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.

The value of a new crop species is usually judged by the overall performance of multiple traits. Therefore, in most quantitative trait locus (QTL) mapping experiments, researchers tend to collect phenotypic records for multiple traits. Some traits may vary continuously and others may vary in a discrete fashion. Although mapping QTLs jointly for multiple traits is more efficient than mapping QTLs separately for individual traits, the latter is still commonly practised in QTL mapping. This is primarily due to the lack of efficient statistical methods and computer software packages to implement the methods. Mapping multiple QTLs simultaneously in a single multivariate model has not been available, especially when categorical traits are involved. In the present study, we developed a Bayesian method to map QTLs of the entire genome for multiple traits with continuous, discrete or both types of phenotypic distribution. Instead of using the reversible jump Markov chain Monte Carlo (MCMC) for model selection, we adopt a parameter shrinkage approach to estimate the genetic effects of all marker intervals. We demonstrate the method by analysing a set of simulated data with both continuous and discrete traits. We also apply the method to mapping QTLs responsible for multiple disease resistances to the blast fungus of rice. A computer program written in SAS/IML that implements the method is freely available, on request, to academic researchers.

General and genetic statistical methods are commonly used to deal with microsatellite data (highly variable neutral genetic markers). In this paper, the self-organizing map (SOM) that belongs to the unsupervised artificial neural networks (ANNs) was applied to analyse the structure of 58 European and two Chinese pig populations (Sus scrofa) including commercial lines, local breeds and cosmopolitan breeds. Results were compared with other unsupervised classification or ordination methods such as factorial correspondence analysis, hierarchical clustering from an allele sharing distance and the Bayesian genetic model and with principal components analysis and neighbour joining from allelic frequencies and genetic distances between populations. Like other methods, SOMs were able to classify individuals according to their breed origin and to visualize similarities between breeds. They provided additional information on the within- and between-population diversity, allowed differences between similar populations to be highlighted and helped differentiate different groups of populations.

Studies on inheritance of fertility are of great importance in wheat breeding. Although substantial progress has been achieved in molecular characterization of male sterility and fertility restoration recently, little effort has been devoted to female sterility. To identify the gene(s) controlling female sterility in wheat efficiently, an investigation was conducted for the seed setting ratio using a set of F2 populations derived from the cross between a female sterile line XND126 and an elite cultivar Gaocheng 8901. Bulked segregation analysis (BSA) method and recessive class approach were adopted to screen for SSR markers potentially linked to female fertility gene loci in 2005. Out of 1080 SSRs in wheat genome, eight markers on chromosome 2D showed a clear difference between two disparate bulks and small recombination frequency values, suggesting a strong linkage signal to the sterility gene. Based on the candidate linked markers, partial linkage maps were constructed with Mapmaker 3.0 (EXP) instead of whole genome maps, and quantitative trait locus (QTL) mapping was implemented with software QTLNetwork 2.0. A major gene locus designated as taf1, was located on chromosome 2DS. The above result was confirmed by the analysis for 2007 data, and taf1 was identified on the same chromosome 2DS with a confidence interval of 2·4 cM, which could explain 44·99% of phenotypic variation. These results provided fundamental information for fine mapping studies and laid the groundwork for wheat fertility genetic studies.

Susceptibility to scrapie is known to be associated with polymorphisms at the prion protein (PrP) gene, and this association is the basis of current selective programmes implemented to control scrapie in many countries. However, these programmes might have unintended consequences for other traits that might be associated with PrP genotype. The objective of this study was to investigate the relationship between PrP genotype and coat colour characteristics in two UK native sheep breeds valued for their distinctive coat colour patterns. Coat colour pattern, darkness and spotting and PrP genotype records were available for 11 674 Badgerfaced Welsh Mountain and 2338 Shetland sheep. The data were analysed with a log–linear model using maximum likelihood. Results showed a strong significant association of PrP genotype with coat colour pattern in Badgerfaced Welsh Mountain and Shetland sheep and with the presence of white spotting in Shetland sheep. Animals with the ARR/ARR genotype (the most scrapie resistant) had higher odds of having a light dorsum and a dark abdomen than the reverse pattern. The implication of these associations is that selection to increase resistance to scrapie based only on PrP genotype could result in change in morphological diversity and affect other associated traits such as fitness.

The patterns of linkage disequilibrium (LD) between dense polymorphic markers are shaped by the ancestral population history. It is therefore possible to use multilocus predictors of LD to infer past population history and to infer sharing of identical alleles in quantitative trait locus (QTL) studies. We develop a multilocus predictor of LD for pairs of haplotypes, which we term haplotype homozygosity (HHn): the probability that any two haplotypes share a given number of n adjacent identical markers or ‘runs of homozygosity’. Our method, based on simplified coalescence theory, accounts for recombination and mutation. We compare our HHn predictions, with HHn in simulated populations and with two published predictors of HHn. Our method performs consistently better across a range of population parameters, including populations with a severe bottleneck followed by expansion, compared to two published methods. We demonstrate that we can predict the pattern of HHn observed in dense single nucleotide polymorphisms (SNPs) genotyped in a cattle population, given appropriate historical changes in population size. Our method is practical for use with very large numbers of individuals and dense genome wide polymorphic DNA data. It has potential applications in inferring ancestral population history and QTL mapping studies.

