It is now clear that the genetic basis of adaptation does not resemble that assumed by the infinitesimal model. Instead, adaptation often involves a modest number of factors of large effect and a greater number of factors of smaller effect. After reviewing relevant experimental studies, I consider recent theoretical attempts to predict the genetic architecture of adaptation from first principles. In particular, I review the history of work on Fisher's geometric model of adaptation, including recent studies which suggest that adaptation should be characterized by exponential distributions of gene effects. I also present the results of new simulation studies that test the robustness of this finding. I explore the effects of changes in the distribution of mutational effects (absolute versus relative) as well as in the nature of the character studied (total phenotypic effect versus single characters). The results show that adaptation towards a fixed optimum is generally characterized by an exponential effects trend.

The situation to which these studies point is not one of a large number of genes all with more or less equal effect. It seems, rather, that a small number of genes with large effects are responsible for most of the response, the remainder of the response being due to a larger number of loci with small effects.

D. S. Falconer (1981)

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's FST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2Neσ2m (1 + FST), where FST is Wright's among-population fixation index, Ne is the eigenvalue effective size of the metapopulation, and σ2m is the mutational variance. The expected additive genetic variance within populations is given by 2Neσ2e(1 − FST), and the variance among demes is given by 4FSTNeσ2m. These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, QST, is shown to be generally equal to FST for the neutral additive model. Thus, for all population structures, a value of QST greater than FST for neutral loci is evidence for spatially divergent evolution by natural selection.

This article outlines theoretical models of clines in additive polygenic traits, which are maintained by stabilizing selection towards a spatially varying optimum. Clines in the trait mean can be accurately predicted, given knowledge of the genetic variance. However, predicting the variance is difficult, because it depends on genetic details. Changes in genetic variance arise from changes in allele frequency, and in linkage disequilibria. Allele frequency changes dominate when selection is weak relative to recombination, and when there are a moderate number of loci. With a continuum of alleles, gene flow inflates the genetic variance in the same way as a source of mutations of small effect. The variance can be approximated by assuming a Gaussian distribution of allelic effects; with a sufficiently steep cline, this is accurate even when mutation and selection alone are better described by the ‘House of Cards’ approximation. With just two alleles at each locus, the phenotype changes in a similar way: the mean remains close to the optimum, while the variance changes more slowly, and over a wider region. However, there may be substantial cryptic divergence at the underlying loci. With strong selection and many loci, linkage disequilibria are the main cause of changes in genetic variance. Even for strong selection, the infinitesimal model can be closely approximated by assuming a Gaussian distribution of breeding values. Linkage disequilibria can generate a substantial increase in genetic variance, which is concentrated at sharp gradients in trait means.

Most of the major genetic concerns in conservation biology, including inbreeding depression, loss of evolutionary potential, genetic adaptation to captivity and outbreeding depression, involve quantitative genetics. Small population size leads to inbreeding and loss of genetic diversity and so increases extinction risk. Captive populations of endangered species are managed to maximize the retention of genetic diversity by minimizing kinship, with subsidiary efforts to minimize inbreeding. There is growing evidence that genetic adaptation to captivity is a major issue in the genetic management of captive populations of endangered species as it reduces reproductive fitness when captive populations are reintroduced into the wild. This problem is not currently addressed, but it can be alleviated by deliberately fragmenting captive populations, with occasional exchange of immigrants to avoid excessive inbreeding. The extent and importance of outbreeding depression is a matter of controversy. Currently, an extremely cautious approach is taken to mixing populations. However, this cannot continue if fragmented populations are to be adequately managed to minimize extinctions. Most genetic management recommendations for endangered species arise directly, or indirectly, from quantitative genetic considerations.

Hypertrophied sexually dimorphic eye stalks have evolved independently in several families of Diptera, with the eyespan of males exceeding their total body length in some species. These structures function in intermale contests for territories and in mate attraction, the classical mechanisms of sexual selection. In the family Diopsidae, species with extremely exaggerated eye stalks and marked sexual dimorphism in relative eyespan also usually have strongly female-biased sex ratios in nature caused by X-linked meiotic drive, whereas species with relatively small eye stalks have little or no sexual dimorphism, often lack meiotic drive and have even sex ratios. We investigate the possible connection between sexual selection and sex-ratio meiotic drive by analysing a three-locus model for the evolution of female choice for a male character associated with meiotic drive. Both meiotic drive and the male character are X-linked and the female preference is autosomal. Our model shows that suppressed recombination between meiotic drive and the male character, e.g. by inversion of the X chromosome, is necessary for sex-ratio selection to promote the origin of female mating preferences and exaggerated secondary sexual characters. With complete suppression of recombination, sexual selection reduces the frequency of meiotic drive, and may eliminate it. Very rare recombination, gene conversion or mutation, at rates characteristic of chromosome inversions in Drosophila, restores the meiotic drive polymorphism to its original equilibrium. Sex-ratio meiotic drive may thus act as a catalyst accelerating the origin of female mating preference and exaggerated male traits.

