A simple and rapid method for calculating identity-by-descent matrices using multiple markers

A fast, partly recursive deterministic method for calculating Identity-by-Descent (IBD) probabilities was developed with the objective of using IBD in Quantitative Trait Locus (QTL) mapping. The method combined a recursive method for a single marker locus with a method to estimate IBD between sibs using multiple markers. Simulated data was used to compare the deterministic method developed in the present paper with a stochastic method (LOKI) for precision in estimating IBD probabilities and performance in the task of QTL detection with the variance component approach. This comparison was made in a variety of situations by varying family size and degree of polymorphism among marker loci. The following were observed for the deterministic method relative to MCMC: (i) it was an order of magnitude faster; (ii) its estimates of IBD probabilities were found to agree closely, even though it does not extract information when haplotypes are not known with certainty; (iii) the shape of the profile for the QTL test statistic as a function of location was similar, although the magnitude of the test statistic was slightly smaller; and (iv) the estimates of QTL variance was similar. It was concluded that the method proposed provided a rapid means of calculating the IBD matrix with only a small loss in precision, making it an attractive alternative to the use of stochastic MCMC methods. Furthermore, developments in marker technology providing denser maps would enhance the relative advantage of this method.     

SNP development from RNA‐seq data in a nonmodel fish: how many individuals are needed for accurate allele frequency prediction?

Single nucleotide polymorphisms (SNPs) are rapidly becoming the marker of choice in population genetics due to a variety of advantages relative to other markers, including higher genomic density, data quality, reproducibility and genotyping efficiency, as well as ease of portability between laboratories. Advances in sequencing technology and methodologies to reduce genomic representation have made the isolation of SNPs feasible for nonmodel organisms. RNA‐seq is one such technique for the discovery of SNPs and development of markers for large‐scale genotyping. Here, we report the development of 192 validated SNP markers for parentage analysis in Tripterygion delaisi (the black‐faced blenny), a small rocky‐shore fish from the Mediterranean Sea. RNA‐seq data for 15 individual samples were used for SNP discovery by applying a series of selection criteria. Genotypes were then collected from 1599 individuals from the same population with the resulting loci. Differences in heterozygosity and allele frequencies were found between the two data sets. Heterozygosity was lower, on average, in the population sample, and the mean difference between the frequencies of particular alleles in the two data sets was 0.135 ± 0.100. We used bootstrap resampling of the sequence data to predict appropriate sample sizes for SNP discovery. As cDNA library production is time‐consuming and expensive, we suggest that using seven individuals for RNA sequencing reduces the probability of discarding highly informative SNP loci, due to lack of observed polymorphism, whereas use of more than 12 samples does not considerably improve prediction of true allele frequencies.     

Estimating genetic diversity across the neutral genome with the use of dense marker maps

Background

With the advent of high throughput DNA typing, dense marker maps have become available to investigate genetic diversity on specific regions of the genome. The aim of this paper was to compare two marker based estimates of the genetic diversity in specific genomic regions lying in between markers: IBD-based genetic diversity and heterozygosity.

Methods

A computer simulated population was set up with individuals containing a single 1-Morgan chromosome and 1665 SNP markers and from this one, an additional population was produced with a lower marker density i.e. 166 SNP markers. For each marker interval based on adjacent markers, the genetic diversity was estimated either by IBD probabilities or heterozygosity. Estimates were compared to each other and to the true genetic diversity. The latter was calculated for a marker in the middle of each marker interval that was not used to estimate genetic diversity.

Results

The simulated population had an average minor allele frequency of 0.28 and an LD (r²) of 0.26, comparable to those of real livestock populations. Genetic diversities estimated by IBD probabilities and by heterozygosity were positively correlated, and correlations with the true genetic diversity were quite similar for the simulated population with a high marker density, both for specific regions (r = 0.19-0.20) and large regions (r = 0.61-0.64) over the genome. For the population with a lower marker density, the correlation with the true genetic diversity turned out to be higher for the IBD-based genetic diversity.