Segmental duplications are enriched within many eukaryote genomes, and their potential consequence is gene duplication. While previous theoretical studies of gene duplication have mainly focused on the gene silencing process after fixation, the process leading to fixation is even more important for segmental duplications, because the majority of duplications would be lost before reaching a significant frequency in a population. Here, by a series of computer simulations, we show that purifying selection against loss-of-function mutations increases the fixation probability of a new duplicate gene, especially when the gene is haplo-insufficient. Theoretically, the probability of simultaneous preservation of both duplicate genes becomes twice the loss-of-function mutation rate (uc) when the population size (N), the degree of dominance of mutations (h) and the recombination rate between the duplicate genes (c) are all sufficiently large (Nuc>1, h>0·1 and c>uc). The preservation probability declines rapidly with h and becomes 0 when h=0 (haplo-sufficiency). We infer that masking deleterious loss-of-function mutations give duplicate genes an immediate selective advantage and, together with effects of increased gene dosage, would predominantly determine the fates of the duplicate genes in the early phase of their evolution.

This paper presents investigations of segregation distortion of six rice F2 populations generated from reciprocal F1 hybrids grown at three locations varied at altitudes from 400 to 2200 m. The F1s were derived from reciprocal crosses between cv. XMG, which is a japonica landrace traditionally grown at 2650 m altitude, and cv. N34, which is a japonica restorer possessing a fertility restoring (Rf) gene and cytoplasm of male sterility (CMS) donated by an indica cultivar. Among nine morphological traits of the F2 populations, only one was in normal distribution, eight were distorted in all or at least one population. Out of 16 polymorphic PCR markers, 10 markers distributed on 7 chromosomes were significantly distorted. Among these markers, RMAN7 and RM257 were distorted in both of the reciprocal populations, which suggested that nuclear genes had strong effects on segregation distortion. The other makers were distorted only in the populations with cytoplasm donated by XMG or N34. The results indicated that segregation of DNA markers was affected by cytoplasm background. Segregation distribution was also affected by altitude, since segregation distortions of most of the markers were detected not in all the three populations generated from F1 grown at the three altitudes, but only in one population from F1 grown at one altitude. Marker M45461, which is located within Rf-1 locus, was severely distorted towards N34 in all the populations with cytoplasm donated by N34, but not in the populations with cytoplasm provided by XMG. The results indicated that interaction between CMS and Rf gene had strong effects on distortion. Results of this study indicated that japonica cytoplasm did not cause distortion favouring a special parent, but indica cytoplasm made distortion favouring a maternal parent. The results suggested that indica cytoplasm was not well compatible with japonica nuclear background, while japonica cytoplasm did not have such trouble with indica nuclei. This study also found that the six F2 populations were divergent into two groups due to difference of cytoplasm background.

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.

Early karyotypic work revealed that female and male recombination rates in many species show pronounced differences, and this pattern of heterochiasmy has also been observed in modern linkage mapping studies. Several hypotheses to explain this phenomenon have been offered, ranging from strictly biological mechanisms related to the gametic differences between the sexes, to more evolutionary models based on sexually antagonistic selection. However, despite the long history of interest in heterochiasmy, empirical data has failed to support any theory or pattern consistently. Here I test two alternative evolutionary hypotheses regarding heterochiasmy across the eutherian mammals, and show that sexual dimorphism, but not sperm competition, is strongly correlated with recombination rate, suggesting that sexual antagonism is an important influence. However, the observed relationship between heterochiasmy and sexual dimorphism runs counter to theoretical predictions, with male recombination higher in species with high levels of sexual dimorphism. This may be the response to male-biased dispersal, which, rather than the static male fitness landscape envisioned in the models tested here, could radically shift optimal male fitness parameters among generations.

