Anisotropic matern correlation and spatial prediction using REML

The Mat´ern correlation function provides great flexibility for modeling spatially correlated random processes in two dimensions, in particular via a smoothness parameter, whose estimation allows data to determine the degree of smoothness of a spatial process. The extension to include anisotropy provides a very general and flexible class of spatial covariance functions that can be used in a model-based approach to geostatistics, in which parameter estimation is achieved via REML and prediction is within the E-BLUP framework. In this article we develop a general class of linear mixed models using an anisotropic Mat´ern class with an extended metric. The approach is illustrated by application to soil salinity data in a rice-growing field in Australia, and to fine-scale soil pH data. It is found that anisotropy is an important aspect of both datasets, emphasizing the value of a straightforward and accessible approach to modeling anisotropy

Simultaneous QTL detection and genomic breeding value estimation using high density SNP chips

Background: The simulated dataset of the 13th QTL-MAS workshop was analysed to i) detect QTL and ii) predict breeding values for animals without phenotypic information. Several parameterisations considering all SNP simultaneously were applied using Gibbs sampling. Results: Fourteen QTL were detected at the different time points. Correlations between estimated breeding values were high between models, except when the model was used that assumed that all SNP effects came from one distribution. The model that used the selected 14 SNP found associated with QTL, gave close to unity correlations with the full parameterisations. Conclusions: Nine out of 18 QTL were detected, however the six QTL for inflection point were missed. Models for genomic selection were indicated to be fairly robust, e.g. with respect to accuracy of estimated breeding values. Still, it is worthwhile to investigate the number QTL underlying the quantitative traits, before choosing the model used for genomic selection

Transcriptomic analysis of wheat near-isogenic lines identifies PM19-A1 and A2 as candidates for a major dormancy QTL

BACKGROUND: Next-generation sequencing technologies provide new opportunities to identify the genetic components responsible for trait variation. However, in species with large polyploid genomes, such as bread wheat, the ability to rapidly identify genes underlying quantitative trait loci (QTL) remains non-trivial. To overcome this, we introduce a novel pipeline that analyses, by RNA-sequencing, multiple near-isogenic lines segregating for a targeted QTL. RESULTS: We use this approach to characterize a major and widely utilized seed dormancy QTL located on chromosome 4AL. It exploits the power and mapping resolution afforded by large multi-parent mapping populations, whilst reducing complexity by using multi-allelic contrasts at the targeted QTL region. Our approach identifies two adjacent candidate genes within the QTL region belonging to the ABA-induced Wheat Plasma Membrane 19 family. One of them, PM19-A1, is highly expressed during grain maturation in dormant genotypes. The second, PM19-A2, shows changes in sequence causing several amino acid alterations between dormant and non-dormant genotypes. We confirm that PM19 genes are positive regulators of seed dormancy. CONCLUSIONS: The efficient identification of these strong candidates demonstrates the utility of our transcriptomic pipeline for rapid QTL to gene mapping. By using this approach we are able to provide a comprehensive genetic analysis of the major source of grain dormancy in wheat. Further analysis across a diverse panel of bread and durum wheats indicates that this important dormancy QTL predates hexaploid wheat. The use of these genes by wheat breeders could assist in the elimination of pre-harvest sprouting in wheat.Jose M. Barrero, Colin Cavanagh, Klara L. Verbyla, Josquin F.G. Tibbits, Arunas P. Verbyla, B. Emma Huang, Garry M. Rosewarne, Stuart Stephen, Penghao Wang, Alex Whan, Philippe Rigault, Matthew J. Hayden, and Frank Guble

Estimating genomic breeding values and detecting QTL using univariate and bivariate models

Background Genomic selection is particularly beneficial for difficult or expensive to measure traits. Since multi-trait selection is an important tool to deal with such cases, an important question is what the added value is of multi-trait genomic selection. Methods The simulated dataset, including a quantitative and binary trait, was analyzed with four univariate and bivariate linear models to predict breeding values for juvenile animals. Two models estimated variance components with REML using a numerator (A), or SNP based relationship matrix (G). Two SNP based Bayesian models included one (BayesA) or two distributions (BayesC) for estimated SNP effects. The bivariate BayesC model sampled QTL probabilities for each SNP conditional on both traits. Genotypes were permuted 2,000 times against phenotypes and pedigree, to obtain significance thresholds for posterior QTL probabilities. Genotypes were permuted rather than phenotypes, to retain relationships between pedigree and phenotypes, such that polygenic effects could still be estimated. Results Correlations between estimated breeding values (EBV) of different SNP based models, for juvenile animals, were greater than 0.93 (0.87) for the quantitative (binary) trait. Estimated genetic correlation was 0.71 (0.66) for model G (A). Accuracies of breeding values of SNP based models were for both traits highest for BayesC and lowest for G. Accuracies of breeding values of bivariate models were up to 0.08 higher than for univariate models. The bivariate BayesC model detected 14 out of 32 QTL for the quantitative trait, and 8 out of 22 for the binary trait. Conclusions Accuracy of EBV clearly improved for both traits using bivariate compared to univariate models. BayesC achieved highest accuracies of EBV and was also one of the methods that found most QTL. Permuting genotypes against phenotypes and pedigree in BayesC provided an effective way to derive significance thresholds for posterior QTL probabilitie

