in Fig. 9.18, it is difficult to test the predictions of Fisher's or Orr's models. The OTLs from dairy cows in Fig. 9.18a have the largest number of OTLs with small effect. In contrast, the effect distribution in Figs 9.18b and 9.18c have more OTLs in the middle effect sizes. Because Fisher's and Orr's models make abstract rather than specific predictions they are difficult to test in practice. In addition, the potential biases and uncertainties in OTL data themselves leave us uncertain whether the distribution of effect sizes has been estimated accurately.

Chapter 9 review

• Variation in quantitative trait values among individuals within a population (Vp) has both genetic and environmental causes. The genetic causes are due to genotypic variance (VG) that can be partitioned into the distinct components of additive (VA), dominance (VD), and epistasis (Vj) variance.

• Phenotypic variation can be caused by genotype-by-environment interaction (VGxE) where genotypes express heterogeneous phenotypic values in response to different environmental conditions.

• The additive component (VA) of the genotypic variance (VG) is caused by the sum of the phenotypic effects of alleles when they are assembled into genotypes. Phenotypic effects of alleles cause the resemblance of parents and offspring as well as the resemblance among relatives.

• Dominance (VD) and epistasis (Vj) components of VG are caused by the effects of genotypes. VD and Vj do not contribute to phenotypic resemblance between parents and offspring because particulate inheritance breaks up genotypes (additive by additive epistasis is an exception).

• The proportion of the total genotypic variance (VG) due to the additive effects of alleles is measured by the narrow-sense heritability h2 = VA/Vp. Parent-offspring regression is one method to estimate h2.

• Response to selection over one generation depends on the force of natural selection and the heritability and is predicted by the breeder's equation R = h2s.

• Because traits show both genetic and phenotypic correlations, response to selection on one trait may change the mean of other correlated traits or be constrained by correlations with other traits.

• Long-term response to natural selection depends on the number of loci that underlie a quantitative trait. Linear response to selection over many generations is expected when many loci with small effects underlie a trait, consistent with the infinitesimal model. In contrast, selection plateaus are consistent with fewer loci of larger effect since selection causes fixation and loss at these loci. Depending on the rate, mutation may replace variation lost due to fixation and loss caused by response to selection.

• The neutral evolution of genotypic variance depends on the balance of genetic variation lost by genetic drift and mutation that replaces variation.

• The individual loci that cause variation in quantitative traits, or OTLs, can be identified by taking advantage of gametic disequilibrium between OTLs and genetic marker loci.

• In an F2 mating design, comparing the phenotypic means of F2 individuals bearing different marker genotypes identifies marker loci near OTLs.

• OTL mapping can only identify alleles that are segregating in the individuals used to found the mapped populations. OTL mapping tends to underestimate the true number of OTLs and overestimate the true effects of OTLs.

• OTL mapping quantifies the genetic architecture of quantitative traits by estimating the number of loci that cause quantitative trait variation, the distribution of OTL phenotypic effects, and the physical organization of OTLs on chromosomes.

Further reading

For a review of the progress over the last one hundred years on fundamental questions in quantitative genetics and the evolution of quantitative traits see:

Roff DA. 2007. A centennial celebration for quantitative genetics. Evolution 61: 1017-32.

More detail on statistical estimators as well as experimental designs used to estimate heritability and map OTLs can be found in:

Lynch M and Walsh B. 1998. Genetics and Analysis of Quantitative Traits. Sinauer Associates, Sunderland, MA.

The response to selection predicted by the breeder's equation is actually an approximation that neglects four other types of parent-offspring phenotype relationship, as explained in:

Heywood JS. 2005. An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection. Evolution 59: 2287-98.

The concepts involved in predicting levels of quantitative genetic variation and the evolution of quantitative traits are reviewed by:

Barton NH and Keightley PD. 2002. Understanding quantitative genetic variation. Nature Reviews Genetics 3: 11-21.

Quantitative trait mapping methods and empirical observations from QTL mapping are reviewed by:

Mackay TFC. 2001. The genetic architecture of quantitative traits. Annual Reviews of Genetics 35: 303-39.

For a review of how epistasis can be detected in QTL mapping studies, see:

Carlborg O and Haley CS. 2004. Opinion: epistasis: too often neglected in complex trait studies? Nature Reviews Genetics 5: 618-25.

For a critical review of the evolutionary inferences about quantitative traits that can be drawn from QTL mapping data, see:

Erickson DL, Fenster CB, Sten0ien HK, and Price D. 2004. Quantitative trait locus analyses and the study of evolutionary process. Molecular Ecology 13: 2505-22.

Problem box answers

Problem box 9.1 answer

For three diallelic loci each with codominance, the expected genotype frequencies in the population can be obtained by expanding

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