencing methodology promise high throughput screening and re-sequencing on a scale orders of magnitude greater than had been previously possible (Chu et al., 1998; Wang et al., 1998), and herald a new era for studying the genetic and environmental causes of variation for quantitative traits.

Lynch and Walsh's masterful treatise, Genetics and Analysis of Quantitative Traits, is thus especially timely. This text is the result of a ten year project that is only half completed: the other half will be a volume dedicated to the applications of quantitative genetics in evolutionary biology. This volume is a comprehensive (indeed, encyclopedic) summary of the biology of quantitative traits and the analytical tools required to study quantitative genetic variation. It covers classical as well as current state-of-the-art empirical and statistical methods. As this is a weighty tome (figuratively and literally), I shall only outline in brief the organization of the text. The book is divided into four parts. The first section serves as an introduction to the basic properties of quantitative traits - the quantitative genetic model, causal components of genetic and environmental variation, resemblance between relatives in random breeding populations, analysis of crosses between inbred lines, and inbreeding depression. It also includes an introduction to the statistical concepts necessary to partition the variance of quantitative traits - variance, covariance, regression, correlation, matrix algebra, linear models and scale transformations.

The feature of this book that most distinguishes it from other texts in quantitative genetics is the second section, on quantitative trait loci. I am not aware of any other single extensive summary of the nature and rates of spontaneous mutations affecting quantitative traits, detection of major genes, and methods and results of mapping QTLs by linkage to molecular markers. This section covers crosses of inbred lines, methods for outbred populations, experimental designs for fine-mapping QTLs, and the power to detect QTLs using the different designs. It should be required reading for all contemplating such a study.

Part three is a comprehensive and detailed synopsis of methods for estimating quantitative genetic parameters (i.e., components of genetic and environmental variance, degree of dominance, epistatic variance, genotype by environment interaction). All of the standard methods are here: offspring-parent regression, analysis of full- and half-sib data, the use of twins and clones, diallel crosses, and the North Carolina III and Triple Test Cross designs. Again, careful consideration is given to the precision of estimates and optimum experimental design for each method. This section also includes detailed coverage of methods for and results of studies to estimate genotype-environment interaction effects, genetic correlations between characters, maternal and sex-specific effects, and threshold traits. Most of the methods discussed are classical experimental designs utilizing individuals with defined relationships. The final two chapters cover methods for estimating breeding values and estimating variance components (best linear unbiased prediction, BLUP, and restricted maximum likelihood, REML, respectively) while utilizing extended pedigree information and accounting for effects of selection and other factors.

The book concludes with five statistical appendices providing details of methods for determining expectations, variances and covariances of compound variables, path analysis, matrix algebra and linear models, maximum likelihood estimation and likelihood ratio tests, and power analyses of statistical tests.

This is an exceptionally well and clearly written book, and it is beautifully produced. Accompanying the text are numerous worked examples, review/summary tables, figures and illustrations. I could not find any topic in general quantitative genetics (including some arcane favorites) that was not covered, with one glaring exception. There is little mention of response of quantitative traits to artificial and natural selection. This topic will be covered in full in the companion text, Evolution and Selection of Quantitative Traits, however, a brief introduction would have been useful because the effects of selection are alluded to throughout. One word of warning: despite the claim that the text is intended for anyone with rudimentary knowledge of genetic and statistics, it is definitely not for the statistically/algebraically challenged among us. A more gentle introduction might serve as a useful warm-up to this text. Nevertheless, 'Lynch and Walsh' is a 'must have' for graduate students and active researchers in the field; it is worth the purchase price for the list of over 2000 references alone. I recommend it most enthusiastically.

Literature Cited

Breese, E. L. and K. Mather. 1957. The organization of polygenic activity within a chromosome in Drosophila. I. Hair characters. Heredity 11:373-395.

Chu, S., J. DeRisi, M. Eisen, J. Mulholland, D. Botstein, P. O. Brown, and I. Herskowitz. 1998. The transcriptional program of sporulation in budding yeast. Science 282:699-705.

Jeffreys, A., V. Wilson, and S. L. Thein. 1985. Hypervariable 'minisatellite' regions in human DNA. Nature 314:67-73.

Lander, E. S., and D. Botstein, D. 1989. Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121:185-189.

Neimann-Sorensen, A., and A. Robertson. 1961. The association between blood groups and several production characteristics in three Danish cattle breeds. Acta Agriculturae Scandinavica 11:163-196.

Sax, K. 1923. The association of size differences with seed-coat pattern and pigmentation in Phaseolus vulgaris. Genetics 8:552-560.

Thoday, J. M. 1961. Location of polygenes. Nature 191:368-370.

Wang, D. G., J.-B Fan, C.-J. Siao, A. Berno, P. Young, et al. 1998. Large-scale identification, mapping, and genotyping of single-nucleotide polymorphisms in the human genome. Science 280:1077-1082.

Wright, S. 1952. The genetics of quantitative variability. pp. 5-14 in Quantitative Inheritance,edited by E. C. R. Reeve and C. H. Waddington. Her Majesty's Stationary Office, London, UK.