Effectiveness of marker-assisted selection (MAS) and quantitative trait locus (QTL) mapping using population-wide linkage disequilibrium (LD) between markers and QTLs depends on the extent of LD and how it declines with distance between markers and QTLs in a population. Marker–QTL LD can be predicted from LD between markers. Our previous work evaluated LD measures between multi-allelic markers as predictors of usable LD of multi-allelic markers with QTLs. Since single nucleotide polymorphisms (SNPs) are the current marker of choice for high-density genotyping and LD-mapping of QTLs, the objective of this study was to use LD between multi-allelic markers to predict LD among biallelic SNPs or between SNPs and QTLs. Observable LD between multi-allelic markers was evaluated using nine measures. These included two pooled and standardized measures of LD between pairs of alleles at two markers based on Lewontin's LD measure, two pooled measures of squared correlations between alleles, one standardized measure using Hardy–Weinberg heterozygosities, and four measures based on the chi-square statistic for testing for association between alleles at two loci. The standardized chi-square measure that best predicted usable LD between multi-allelic markers and QTLs, based on our previous work, overestimated usable SNP–SNP or SNP–QTL LD. Instead, three other measures were found to be good predictors of usable SNP–SNP or SNP–QTL LD when LD is generated by drift. Therefore, the LD measure between multi-allelic markers that is best for predicting usable LD in a population depends on the type of markers (i.e. multi-allelic or biallelic) that will eventually be used for QTL mapping or MAS.

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of non-recombining genomes, such as the mitochondria, the degeneration of the Y chromosome, and the evolution of sex and recombination. Here we study the speed of Muller's ratchet in a spatially structured population which is subdivided into many small populations (demes) connected by migration, and distributed on a graph. We studied different types of networks: regular networks (similar to the stepping-stone model), small-world networks and completely random graphs. We show that at the onset of the small-world network – which is characterized by high local connectivity among the demes but low average path length – the speed of the ratchet starts to decrease dramatically. This result is independent of the number of demes considered, but is more pronounced the larger the network and the stronger the deleterious effect of mutations. Furthermore, although the ratchet slows down with increasing migration between demes, the observed decrease in speed is smaller in the stepping-stone model than in small-world networks. As migration rate increases, the structured populations approach, but never reach, the result in the corresponding panmictic population with the same number of individuals. Since small-world networks have been shown to describe well the real contact networks among people, we discuss our results in the light of the evolution of microbes and disease epidemics.

The importance of variance modelling is now widely known for the analysis of microarray data. In particular the power and accuracy of statistical tests for differential gene expressions are highly dependent on variance modelling. The aim of this paper is to use a structural model on the variances, which includes a condition effect and a random gene effect, and to propose a simple estimation procedure for these parameters by working on the empirical variances. The proposed variance model was compared with various methods on both real and simulated data. It proved to be more powerful than the gene-by-gene analysis and more robust to the number of false positives than the homogeneous variance model. It performed well compared with recently proposed approaches such as SAM and VarMixt even for a small number of replicates, and performed similarly to Limma. The main advantage of the structural model is that, thanks to the use of a linear mixed model on the logarithm of the variances, various factors of variation can easily be incorporated in the model, which is not the case for previously proposed empirical Bayes methods. It is also very fast to compute and is adapted to the comparison of more than two conditions.

Whether there are different genes involved in response to different environmental signals and how these genes interact to determine the final expression of the trait are of fundamental importance in agricultural and biological research. We present a statistical framework for mapping environment-induced genes (or quantitative trait loci, QTLs) of major effects on the expression of a trait that respond to changing environments. This framework is constructed with a maximum-likelihood-based mixture model, in which the mean and covariance structure of environment-induced responses is modelled. The means for responses to continuous environmental states, referred to as reaction norms, are approximated for different QTL genotypes by mathematical equations that were derived from fundamental biological principles or based on statistical goodness-of-fit to observational data. The residual covariance between different environmental states was modelled by autoregressive processes. Such an approach to studying the genetic control of reaction norms can be expected to be advantageous over traditional mapping approaches in which no biological principles and statistical structures are considered. We demonstrate the analytical procedure and power of this approach by modelling the photosynthetic rate process as a function of temperature and light irradiance. Our approach allows for testing how a QTL affects the reaction norm of photosynthetic rate to a specific environment and whether there exist different QTLs to mediate photosynthetic responses to temperature and light irradiance, respectively.

European water frog hybrids Rana esculenta (R. ridibunda×R. lessonae) reproduce hemiclonally, by hybridogenesis: in the germ line they exclude the genome of one parental species and produce haploid gametes with an unrecombined genome of the other parental species. In the widespread L-E population system, both sexes of hybrids (E) coexist with R. lessonae (L). They exclude the lessonae genome and produce ridibunda gametes. In the R-E system, hybrid males coexist with R. ridibunda (R); they exclude either their ridibunda or their lessonae genome and produce sperm with a lessonae or with a ridibunda genome or a mixture of both kinds of sperm. We examined 13 male offspring, 12 of which were from crosses between L-E system and R-E system frogs. All were somatically hybrid. With one exception, they excluded the lessonae genome in the germ line and subsequently endoreduplicated the ridibunda genome. Spermatogonial metaphases contained a haploid or a diploid number of ridibunda chromosomes, identified through in situ hybridization to a satellite DNA marker, and by spermatocyte I metaphases containing a haploid number of ridibunda bivalents. The exception, an F1 hybrid between L-E system R. lessonae and R-E system R. ridibunda, was not hybridogenetic, showed no genome exclusion, and evidenced a disturbed gametogenesis resulting from the combination of two heterospecific genomes. None of the hybridogenetic hybrids showed any cell lines excluding the ridibunda genome, the pattern most frequent in hybrids of the R-E system, unique to that system, and essential for its persistence. A particular combination of R-E system lessonae and R-E system ridibunda genomes seems necessary to induce the R-E system type of hemiclonal gametogenesis.

Multiple-trait analyses have been shown to improve the detection of quantitative trait loci (QTLs) with multiple effects. Here we applied a multiple-trait approach on obesity- and growth-related traits that were surveyed in 275 F2 mice generated from an intercross between the high body weight selected line NMRI8 and DBA/2 as lean control. The parental lines differed 2·5-fold in body weight at the age of 6 weeks. Within the F2 population, the correlations between body weight and weights of abdominal fat weight, muscle, liver and kidney at the age of 6 weeks were about 0·8. A least squares multiple-trait QTL analysis was performed on these data to understand more precisely the cause of the genetic correlation between body weight, body composition traits and weights of inner organs. Regions on Chr 1, 2, 7 and 14 for body weights at different early ages and regions on Chr 1, 2, 4, 7, 14, 17 and 19 for organ weights at 6 weeks were found to have significant multiple effects at the genome-wide level.