Conclusions

Genetic diversities of ungenotyped regions of the genome (i.e. between markers) estimated by IBD-based methods and heterozygosity give similar results for the simulated population with a high marker density. However, for a population with a lower marker density, the IBD-based method gives a better prediction, since variation and recombination between markers are missed with heterozygosity.     

Effects of the number of markers per haplotype and clustering of haplotypes on the accuracy of QTL mapping and prediction of genomic breeding values

The aim of this paper was to compare the effect of haplotype definition on the precision of QTL-mapping and on the accuracy of predicted genomic breeding values. In a multiple QTL model using identity-by-descent (IBD) probabilities between haplotypes, various haplotype definitions were tested i.e. including 2, 6, 12 or 20 marker alleles and clustering base haplotypes related with an IBD probability of > 0.55, 0.75 or 0.95. Simulated data contained 1100 animals with known genotypes and phenotypes and 1000 animals with known genotypes and unknown phenotypes. Genomes comprising 3 Morgan were simulated and contained 74 polymorphic QTL and 383 polymorphic SNP markers with an average r² value of 0.14 between adjacent markers. The total number of haplotypes decreased up to 50% when the window size was increased from two to 20 markers and decreased by at least 50% when haplotypes related with an IBD probability of > 0.55 instead of > 0.95 were clustered. An intermediate window size led to more precise QTL mapping. Window size and clustering had a limited effect on the accuracy of predicted total breeding values, ranging from 0.79 to 0.81. Our conclusion is that different optimal window sizes should be used in QTL-mapping versus genome-wide breeding value prediction.     

A comparison of simple sequence repeat and single nucleotide polymorphism marker technologies for the genotypic analysis of maize (<Emphasis Type="Italic">Zea mays</Emphasis> L.)

We report on the comparative utilities of simple sequence repeat (SSR) and single nucleotide polymorphism (SNP) markers for characterizing maize germplasm in terms of their informativeness, levels of missing data, repeatability and the ability to detect expected alleles in hybrids and DNA pools. Two different SNP chemistries were compared; single-base extension detected by Sequenom MassARRAY, and invasive cleavage detected by Invader chemistry with PCR. A total of 58 maize inbreds and four hybrids were genotyped with 80 SSR markers, 69 Invader SNP markers and 118 MassARRAY SNP markers, with 64 SNP loci being common to the two SNP marker chemistries. Average expected heterozygosity values were 0.62 for SSRs, 0.43 for SNPs (pre-selected for their high level of polymorphism) and 0.63 for the underlying sequence haplotypes. All individual SNP markers within the same set of sequences had an average expected heterozygosity value of 0.26. SNP marker data had more than a fourfold lower level of missing data (2.1-3.1%) compared with SSRs (13.8%). Data repeatability was higher for SNPs (98.1% for MassARRAY SNPs and 99.3% for Invader) than for SSRs (91.7%). Parental alleles were observed in hybrid genotypes in 97.0% of the cases for MassARRAY SNPs, 95.5% for Invader SNPs and 81.9% for SSRs. In pooled samples with mixtures of alleles, SSRs, MassARRAY SNPs and Invader SNPs were equally capable of detecting alleles at mid to high frequencies. However, at low frequencies, alleles were least likely to be detected using Invader SNP markers, and this technology had the highest level of missing data. Collectively, these results showed that SNP technologies can provide increased marker data quality and quantity compared with SSRs. The relative loss in polymorphism compared with SSRs can be compensated by increasing SNP numbers and by using SNP haplotypes. Determining the most appropriate SNP chemistry will be dependent upon matching the technical features of the method within the context of application, particularly in consideration of whether genotypic samples will be pooled or assayed individually.     

