Bayesian QTL Research Articles

Efficiency of Bayesian quantitative trait loci mapping with full‐sib progeny

AbstractQuantitative trait loci (QTL) mapping with perennial crops is based on one or more full‐sib progeny because homozygous genotypes are difficult to obtain. The objective of this study was to assess the efficiency of Bayesian QTL mapping with full‐sib progeny. The analyses used two simulated data sets, one assuming genotyping for 292 simple sequence repeats (SSR) loci (density of 10 cM) and the other assuming genotyping for 2969 single nucleotide polymorphisms (SNPs) (density of 1 cM). Each data set consisted of 50 replications of 40 full‐sib progeny of size 400. We assumed a broad sense heritability of 60%, genetic control by 10 QTLs and 90 minor genes, and positive dominance. The QTL heritability values ranged from 1 to 12%. The scenarios included one and multiple progeny. In the best scenarios for the low (four progeny of size 400) and high marker density (one progeny of size 400), the average power of detection was 52 and 67% for the low heritability QTLs, 83 and 95% for the average heritability QTLs, and 95 and 94% for the high heritability QTLs, respectively. The observed false discovery rate (FDR) was 15 and 9% with low and high density, respectively. The Bayesian QTL mapping provides a precise localization of candidate genes with a bias in the QTL position of approximately 4–6 cM. The polygenic effect is important to control the false discovery rate (FDR) and to provide a higher power of QTL detection with multiple progeny.

Bayesian QTL mapping using genome-wide SSR markers and segregating population derived from a cross of two commercial F1 hybrids of tomato

Using newly developed euchromatin-derived genomic SSR markers and a flexible Bayesian mapping method, 13 significant agricultural QTLs were identified in a segregating population derived from a four-way cross of tomato. So far, many QTL mapping studies in tomato have been performed for progeny obtained from crosses between two genetically distant parents, e.g., domesticated tomatoes and wild relatives. However, QTL information of quantitative traits related to yield (e.g., flower or fruit number, and total or average weight of fruits) in such intercross populations would be of limited use for breeding commercial tomato cultivars because individuals in the populations have specific genetic backgrounds underlying extremely different phenotypes between the parents such as large fruit in domesticated tomatoes and small fruit in wild relatives, which may not be reflective of the genetic variation in tomato breeding populations. In this study, we constructed F2 population derived from a cross between two commercial F1 cultivars in tomato to extract QTL information practical for tomato breeding. This cross corresponded to a four-way cross, because the four parental lines of the two F1 cultivars were considered to be the founders. We developed 2510 new expressed sequence tag (EST)-based (euchromatin-derived) genomic SSR markers and selected 262 markers from these new SSR markers and publicly available SSR markers to construct a linkage map. QTL analysis for ten agricultural traits of tomato was performed based on the phenotypes and marker genotypes of F2 plants using a flexible Bayesian method. As results, 13 QTL regions were detected for six traits by the Bayesian method developed in this study.

QTL mapping of pomological traits in peach and related species breeding germplasm

Peach is an economically important fruit tree crop that exhibits high phenotypic variability yet suffers from diversity-limited gene pool. Genetic introgression of novel alleles from related species is being pursued to expand genetic diversity. This process is, however, challenging and requires the incorporation of innovative genomic and statistical tools to facilitate efficient transfer of these exotic alleles across the multiple generations required for introgression. In this study, pedigree-based analysis (PBA) in a Bayesian QTL mapping framework was applied to a diverse peach pedigree introgressed with almond and other related Prunus species. The aim was to investigate the genetic control of eight commercially important fruit productivity and fruit quality traits over two subsequent years. Fifty-two QTLs with at least positive evidence explaining up to 98 % of the phenotypic variance across all trait/year combinations were mapped separately per trait and year. Several QTLs exhibited variable association with traits between years. By using the peach genome sequence as a reference, the intrachromosomal positions for several QTLs were shown to differ from those previously reported in peach. The inclusion of introgressed germplasm and the explicit declaration of the genetic structure of the pedigree as covariate in PBA enhanced the mapping and interpretation of QTLs. This study serves as a model study for PBA in a diverse peach breeding program, and the results highlight the ability of this strategy to identify genomic resources for direct utilization in marker-assisted breeding.

