In mapping of quantitative trait loci (QTLs), performing hypothesis tests of linkage to a phenotype of interest across an entire genome involves multiple comparisons. Furthermore, linkage among loci induces correlation among tests. Under many multiple comparison frameworks, these problems are exacerbated when mapping multiple QTLs. Traditionally, significance thresholds have been subjectively set to control the probability of detecting at least one false positive outcome, although such thresholds are known to result in excessively low power to detect true positive outcomes. Recently, false discovery rate (FDR)-controlling procedures have been developed that yield more power both by relaxing the stringency of the significance threshold and by retaining more power for a given significance threshold. However, these procedures have been shown to perform poorly for mapping QTLs, principally because they ignore recombination fractions between markers. Here, I describe a procedure that accounts for recombination fractions and extends FDR control to include simultaneous control of the false non-discovery rate, i.e. the overall error rate is controlled. This procedure is developed in the Bayesian framework using a direct posterior probability approach. Data-driven significance thresholds are determined by minimizing the expected loss. The procedure is equivalent to jointly maximizing positive and negative predictive values. In the context of mapping QTLs for experimental crosses, the procedure is applicable to mapping main effects, gene–gene interactions and gene–environment interactions.

Increasing resistance to acute salmonellosis (defined as bacteraemia in animals showing symptoms) is not sufficient for food safety, because of the risk of carrier state (when animals excrete bacteria without showing any symptoms). Increased resistance to Salmonella carrier state is therefore needed. Two experiments of divergent selection on resistance at a younger and a later age lead to significant differences between lines and allowed estimating genetic parameters on 4262 animals. Heritability of resistance was estimated at 0·16 in chicks, while it varied from 0·14 to 0·23 with analysed organ in adult hens. Genetic correlations between contamination of the different organs ranged from 0·46 to 0·67, while correlations between resistance at both ages were estimated at −0·50, showing that increasing genetic resistance of hens will reduce resistance in chicks. Highest estimated absolute values of genetic correlations between resistance and production traits were, for chicken contamination level, with number of eggs laid between 41 and 60 (0·37) and, for adult contamination, with number of eggs laid between 18 and 24 (0·37) or 25 and 40 (−0·33) weeks of age.

Fine scale analyses of signatures of selection allow assessing quantitative aspects of a species' evolutionary genetic history, such as the strength of selection on genes. When several selected loci lie in the same genomic region, their epistatic interactions may also be investigated. Here, we study how the neutral polymorphism pattern was shaped by two close recombining loci that cause ‘sex-ratio’ meiotic drive in Drosophila simulans, as an example of strong selection with potentially strong epistasis. We compare the polymorphism data observed in a natural population with the results of forward stochastic simulations under several contexts of epistasis between the candidate loci for the drive. We compute the likelihood of different possible scenarios, in order to determine which configuration is most consistent with the data. Our results highlight that fine scale analyses of well-chosen candidate genomic regions provide information-rich data that can be used to investigate the genotype–phenotype–fitness map, which can hardly be studied in genome-wide analyses. We also emphasize that initial conditions and time of observation (here, time after the interruption of a partial selective sweep) are crucial parameters in the interpretation of real data, while these are often overlooked in theoretical studies.

Correlation statistics can be used to measure the amount of linkage disequilibrium (LD) between two loci in subdivided populations. Within populations, the square of the correlation of gene frequencies, r2, is a convenient measure of LD. Between populations, the statistic rirj, for populations i and j, measures the relatedness of LD. Recurrence relationships for these two parameters are derived for the island model of population subdivision, under the assumptions of the linked identity-by-descent (LIBD) model in which correlation measures are equated to probability measures. The recurrence relationships closely predict the build-up of r2 and rirj following population subdivision in computer simulations. The LIBD model predicts that a steady state will be reached with r2 equal to 1/[1+4Nec(1+(k−1)ρ)], where k is the number of island populations, Ne is the effective local population (island) size, and ρ measures the ratio of migration (m) to recombination (c) and is equal to m/[c(k−1)+m]. For low values of m/c, ρ=0, and E(r2) is equal to 1/(1+4Nec). For high values of m/c, ρ=1, and E(r2) is equal to 1/(1+4kNec). The value of rirj following separation eventually settles down to a steady state whose expectation, E(rirj), is equal to E(r2) multiplied by ρ. Equations predicting the change in rirj values are applied to the separation of African (Yoruba – YRI) and non-African (European – CEU) populations, using data from Hapmap. The primary data lead to an estimate of separation time of less than 1000 generations if there has been no migration, which is around one-third of minimum current estimates. Ancient rather than recent migration can explain the form of the data.

In self-pollinating populations, individuals are characterized by a high degree of inbreeding. Additionally, phenotypic observations are highly influenced by genotype-by-environment interaction effects. Usually, Bayesian approaches to predict breeding values (in self-pollinating crops) omit genotype-by-environment interactions in the statistical model, which may result in biased estimates. In our study, a Bayesian Gibbs sampling algorithm was developed that is adapted to the high degree of inbreeding in self-pollinated crops and accounts for interaction effects between genotype and environment. As related lines are supposed to show similar genotype-by-environment interaction effects, an extended genetic relationship matrix is included in the Bayesian model. Additionally, since the coefficient matrix C in the mixed model equations can be characterized by rank deficiencies, the pseudoinverse of C was calculated by using the nullspace, which resulted in a faster computation time. In this study, field data of spring barley lines and data of a ‘virtual’ parental population of self-pollinating crops, generated by computer simulation, were used. For comparison, additional breeding values were predicted by a frequentist approach. In general, standard Bayesian Gibbs sampling and a frequentist approach resulted in similar estimates if heritability of the regarded trait was high. For low heritable traits, the modified Bayesian model, accounting for relatedness between lines in genotype-by-environment interaction, was superior to the standard model.

We present an approach to describe and evaluate changes in genetic diversity and to calculate bounds for improvement. This pedigree-based analysis was applied to the Kromfohrländer dog (FCI Gr9 Sec10). Pedigrees trace back to the foundation of the breed and were available for 5527 individuals. Based on this dataset the population structure and historical bottlenecks were studied. Distributions of allele frequencies were estimated by Monte Carlo simulation. To monitor changes in mating systems throughout the breeding history, the homozygosity of alleles was compared with their expectations in Hardy–Weinberg equilibrium. Different breeding lines were identified by hierarchical cluster analysis and were characterized by ancestor contributions. Our calculations showed that the founder event in 1945 was followed by two bottlenecks. One was caused by strong selection in a very small population, and the other was triggered by rigorous disease management. The necessary amount of purging that arised due to the bottlenecks was also discussed.