Investigation of altering single-nucleotide polymorphism density on the power to detect trait loci and frequency of false positive in nonparametric linkage analyses of qualitative traits

Genome-wide linkage analysis using microsatellite markers has been successful in the identification of numerous Mendelian and complex disease loci. The recent availability of high-density single-nucleotide polymorphism (SNP) maps provides a potentially more powerful option. Using the simulated and Collaborative Study on the Genetics of Alcoholism (COGA) datasets from the Genetics Analysis Workshop 14 (GAW14), we examined how altering the density of SNP marker sets impacted the overall information content, the power to detect trait loci, and the number of false positive results. For the simulated data we used SNP maps with density of 0.3 cM, 1 cM, 2 cM, and 3 cM. For the COGA data we combined the marker sets from Illumina and Affymetrix to create a map with average density of 0.25 cM and then, using a sub-sample of these markers, created maps with density of 0.3 cM, 0.6 cM, 1 cM, 2 cM, and 3 cM. For each marker set, multipoint linkage analysis using MERLIN was performed for both dominant and recessive traits derived from marker loci. Our results showed that information content increased with increased map density. For the homogeneous, completely penetrant traits we created, there was only a modest difference in ability to detect trait loci. Additionally, as map density increased there was only a slight increase in the number of false positive results when there was linkage disequilibrium (LD) between markers. The presence of LD between markers may have led to an increased number of false positive regions but no clear relationship between regions of high LD and locations of false positive linkage signals was observed.     

Matrix representation of the Haseman-Elston method.

The Hasemann-Elston method of linkage detection is based on the probabilities of a sib pair having 0, 1, or 2 alleles identical by descent (IBD) at a marker and a trait locus. These probabilities form a 3x3 matrix. Here, the characteristic values and characteristic vectors of this matrix were used to clarify the structure of the equations and to simplify calculations. As examples, the regression coefficients were derived for three genetic systems: a trait and a marker, two epistatic traits and two markers, and one trait locus and two markers. The last model was studied under the assumption of no crossover interference, the expression for allele IBD sharing at a trait locus was derived as a function of allele IBD sharing at two marker loci, and the regression is shown to be non-linear.     

Using Next Generation Sequencing for Multiplexed Trait-Linked Markers in Wheat

With the advent of next generation sequencing (NGS) technologies, single nucleotide polymorphisms (SNPs) have become the major type of marker for genotyping in many crops. However, the availability of SNP markers for important traits of bread wheat ( Triticum aestivum L.) that can be effectively used in marker-assisted selection (MAS) is still limited and SNP assays for MAS are usually uniplex. A shift from uniplex to multiplex assays will allow the simultaneous analysis of multiple markers and increase MAS efficiency. We designed 33 locus-specific markers from SNP or indel-based marker sequences that linked to 20 different quantitative trait loci (QTL) or genes of agronomic importance in wheat and analyzed the amplicon sequences using an Ion Torrent Proton Sequencer and a custom allele detection pipeline to determine the genotypes of 24 selected germplasm accessions. Among the 33 markers, 27 were successfully multiplexed and 23 had 100% SNP call rates. Results from analysis of "kompetitive allele-specific PCR" (KASP) and sequence tagged site (STS) markers developed from the same loci fully verified the genotype calls of 23 markers. The NGS-based multiplexed assay developed in this study is suitable for rapid and high-throughput screening of SNPs and some indel-based markers in wheat.     

Simultaneous fine mapping of multiple closely linked quantitative trait Loci using combined linkage disequilibrium and linkage with a general pedigree

Within a small region (e.g., <10 cM), there can be multiple quantitative trait loci (QTL) underlying phenotypes of a trait. Simultaneous fine mapping of closely linked QTL needs an efficient tool to remove confounded shade effects among QTL within such a small region. We propose a variance component method using combined linkage disequilibrium (LD) and linkage information and a reversible jump Markov chain Monte Carlo (MCMC) sampling for model selection. QTL identity-by-descent (IBD) coefficients between individuals are estimated by a hybrid MCMC combining the random walk and the meiosis Gibbs sampler. These coefficients are used in a mixed linear model and an empirical Bayesian procedure combines residual maximum likelihood (REML) to estimate QTL effects and a reversible jump MCMC that samples the number of QTL and the posterior QTL intensities across the tested region. Note that two MCMC processes are used, i.e., an (internal) MCMC for IBD estimation and an (external) MCMC for model selection. In a simulation study, the use of the multiple-QTL model clearly removes the shade effects between three closely linked QTL located at 1.125, 3.875, and 7.875 cM across the region of 10 cM, using 40 markers at 0.25-cM intervals. It is shown that the use of combined LD and linkage information gives much more useful information compared to using linkage information alone for both single- and multiple-QTL analyses. When using a lower marker density (11 markers at 1-cM intervals), the signal of the second QTL can disappear. Extreme values of past effective size (resulting in extreme levels of LD) decrease the mapping accuracy.     

