Gene action underlying selection responses has been studied using crossbreeding. Maximum likelihood based segregation analysis has been presented for analysing backcross data for the presence of genes with a large effect. Two sets of divergently selected lines (P-lines for body weight and F-lines for fat content) were reciprocally crossed and the F1s were crossed to the high and low lines to produce all possible backcrosses. Earlier analysis had shown that the difference in body weight at 10 weeks (n = 595) between the high and low P-lines was largely (75–80%) explained by autosomal, additive genes with the remainder explained by additive genes on the X chromosome. Maximum likelihood segregation analysis suggested the presence of a major effect on the X chromosome, but as there was only one round of recombination between the X chromosomes in the forming of the backcrosses, linked genes on the X chromosome could have acted together to give the appearance of a single major gene. The difference in fat content between the F-lines (n = 578) could be explained by autosomal genes of largely additive effect. Segregation analysis suggested the presence of a major gene with complete dominance, but this was attributed to a relationship between the mean and the variance: transformation of the data resulted in only polygenic additive genes being of importance. This study concluded that maximum likelihood based analysis and crosses between selected lines provide a powerful means for studying the gene action underlying responses to selection.

We used simultaneous mapping of interacting quantitative trait locus (QTL) pairs to study various growth traits in a chicken F2 intercross. The method was shown to increase the number of detected QTLs by 30% compared with a traditional method detecting QTLs by their marginal genetic effects. Epistasis was shown to be an important contributor to the genetic variance of growth, with the largest impact on early growth (before 6 weeks of age). There is also evidence for a discrete set of interacting loci involved in early growth, supporting the previous findings of different genetic regulation of early and late growth in chicken. The genotype–phenotype relationship was evaluated for all interacting QTL pairs and 17 of the 21 evaluated QTL pairs could be assigned to one of four clusters in which the pairs in a cluster have very similar genetic effects on growth. The genetic effects of the pairs indicate commonly occurring dominance-by-dominance, heterosis and multiplicative interactions. The results from this study clearly illustrate the increase in power obtained by using this novel method for simultaneous detection of epistatic QTL, and also how visualization of genotype–phenotype relationships for epistatic QTL pairs provides new insights to biological mechanisms underlying complex traits.

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.

Previous studies have noted that the estimated positions of a large proportion of mapped quantitative trait loci (QTLs) coincide with marker locations and have suggested that this indicates a bias in the mapping methodology. In this study we predict the expected proportion of QTLs with positions estimated to be at the location of a marker and further examine the problem using simulated data. The results show that the higher proportion of putative QTLs estimated to be at marker positions compared with non-marker positions is an expected consequence of the estimation methods. The study initially focused on a single interval with no QTLs and was extended to include multiple intervals and QTLs of large effect. Further, the study demonstrated that the larger proportion of estimated QTL positions at the location of markers was not unique to linear regression mapping. Maximum likelihood produced similar results, although the accumulation of positional estimates at outermost markers was reduced when regions outside the linkage group were also considered. The bias towards marker positions is greatest under the null hypothesis of no QTLs or when QTL effects are small. This study discusses the impact the findings could have on the calculation of thresholds and confidence intervals produced by bootstrap methods.

Haseman and Elston (1972) developed a robust regression method for the detection of linkage between a marker and a quantitative trait locus (QTL) using sib pair data. The principle underlying this method is that the difference in phenotypes between pairs of sibs becomes larger as they share a decreasing number of alleles at a particular QTL identical by descent (IBD) from their parents. In this case, phenotypically very different sibs will also on average share a proportion of alleles IBD at any marker linked to the QTL that is lower than the expected value of 0·5. Thus, the deviation of the proportion of marker alleles IBD from the expected value in pairs of sibs selected to be phenotypically different (i.e. discordant) can provide a test for the presence of a QTL. A simple regression method for QTL detection in sib pairs selected for high phenotypic differences is presented here. The power of the analytical method was found to be greater than the power obtained using the standard analysis when samples of sib pairs with high phenotypic differences were used. However, the use of discordant sib pairs was found to be less powerful for QTL detection than alternative selective genotyping schemes based on the phenotypic values of the sibs except with intense selection, when its advantage was only marginal. The most effective selection scheme overall was the use of sib pairs from entire families selected on the basis of high within-family variance for the trait in question. There is little effect of selection on QTL position estimates, which are in good agreement with the simulated values. However, QTL variance estimates are biased to a greater or lesser degree, depending on the selection method.

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) by interval mapping was investigated using simulation. Confidence intervals were created using a non-parametric (resampling method) and parametric (resimulation method) bootstrap for a backcross population derived from inbred lines. QTLs explaining 1%, 5% and 10% of the phenotypic variance were tested in populations of 200 or 500 individuals. Results from the two methods were compared at all locations along one half of the chromosome. The non-parametric bootstrap produced results close to expectation at all non-marker locations, but confidence intervals when the QTL was located at the marker were conservative. The parametric method performed poorly; results varied from conservative confidence intervals at the location of the marker, to anti-conservative intervals midway between markers. The results were shown to be influenced by a bias in the mapping procedure and by the accumulation of type 1 errors at the location of the markers. The parametric bootstrap is not a suitable method for constructing confidence intervals in QTL mapping. The confidence intervals from the non-parametric bootstrap are accurate and suitable for practical use.