We used a least absolute shrinkage and selection operator (LASSO) approach to estimate marker effects for genomic selection. The least angle regression (LARS) algorithm and cross-validation were used to define the best subset of markers to include in the model. The LASSO–LARS approach was tested on two data sets: a simulated data set with 5865 individuals and 6000 Single Nucleotide Polymorphisms (SNPs); and a mouse data set with 1885 individuals genotyped for 10 656 SNPs and phenotyped for a number of quantitative traits. In the simulated data, three approaches were used to split the reference population into training and validation subsets for cross-validation: random splitting across the whole population; random sampling of validation set from the last generation only, either within or across families. The highest accuracy was obtained by random splitting across the whole population. The accuracy of genomic estimated breeding values (GEBVs) in the candidate population obtained by LASSO–LARS was 0·89 with 156 explanatory SNPs. This value was higher than those obtained by Best Linear Unbiased Prediction (BLUP) and a Bayesian method (BayesA), which were 0·75 and 0·84, respectively. In the mouse data, 1600 individuals were randomly allocated to the reference population. The GEBVs for the remaining 285 individuals estimated by LASSO–LARS were more accurate than those obtained by BLUP and BayesA for weight at six weeks and slightly lower for growth rate and body length. It was concluded that LASSO–LARS approach is a good alternative method to estimate marker effects for genomic selection, particularly when the cost of genotyping can be reduced by using a limited subset of markers.

The degree of starshape of a genealogy is readily detectable using summary statistics and can be taken as a surrogate for the effect of past demography and other non-neutral forces. Summary statistics such as Tajima's D and related measures are commonly used for this. However, it is well known that because of their neglect of the genealogy underlying a sample such neutrality tests are far from ideal. Here, we investigate the properties of two types of summary statistics that are derived by considering the genealogy: (i) genealogical ratios based on the number of mutations on the rootward branches, which can be inferred from sequence data using a simple algorithm and (ii) summary statistics that use properties of a perfectly star-shaped genealogy. The power of these measures to detect a history of exponential growth is compared with that of standard summary statistics and a likelihood method for the single and multi-locus case. Statistics that depend on pairwise measures such as Tajima's D have comparatively low power, being sensitive to the random topology of the underlying genealogy. When analysing multi-locus data, we find that the genealogical measures are most powerful. Provided reliable outgroup information is available they may constitute a useful alternative to full likelihood estimation and standard tests of neutrality.

Dense marker genotypes allow the construction of the realized relationship matrix between individuals, with elements the realized proportion of the genome that is identical by descent (IBD) between pairs of individuals. In this paper, we demonstrate that by replacing the average relationship matrix derived from pedigree with the realized relationship matrix in best linear unbiased prediction (BLUP) of breeding values, the accuracy of the breeding values can be substantially increased, especially for individuals with no phenotype of their own. We further demonstrate that this method of predicting breeding values is exactly equivalent to the genomic selection methodology where the effects of quantitative trait loci (QTLs) contributing to variation in the trait are assumed to be normally distributed. The accuracy of breeding values predicted using the realized relationship matrix in the BLUP equations can be deterministically predicted for known family relationships, for example half sibs. The deterministic method uses the effective number of independently segregating loci controlling the phenotype that depends on the type of family relationship and the length of the genome. The accuracy of predicted breeding values depends on this number of effective loci, the family relationship and the number of phenotypic records. The deterministic prediction demonstrates that the accuracy of breeding values can approach unity if enough relatives are genotyped and phenotyped. For example, when 1000 full sibs per family were genotyped and phenotyped, and the heritability of the trait was 0·5, the reliability of predicted genomic breeding values (GEBVs) for individuals in the same full sib family without phenotypes was 0·82. These results were verified by simulation. A deterministic prediction was also derived for random mating populations, where the effective population size is the key parameter determining the effective number of independently segregating loci. If the effective population size is large, a very large number of individuals must be genotyped and phenotyped in order to accurately predict breeding values for unphenotyped individuals from the same population. If the heritability of the trait is 0·3, and Ne=1000, approximately 5750 individuals with genotypes and phenotypes are required in order to predict GEBVs of un-phenotyped individuals in the same population with an accuracy of 0·7.

In this study, we attempted a molecular characterization of the 5S rDNA in two closely related species of carcharhiniform sharks, Rhizoprionodon lalandii and Rhizoprionodon porosus, as well as a further comparative analysis of available data on lampreys, several fish groups and other vertebrates. Our data show that Rhizoprionodon sharks carry two 5S rDNA classes in their genomes: a short repeat class (termed class I) composed of ~185 bp repeats, and a large repeat class (termed class II) arrayed in ~465 bp units. These classes were differentiated by several base substitutions in the 5S coding region and by completely distinct non-transcribed spacers (NTS). In class II, both species showed a similar composition for both the gene coding region and the NTS region. In contrast, class I varied extensively both within and between the two shark species. A comparative analysis of 5S rRNA gene sequences of elasmobranchs and other vertebrates showed that class I is closely related to the bony fishes, whereas the class II gene formed a separate cartilaginous clade. The presence of two variant classes of 5S rDNA in sharks likely maintains the tendency for dual ribosomal classes observed in other fish species. The present data regarding the 5S rDNA organization provide insights into the dynamics and evolution of this multigene family in the fish genome, and they may also be useful in clarifying aspects of vertebrate genome evolution.