Multiplexed,linkage group-specific SNP marker sets for rapid genetic mapping and fingerprinting of sugar beet (<Emphasis Type="Italic">Beta vulgaris</Emphasis> L.)

A set of single nucleotide polymorphism (SNP) markers has been developed for each of the nine linkage groups of sugar beet. Each set can monitor the polymorphic state at five to six linked marker loci. In each set, the loci selected for marker development are first amplified in a multiplexed reaction. These amplification products are the basis for sequence-specific elongation of primers adjacent to SNP positions. The extension step revealing SNP loci is based on fluorescently labelled nucleotides. In each set, primers developed to reveal SNP alleles differ in length to allow clear peak resolution in capillary electrophoresis. The nine linkage group (LG) –specific sets provide information on the polymorphism at a total of 52 SNP marker loci. Using the SNP-based tool, groups of concerned loci have been anchored to three different linkage maps of sugar beet. In a second experiment, sugar beet breeding lines have been fingerprinted. The use of the nine sets of LG-specific markers in sugar beet genetics and breeding is discussed. The information necessary to specify the 52 marker loci, as well as their map location, and all details concerning SNP assays, including allele type and nature of mutation, are reported.     

Comparison of SNPs and microsatellites for fine-scale application of genetic stock identification of Chinook salmon in the Columbia River Basin

Genetic stock identification (GSI) is an important tool in fisheries management. Microsatellites (μSATs) have been the dominant genetic marker for GSI; however, increasing availability and numerous advantages of single-nucleotide polymorphism (SNP) markers make them an appealing alternative. We tested performance of 13 μSAT vs. 92 SNP loci in a fine-scale application of GSI, using a new baseline for Chinook salmon consisting of 49 collections (n = 4014) distributed across the Columbia River Basin. In GSI, baseline genotypes for both marker sets were used independently to analyse a real fishery mixture (n = 2731) representing the total run of Chinook salmon passing Bonneville Dam in the Columbia River. Marker sets were evaluated using three criteria: (i) ability to differentiate reporting groups, (ii) proportion of correct assignment in mixture simulation tests and baseline leave-one-out analyses and (iii) individual assignment and confidence intervals around estimated stock proportions of a real fishery mixture. The μSATs outperformed the SNPs in resolving fine-scale relationships, but all 105 markers combined provided greatest power for GSI. SNPs were ranked by relative information content based on both an iterative procedure that optimized correct assignment to the baseline and ranking by minor allele frequency. For both methods, we identified a subset of the top 50 ranked loci, which were similar in assignment accuracy, and both reached maximum available power of the total 92 SNP loci (correct assignment = 73%). Our estimates indicate that between 100 and 200 highly informative SNP loci are required to meet management standards (correct assignment > 90%) for resolving stocks in finer-scale GSI applications.     

Comparative analysis of the effectiveness of STR and SNP markers for intraspecific and interspecific differentiation of the genus <Emphasis Type="Italic">Ovis</Emphasis>

A comparative study of the informativeness of SNP and STR markers for interspecific and intraspecific differentiation of the two species of the genus Ovis, snow sheep (O. nivicola) and domestic sheep (O. aries), was conducted. Eleven STR loci combined into two multiplex panels were examined. SNP analysis was performed with the DNA microarray OvineSNP50K BeadChip featuring 54241 SNPs. The possibility of clear differentiation of the studied Ovis species with both types of genetic markers was demonstrated. The advantages of SNP markers for intraspecific differentiation of the O. aries breeds and O. nivicola geographical groups were revealed. The areas of application of the studied types of DNA markers are discussed.     