Bayesian QTL mapping for recombinant inbred lines derived from a four-way cross

Recombinant inbred lines (RILs) are created by a cross between inbred lines followed by repeated selfing or sib-mating, which include many different types of new inbred lines with many recombination events on the genome. The phenotype of each RIL can be assessed based on multiple individuals within the same line to reduce non-genetic variability. Therefore, RILs are useful tools for QTL mapping allowing effective detection and fine localization of QTL. Usually only two inbred lines are involved to create RILs. In such two-way RILs, however, there are at most two different alleles at QTL and only QTL segregating between two parental lines can be detected. Recently a new crossing design using multiple founders for creating RILs was proposed in Arabidopsis thaliana and mice, where the genome of each RIL is a mosaic of the genomes from multiple parents. Such multi-way RILs are more useful to improve the efficiency in QTL detection than two-way RILs because of the increased chance of QTL segregation among multiple lines, leading to the successful detection of many QTL. In this paper, we propose a Bayesian method for mapping multiple QTL simultaneously in four-way RILs allowing the inference about the equivalence relationship among the four possible alleles descended from the four founder lines as well as the estimation of QTL locations and effects via a MCMC algorithm. Simulation experiments show that our method has the practical ability to detect QTL and to provide the information of equivalence relationship among alleles at detected QTL using four-way RILs.

A Bayesian QTL linkage analysis of the common dataset from the 12thQTLMAS workshop

To compare the power of various QTL mapping methodologies, a dataset was simulated within the framework of 12th QTLMAS workshop. A total of 5865 diploid individuals was simulated, spanning seven generations, with known pedigree. Individuals were genotyped for 6000 SNPs across six chromosomes. We present an illustration of a Bayesian QTL linkage analysis, as implemented in the special purpose software FlexQTL. Most importantly, we treated the number of bi-allelic QTL as a random variable and used Bayes Factors to infer plausible QTL models. We investigated the power of our analysis in relation to the number of phenotyped individuals and SNPs. We report clear posterior evidence for 12 QTL that jointly explained 30% of the phenotypic variance, which was very close to the total of included simulation effects, when using all phenotypes and a set of 600 SNPs. Decreasing the number of phenotyped individuals from 4665 to 1665 and/or the number of SNPs in the analysis from 600 to 120 dramatically reduced the power to identify and locate QTL. Posterior estimates of genome-wide breeding values for a small set of individuals were given. We presented a successful Bayesian linkage analysis of a simulated dataset with a pedigree spanning several generations. Our analysis identified all regions that contained QTL with effects explaining more than one percent of the phenotypic variance. We showed how the results of a Bayesian QTL mapping can be used in genomic prediction.

Bayesian QTL mapping for multiple families derived from crossing a set of inbred lines to a reference line

In some crop species, germplasm collections consisting of a large number of accessions that include traditional landraces, modern cultivars and wild species have recently been established. Such collections are regarded as useful stocks of genes for breeding programs. However, to efficiently utilize these collections for plant breeding, understanding genetic variation in agronomic traits at the QTL level between the accessions is indispensable. One effective way to extract the actual QTL information included in these collections is to perform QTL analysis jointly for multiple families derived from crossing some accessions of the collection with a single reference line such as a standard commercial variety. We developed a Bayesian method for jointly analyzing QTL in such interconnected multiple families derived from a set of inbred lines crossed to the reference line, to detect QTL segregating between any of the inbred lines and the reference line. In this study, we considered multiple recombinant inbred lines, each of which was derived from crossing each of the inbred lines to the reference line. The method was evaluated through the use of simulated data sets for its efficiency in detecting QTL and identifying families segregating at each QTL.

Bayesian QTL mapping using skewed Student-t distributions.

In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.

Bayesian QTL mapping using skewed Student-t distributions

In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.

A statistical framework for quantitative trait mapping.

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.

Cortisone in ulcerative colitis; final report on a therapeutic trial.

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.