Information on the genetic correlation between traits provides fundamental insight into the constraints on the evolutionary process. Estimates of such correlations are conventionally obtained by raising individuals of known relatedness in artificial environments. However, many species are not readily amenable to controlled breeding programmes, and considerable uncertainty exists over the extent to which estimates derived under benign laboratory conditions reflect the properties of populations in natural settings. Here, non-invasive methods that allow the estimation of genetic correlations from phenotypic measurements derived from individuals of unknown relatedness are introduced. Like the conventional approach, these methods demand large sample sizes in order to yield reasonably precise estimates, and special precautions need to be taken to eliminate bias from shared environmental effects. Provided the sample consists of at least 20% or so relatives, informative estimates of the genetic correlation are obtainable with sample sizes of several hundred individuals, particularly if supplemental information on relatedness is available from polymorphic molecular markers.

Many phenotypes respond physiologically or developmentally to continuously distributed environmental variables such as temperature and nutritional quality. Information about phenotypic plasticity can be used to improve the efficiency of artificial selection. Here we show that the quantitative genetic theory for ‘infinite-dimensional’ traits such as reaction norms provides a natural framework to accomplish this goal. It is expected to improve selection responses by making more efficient use of information about environmental effects than do conventional methods. The approach is illustrated by deriving an index for mass selection of a phenotypically plastic trait. We suggest that the same approach could be extended directly to more general and efficient breeding schemes, such as those based on general best linear unbiased prediction. Methods for estimating genetic covariance functions are reviewed.

We examine the relationships between a genetic marker and a locus affecting a quantitative trait by decomposing the genetic effects of the marker locus into additive and dominance effects under a classical genetic model. We discuss the structure of the associations between the marker and the trait locus, paying attention to non-random union of gametes, multiple alleles at the marker and trait loci, and non-additivity of allelic effects at the trait locus. We consider that this greater-than-usual level of generality leads to additional insights, in a way reminiscent of Cockerham's decomposition of genetic variance into five terms: three terms in addition to the usual additive and dominance terms. Using our framework, we examine several common tests of association between a marker and a trait.

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated parameters. Multiple interval mapping, which was recently proposed for simultaneously mapping multiple quantitative trait loci (QTL), is well suited to the identification and estimation of the genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance. With multiple traits and multiple environments involved in a QTL mapping experiment, pleiotropic effects and QTL by environment interactions can also be estimated. We review the method and discuss issues associated with multiple interval mapping, such as likelihood analysis, model selection, stopping rules and parameter estimation. The potential power and advantages of the method for mapping multiple QTL and estimating the genetic architecture are discussed. We also point out potential problems and difficulties in resolving the details of the genetic architecture as well as other areas that require further investigation. One application of the analysis is to improve genome-wide marker-assisted selection, particularly when the information about epistasis is used for selection with mating.

To test for epistasis and allele-specific environmental responses among quantitative trait loci (QTL) involved in the evolution of maize from its ancestor (teosinte), teosinte alleles of two QTL previously shown to control much of the morphological difference between these plants were introgressed into an isogenic maize background. Plants of each of the four two-locus homozygous classes for the two QTL were grown in two environments. Three morphological traits and the level of mRNA accumulation for one QTL (teosinte branched1, tb1) were measured. tb1 has a large additive effect on morphology that was correlated with its message level. The second QTL had only negligible effects on morphology when isolated in an isogenic background, but exhibited a strong interaction effect on morphology in combination with tb1. This interaction is also evident in tb1 message levels, suggesting that this second QTL may act as an upstream regulator of tb1. The combined effect of the maize alleles at the two QTL makes tb1 message levels over fourfold higher. Plants homozygous for the teosinte allele at tb1 showed greater phenotypic plasticity across environments than plants homozygous for the maize allele. Our results support two hypotheses. First, maize plant architecture may have evolved by selection for a gene complex rather than the additive effects of individual loci alone. Secondly, selection during maize domestication for an allele of tb1 which lacks environmental plasticity may have led to the fixation of a morphological form that can be induced in teosinte by environmental conditions.

We evaluated the hypothesis that the Drosophila melanogaster second chromosome gene scabrous (sca), a candidate sensory bristle number quantitative trait locus (QTL), contributes to naturally occurring variation in bristle number. Variation in abdominal and sternopleural bristle number was quantified for wild-derived sca alleles in seven genetic backgrounds: as homozygous second chromosomes (C2) in an isogenic background, homozygous lines in which approximately 20 cM including the sca locus had been introgressed into the isogenic background (sca BC), as C2 and sca BC heterozygotes and hemizygotes against a P element insertional sca allele and a P-induced sca deficiency in the same isogenic background, and as sca BC heterozygotes against the wild-type sca allele of isogenic strain. Molecular restriction map variation was determined for a 45 kb region including the sca locus, and single-stranded conformational polymorphism (SSCP) was examined for the third intron and parts of the third and fourth exons. Associations between each of the 27 molecular polymorphisms and bristle number were evaluated within each genotype and on the first principal component score determined from all seven genotypes, separately for each sex and bristle trait. Permutation tests were used to assess the empirical significance thresholds, accounting for multiple, correlated tests, and correlated markers. Three sites in regulatory regions were associated with female-specific variation in abdominal bristle number, one of which was an SSCP site in the region of the gene associated with regulation of sca in embryonic abdominal segments.