Analysis and Optimization of Bulk DNA Sampling with Binary Scoring for Germplasm Characterization

The strategy of bulk DNA sampling has been a valuable method for studying large numbers of individuals through genetic markers. The application of this strategy for discrimination among germplasm sources was analyzed through information theory, considering the case of polymorphic alleles scored binarily for their presence or absence in DNA pools. We defined the informativeness of a set of marker loci in bulks as the mutual information between genotype and population identity, composed by two terms: diversity and noise. The first term is the entropy of bulk genotypes, whereas the noise term is measured through the conditional entropy of bulk genotypes given germplasm sources. Thus, optimizing marker information implies increasing diversity and reducing noise. Simple formulas were devised to estimate marker information per allele from a set of estimated allele frequencies across populations. As an example, they allowed optimization of bulk size for SSR genotyping in maize, from allele frequencies estimated in a sample of 56 maize populations. It was found that a sample of 30 plants from a random mating population is adequate for maize germplasm SSR characterization. We analyzed the use of divided bulks to overcome the allele dilution problem in DNA pools, and concluded that samples of 30 plants divided into three bulks of 10 plants are efficient to characterize maize germplasm sources through SSR with a good control of the dilution problem. We estimated the informativeness of 30 SSR loci from the estimated allele frequencies in maize populations, and found a wide variation of marker informativeness, which positively correlated with the number of alleles per locus.     

Accuracy of genomic selection for a sib-evaluated trait using identity-by-state and identity-by-descent relationships

Background

GBLUP (genomic best linear unbiased prediction) uses high-density single nucleotide polymorphism (SNP) markers to construct genomic identity-by-state (IBS) relationship matrices. However, identity-by-descent (IBD) relationships can be accurately calculated for extremely sparse markers. Here, we compare the accuracy of prediction of genome-wide breeding values (GW-BV) for a sib-evaluated trait in a typical aquaculture population, assuming either IBS or IBD genomic relationship matrices, and by varying marker density and size of the training dataset.

Methods

A simulation study was performed, assuming a population with strong family structure over three subsequent generations. Traditional and genomic BLUP were used to estimate breeding values, the latter using either IBS or IBD genomic relationship matrices, with marker densities ranging from 10 to ~1200 SNPs/Morgan (M). Heritability ranged from 0.1 to 0.8, and phenotypes were recorded on 25 to 45 sibs per full-sib family (50 full-sib families). Models were compared based on their predictive ability (accuracy) with respect to true breeding values of unphenotyped (albeit genotyped) sibs in the last generation.

Results

As expected, genomic prediction had greater accuracy compared to pedigree-based prediction. At the highest marker density, genomic prediction based on IBS information (IBS-GS) was slightly superior to that based on IBD information (IBD-GS), while at lower densities (≤100 SNPs/M), IBD-GS was more accurate. At the lowest densities (10 to 20 SNPs/M), IBS-GS was even outperformed by the pedigree-based model. Accuracy of IBD-GS was stable across marker densities performing well even down to 10 SNPs/M (2.5 to 6.1% reduction in accuracy compared to ~1200 SNPs/M). Loss of accuracy due to reduction in the size of training datasets was moderate and similar for both genomic prediction models. The relative superiority of (high-density) IBS-GS over IBD-GS was more pronounced for traits with a low heritability.

Conclusions

Using dense markers, GBLUP based on either IBD or IBS relationship matrices proved to perform better than a pedigree-based model. However, accuracy of IBS-GS declined rapidly with decreasing marker densities, and was even outperformed by a traditional pedigree-based model at the lowest densities. In contrast, the accuracy of IBD-GS was very stable across marker densities.     