Accuracy of genomic breeding values in multi-breed dairy cattle populations

<p>Abstract</p> <p>Background</p> <p>Two key findings from genomic selection experiments are 1) the reference population used must be very large to subsequently predict accurate genomic estimated breeding values (GEBV), and 2) prediction equations derived in one breed do not predict accurate GEBV when applied to other breeds. Both findings are a problem for breeds where the number of individuals in the reference population is limited. A multi-breed reference population is a potential solution, and here we investigate the accuracies of GEBV in Holstein dairy cattle and Jersey dairy cattle when the reference population is single breed or multi-breed. The accuracies were obtained both as a function of elements of the inverse coefficient matrix and from the realised accuracies of GEBV.</p> <p>Methods</p> <p>Best linear unbiased prediction with a multi-breed genomic relationship matrix (GBLUP) and two Bayesian methods (BAYESA and BAYES_SSVS) which estimate individual SNP effects were used to predict GEBV for 400 and 77 young Holstein and Jersey bulls respectively, from a reference population of 781 and 287 Holstein and Jersey bulls, respectively. Genotypes of 39,048 SNP markers were used. Phenotypes in the reference population were de-regressed breeding values for production traits. For the GBLUP method, expected accuracies calculated from the diagonal of the inverse of coefficient matrix were compared to realised accuracies.</p> <p>Results</p> <p>When GBLUP was used, expected accuracies from a function of elements of the inverse coefficient matrix agreed reasonably well with realised accuracies calculated from the correlation between GEBV and EBV in single breed populations, but not in multi-breed populations. When the Bayesian methods were used, realised accuracies of GEBV were up to 13% higher when the multi-breed reference population was used than when a pure breed reference was used. However no consistent increase in accuracy across traits was obtained.</p> <p>Conclusion</p> <p>Predicting genomic breeding values using a genomic relationship matrix is an attractive approach to implement genomic selection as expected accuracies of GEBV can be readily derived. However in multi-breed populations, Bayesian approaches give higher accuracies for some traits. Finally, multi-breed reference populations will be a valuable resource to fine map QTL.</p

Estimated breeding values and association mapping for persistency and total milk yield using natural cubic smoothing splines

BackgroundFor dairy producers, a reliable description of lactation curves is a valuable tool for management and selection. From a breeding and production viewpoint, milk yield persistency and total milk yield are important traits. Understanding the genetic drivers for the phenotypic variation of both these traits could provide a means for improving these traits in commercial production.MethodsIt has been shown that Natural Cubic Smoothing Splines (NCSS) can model the features of lactation curves with greater flexibility than the traditional parametric methods. NCSS were used to model the sire effect on the lactation curves of cows. The sire solutions for persistency and total milk yield were derived using NCSS and a whole-genome approach based on a hierarchical model was developed for a large association study using single nucleotide polymorphisms (SNP).ResultsEstimated sire breeding values (EBV) for persistency and milk yield were calculated using NCSS. Persistency EBV were correlated with peak yield but not with total milk yield. Several SNP were found to be associated with both traits and these were used to identify candidate genes for further investigation.ConclusionNCSS can be used to estimate EBV for lactation persistency and total milk yield, which in turn can be used in whole-genome association studies.Klara L. Verbyla and Arunas P. Verbyl

Quantitative trait loci analysis of zinc efficiency and grain zinc concentration in wheat using whole genome average interval mapping

Zinc (Zn) deficiency is a widespread problem which reduces yield and grain nutritive value in many cereal growing regions of the world. While there is considerable genetic variation in tolerance to Zn deficiency (also known as Zn efficiency), phenotypic selection is difficult and would benefit from the development of molecular markers. A doubled haploid population derived from a cross between the Zn inefficient genotype RAC875-2 and the moderately efficient genotype Cascades was screened in three experiments to identify QTL linked to growth under low Zn and with the concentrations of Zn and iron (Fe) in leaf tissue and in the grain. Two experiments were conducted under controlled conditions while the third examined the response to Zn in the field. QTL were identified using an improved method of analysis, whole genome average interval mapping. Shoot biomass and shoot Zn and Fe concentrations showed significant negative correlations, while there were significant genetic correlations between grain Zn and Fe concentrations. Shoot biomass, tissue and grain Zn concentrations were controlled by a number of genes, many with a minor effect. Depending on the traits and the site, the QTL accounted for 12–81% of the genetic variation. Most of the QTL linked to seedling growth under Zn deficiency and to Zn and Fe concentrations were associated with height genes with greater seedling biomass associated with lower Zn and Fe concentrations. Four QTL for grain Zn concentration and a single QTL for grain Fe concentration were also identified. A cluster of adjacent QTL related to the severity of symptoms of Zn deficiency, shoot Zn concentration and kernel weight was found on chromosome 4A and a cluster of QTL associated with shoot and grain Fe concentrations and kernel weight was found on chromosome 3D. These two regions appear promising areas for further work to develop markers for enhanced growth under low Zn and for Zn and Fe uptake. Although there was no significant difference between the parents, the grain Zn concentration ranged from 29 to 43 mg kg−1 within the population and four QTL associated with grain Zn concentration were identified. These were located on chromosomes 3D, 4B, 6B and 7A and they described 92% of the genetic variation. Each QTL had a relatively small effect on grain Zn concentration but combining the four high Zn alleles increased the grain Zn by 23%. While this illustrates the potential for pyramiding genes to improve grain Zn, breeding for increased grain Zn concentration requires identification of individual QTL with large effects, which in turn requires construction and testing of new mapping populations in the future