Over 20 years ago, D. S. Falconer and others launched an important avenue of research into the quantitative of body size growth in mice. This study continues in that tradition by locating quantitative trait loci (QTLs) responsible for murine growth, such as age-specific weights and growth periods, and examining the genetic architecture for body weight. We identified a large number of potential QTLs in an earlier F2 intercross (Intercross I) of the SM/J and LG/J inbred mouse strains. Many of these QTLs are replicated in a second F2 intercross (Intercross II) between the same two strains. These replicated regions provide candidate regions for future fine-mapping studies. We also examined body size and growth QTLs using the combined data set from these two intercrosses, resulting in 96 microsatellite markers being scored for 1045 individuals. An examination of the genetic architecture for age-specific weight and growth periods resulted in locating 20 separate QTLs, which were mainly additive in nature, although dominance was found to affect early growth and body size. QTLs affecting early and late growth were generally distinct, mapping to separate chromosome locations. This QTL pattern indicates largely separate genetic and physiological systems for early and later murine growth, as Falconer suggested. We also found sex-specific QTLs for body size with implications for the evolution of sexual dimorphism.

There are several instances in which quantitative trait locus (QTL) mapping experiments have been independently carried out for similar traits in different laboratories. We develop a permutation test of the correspondence between the test statistics obtained from genome-wide QTL scans in two such experiments to test whether the same QTLs are segregating in the experimental pair. In simulations, we show that the permutation test has the desired properties if chromosomes are of equal length, but bias can occur if chromosomes are of unequal length, a problem connected with autocorrelation of test statistic values. We apply the test to data from three recent mouse body weight QTL mapping experiments. The results from the test are non-significant, and imply a lack of overall concordance between the QTLs that were segregating in these experiments.

Data on the effects of inbreeding on fitness components are reviewed in the light of population genetic models of the possible genetic causes of inbreeding depression. Deleterious mutations probably play a major role in causing inbreeding depression. Putting together the different kinds of quantitative genetic data, it is difficult to account for the very large effects of inbreeding on fitness in Drosophila and outcrossing plants without a significant contribution from variability maintained by selection. Overdominant effects of alleles on fitness components seem not to be important in most cases. Recessive or partially recessive deleterious effects of alleles, some maintained by mutation pressure and some by balancing selection, thus seem to be the most important source of inbreeding depression. Possible experimental approaches to resolving outstanding questions are discussed.

Recent mutation accumulation results from invertebrate species suggest that mild deleterious mutation is far less frequent than previously thought, implying smaller expressed mutational loads. Although the rate (λ) and effect (s) of very slight deleterious mutation remain unknown, most mutational fitness decline would come from moderately deleterious mutation (s ≈ 0·2, λ ≈ 0·03), and this situation would not qualitatively change in harsh environments. Estimates of the average coefficient of dominance (h¯) of non-severe deleterious mutations are controversial. The typical value of h¯ = 0·4 can be questioned, and a lower estimate (about 0·1) is suggested. Estimated mutational parameters are remarkably alike for morphological and fitness component traits (excluding lethals), indicating low mutation rates and moderate mutational effects, with a distribution generally showing strong negative asymmetry and little leptokurtosis. New mutations showed considerable genotype–environment interaction. However, the mutational variance of fitness-component traits due to non-severe detrimental mutations did not increase with environmental harshness. For morphological traits, a class of predominantly additive mutations with no detectable effect on fitness and relatively small effect on the trait was identified. This should be close to that responsible for standing variation in natural populations.

To elucidate the involvement of growth hormone (GH) in the genetic change produced by long-term selection in growth and fatness, a ‘GH knock-out study’ on over 900 mice was undertaken. Lines used had been selected for more than 50 generations for high (PH) and low (PL) body weight (initially protein mass) at 70 d(ays) and for high (F) and low fat content (L) at 98 d, producing a 3-fold difference in body weight and a 5-fold difference in fat content. GH deficiency was achieved by repeated backcrossing into each line a recessive mutant gene (lit) which has a defective GH releasing factor receptor. In the absence of GH, the P lines still differ in body weight (21 d to 98 d): e.g. at 98 d homozygous lit/lit: PH = 24·2 g, PL = 10·0 g; wild-type (wt): PH = 57·4 g, PL = 18·7 g. The effect of the GH deficiency on body weight (untransformed) was very much larger in the PH than in the PL line, but the interaction was much smaller, although still significant, on the log scale. This indicates that changes in the GH system contribute only a small part of the selection response in growth. GH deficiency increased fat percentage in all lines (including P), especially in males (99 d, males lit/lit: F = 26·4%, L = 6·9%; wt: F = 22·0%, L = 4·8%; females: 20·2%, 5·2%, 20·7%, 3·0%) with significant genotype×line and genotype×sex interactions. The interactions between the effects of the lit gene and the genetic background were, however, relatively small compared with these main effects and again indicate that other systems contributed most of the selection response.