Power and precision of alternate methods for linkage disequilibrium mapping of quantitative trait loci

Linkage disequilibrium (LD) analysis in outbred populations uses historical recombinations to detect and fine map quantitative trait loci (QTL). Our objective was to evaluate the effect of various factors on power and precision of QTL detection and to compare LD mapping methods on the basis of regression and identity by descent (IBD) in populations of limited effective population size (N(e)). An 11-cM region with 6-38 segregating single-nucleotide polymorphisms (SNPs) and a central QTL was simulated. After 100 generations of random mating with N(e) of 50, 100, or 200, SNP genotypes and phenotypes were generated on 200, 500, or 1000 individuals with the QTL explaining 2 or 5% of phenotypic variance. To detect and map the QTL, phenotypes were regressed on genotypes or (assumed known) haplotypes, in comparison with the IBD method. Power and precision to detect QTL increased with sample size, marker density, and QTL effect. Power decreased with N(e), but precision was affected little by N(e). Single-marker regression had similar or greater power and precision than other regression models, and was comparable to the IBD method. Thus, for rapid initial screening of samples of adequate size in populations in which drift is the primary force that has created LD, QTL can be detected and mapped by regression on SNP genotypes without recovering haplotypes.     

A Fast EM Algorithm for BayesA-Like Prediction of Genomic Breeding Values

Prediction accuracies of estimated breeding values for economically important traits are expected to benefit from genomic information. Single nucleotide polymorphism (SNP) panels used in genomic prediction are increasing in density, but the Markov Chain Monte Carlo (MCMC) estimation of SNP effects can be quite time consuming or slow to converge when a large number of SNPs are fitted simultaneously in a linear mixed model. Here we present an EM algorithm (termed “fastBayesA”) without MCMC. This fastBayesA approach treats the variances of SNP effects as missing data and uses a joint posterior mode of effects compared to the commonly used BayesA which bases predictions on posterior means of effects. In each EM iteration, SNP effects are predicted as a linear combination of best linear unbiased predictions of breeding values from a mixed linear animal model that incorporates a weighted marker-based realized relationship matrix. Method fastBayesA converges after a few iterations to a joint posterior mode of SNP effects under the BayesA model. When applied to simulated quantitative traits with a range of genetic architectures, fastBayesA is shown to predict GEBV as accurately as BayesA but with less computing effort per SNP than BayesA. Method fastBayesA can be used as a computationally efficient substitute for BayesA, especially when an increasing number of markers bring unreasonable computational burden or slow convergence to MCMC approaches.     

SNP identification and marker assay development for high-throughput selection of soybean cyst nematode resistance

Background

Soybean cyst nematode (SCN) is the most economically devastating pathogen of soybean. Two resistance loci, Rhg1 and Rhg4 primarily contribute resistance to SCN race 3 in soybean. Peking and PI 88788 are the two major sources of SCN resistance with Peking requiring both Rhg1 and Rhg4 alleles and PI 88788 only the Rhg1 allele. Although simple sequence repeat (SSR) markers have been reported for both loci, they are linked markers and limited to be applied in breeding programs due to accuracy, throughput and cost of detection methods. The objectives of this study were to develop robust functional marker assays for high-throughput selection of SCN resistance and to differentiate the sources of resistance.

Results

Based on the genomic DNA sequences of 27 soybean lines with known SCN phenotypes, we have developed Kompetitive Allele Specific PCR (KASP) assays for two Single nucleotide polymorphisms (SNPs) from Glyma08g11490 for the selection of the Rhg4 resistance allele. Moreover, the genomic DNA of Glyma18g02590 at the Rhg1 locus from 11 soybean lines and cDNA of Forrest, Essex, Williams 82 and PI 88788 were fully sequenced. Pairwise sequence alignment revealed seven SNPs/insertion/deletions (InDels), five in the 6th exon and two in the last exon. Using the same 27 soybean lines, we identified one SNP that can be used to select the Rhg1 resistance allele and another SNP that can be employed to differentiate Peking and PI 88788-type resistance. These SNP markers have been validated and a strong correlation was observed between the SNP genotypes and reactions to SCN race 3 using a panel of 153 soybean lines, as well as a bi-parental population, F₅–derived recombinant inbred lines (RILs) from G00-3213 x LG04-6000.

Conclusions

Three functional SNP markers (two for Rhg1 locus and one for Rhg4 locus) were identified that could provide genotype information for the selection of SCN resistance and differentiate Peking from PI 88788 source for most germplasm lines. The robust KASP SNP marker assays were developed. In most contexts, use of one or two of these markers is sufficient for high-throughput marker-assisted selection of plants that will exhibit SCN resistance.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1531-3) contains supplementary material, which is available to authorized users.     

