A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation–selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.

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.

Genetic markers throughout the genome can be used to speed up ‘recovery’ of the recipient genome in the backcrossing phase of the construction of a congenic strain. The prediction of the genomic proportion during backcrossing depends on the assumptions regarding the distribution of chromosome segments, the population structure, the marker spacing and the selection strategy. In this study simulation was used to investigate the rate of recovery of the recipient genome for a mouse, Drosophila and Arabidopsis genome. It was shown that an incorrect assumption of a binomial distribution of chromosome segments, and failing to take account of a reduction in variance in genomic proportion due to selection, can lead to a downward bias of up to two generations in the estimation of the number of generations required for the formation of a congenic strain.

Estimation of variance components with the finite polygenic model (FPM) was evaluated. Phenotypic data for a 6300-pedigree simulated under a wide range of additive genetic models were analysed with constant homozygote difference across loci using deterministic Maximum Likelihood (DML) and a Bayesian method implemented via Gibbs sampling (BGS). Results indicate that under no selection, both DML and BGS accurately estimated the variance components, with a FPM of 5 loci or more. When both analysis methods were applied to equivalent data sets on populations that had undergone selection, the DML method produced upward biased estimates of additive genetic variation and heritability due to its use of pedigree loop cutting, while BGS provided more accurate estimation. BGS was extended to non-additive FPMs with variable homozygote differences and dominance effect across loci. This method was used to analyse data simulated under two genetic models with positive, completely dominant gene action at all loci. Results indicate that the estimates of additive and dominance variances slowly increase as the number of loci in the FPM for analysis increases, while accuracy of predicting individual breeding values and dominance deviations remains unaffected. For the simulated pedigree structure, a FPM with 10 loci or slightly fewer appears to be appropriate for variance component estimation in the presence of dominance.

A recent paper in this journal by Deng, Li and Li has investigated methods to estimate rates and effects of polygenic mutations using data from mutation accumulation experiments. Here, I evaluate a number of critical points in this paper concerning a maximum likelihood (ML) procedure to analyse mutation accumulation data. I show that Deng, Li and Li's criticisms are based on misunderstandings, or numerical problems they encountered that could have been readily overcome. In Monte Carlo simulations, I show that ML can give a considerable increase in precision over the method of moments that is traditionally used to analyse mutation accumulation data. Furthermore, ML allows the comparison of the fit of different models for the distribution of mutation effects.

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.

In dairy cattle, quantitative trait loci (QTL) are usually mapped using the grand-daughter design (GDD), i.e. sets of progeny-tested paternal half-brothers. Linkage information is typically extracted from the segregation of the sire chromosomes amongst their sons. We herein propose to increase the power of a GDD by exploiting the frequently occurring relationship between sires and grandsons which has so far been ignored in most methods of analysis. The proposed approach is a multipoint interval mapping method based on the Wilcoxon sum-of-rank test. Three alternative approaches to combine information from sons and grandsons are evaluated by simulation. In these either (i) sons and grandsons are ranked separately, (ii) sons and grandsons are ranked separately but the sign of the QTL effect is constrained to be the same in both generations, or (iii) sons and grandsons are ranked jointly. The proposed methods have been applied on a real data-set in which a GDD including 907 sons is analysed with a marker map comprising nine microsatellites spanning 46 cM on bovine chromosome 6.

Sponsored by: The Wellcome Trust and B & K Universal Group Limited

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.