Marker-assisted introgression using non-unique marker alleles II: selection on probability of presence of the introgressed allele

If marker alleles that identify a gene for introgression are not completely unique to the different base populations, the trait allele can be lost quickly during the process of backcrossing. This study considers ways to deal with incompletely informative markers in order to retain the desired allele. Selection was based on the probability of the presence of the desired (introgressed) trait allele, which was calculated for each marker genotype, using a single marker or a diallelic or triallelic marker bracket. The percentage of individuals retaining the introgressed allele was calculated over five generations of backcrossing, for selected fractions between 0 and 1, for marker alleles that could occur in both base populations. The best results were obtained with a rather large selected fraction, when all individuals, heterozygous and homozygous for the most desirable allele at the marker loci, were selected. Additional selection against marker homozygotes (which might have the highest probability of carrying the desired-trait allele, but produce uninformative gametes) altered the optimum selected fraction, making the selected fraction more consistently inversely related to a better retention of the desired-trait allele. A marker bracket was found to give a better retention of the desired-trait allele than a single marker and triallelic markers were better than diallelic markers, giving a retention of almost 50%. The earlier that preselection of parents (on informativeness) took place the better the overall result; preselection should occur preferably in the base populations. Preselection could make marker alleles unique to alternative base populations and markers would effectively become fully informative. Selection in the base populations might not be possible or not desirable, for example, because of the available number of individuals. This is unlikely to be a problem when parents are paired up to exclude any common marker alleles.     

Log-linear models for gene mapping with affected sib pair data

In genome-wide screens of genetic marker loci, non-mendelian inheritance of a marker is taken to indicate its vicinity to a disease locus. Heritable complex traits are thought to be under the influence of multiple possibly interacting susceptibility loci yet the most frequently used methods of linkage and association analysis focus on one susceptibility locus at a time. Here we introduce log-linear models for the joint analysis of multiple marker loci and interaction effects between them. Our approach focuses on affected sib pair data and identical by descent (IBD) allele sharing values observed on them. For each heterozygous parent, the IBD values at linked markers represent a sequence of dependent binary variables. We develop log-linear models for the joint distribution of these IBD values. An independence log-linear model is proposed to model the marginal means and the neighboring interaction model is advocated to account for associations between adjacent markers. Under the assumption of conditional independence, likelihood methods are applied to simulated data containing one or two susceptibility loci. It is shown that the neighboring interaction log-linear model is more efficient than the independence model, and incorporating interaction in the two-locus analysis provides increased power and accuracy for mapping of the trait loci.     

Discovery and assay of single-nucleotide polymorphisms in barley (Hordeum vulgare)

The least ambiguous genetic markers are those based on completely characterized DNA sequence polymorphisms. Unfortunately, assaying allele states by allele sequencing is slow and cumbersome. The most desirable type of genetic marker would be unambiguous, inexpensive to assay and would be assayable singly or in parallel with hundreds of other markers (multiplexable). In this report we sequenced alleles at 54 barley (Hordeum vulgare ssp. vulgare) loci, 38 of which contained single-nucleotide polymorphisms (SNPs). Many of these 38 loci contained multiple polymorphisms, and a total of 112 polymorphisms were scored in five barley genotypes. The polymorphism data set was analyzed both by using the individual mutations as cladistic characters and by reducing data for each locus to haplotypes. We compared the informativeness of these two approaches by consensus tree construction and bootstrap analysis. Both approaches provided similar results. Since some of the loci sequenced contained insertion/deletion events and multiple point mutations, we thought that these multiple-mutated loci might represent old alleles that predated the divergence of barley from H. spontaneum. We evaluated sequences from a sample of H. spontaneum accessions from the Eastern Mediterranean, and observed similar alleles present in both cultivated barley and H. spontaneum, suggesting either multiple domestication events or multiple transfers of genes between barley and its wild ancestor.