An Expectation-Maximization Algorithm for Combining a Sample of Partially Overlapping Covariance Matrices.

The generation of unprecedented amounts of data brings new challenges in data management, but also an opportunity to accelerate the identification of processes of multiple science disciplines. One of these challenges is the harmonization of high-dimensional unbalanced and heterogeneous data. In this manuscript, we propose a statistical approach to combine incomplete and partially-overlapping pieces of covariance matrices that come from independent experiments. We assume that the data are a random sample of partial covariance matrices sampled from Wishart distributions and we derive an expectation-maximization algorithm for parameter estimation. We demonstrate the properties of our method by (i) using simulation studies and (ii) using empirical datasets. In general, being able to make inferences about the covariance of variables not observed in the same experiment is a valuable tool for data analysis since covariance estimation is an important step in many statistical applications, such as multivariate analysis, principal component analysis, factor analysis, and structural equation modeling.

Genetic gain and inbreeding from simulation of different genomic mating schemes for pig improvement.

BACKGROUND: Genomic selection involves choosing as parents those elite individuals with the higher genomic estimated breeding values (GEBV) to accelerate the speed of genetic improvement in domestic animals. But after multi-generation selection, the rate of inbreeding and the occurrence of homozygous harmful alleles might increase, which would reduce performance and genetic diversity. To mitigate the above problems, we can utilize genomic mating (GM) based upon optimal mate allocation to construct the best genotypic combinations in the next generation. In this study, we used stochastic simulation to investigate the impact of various factors on the efficiencies of GM to optimize pairing combinations after genomic selection of candidates in a pig population. These factors included: the algorithm used to derive inbreeding coefficients; the trait heritability (0.1, 0.3 or 0.5); the kind of GM scheme (focused average GEBV or inbreeding); the approach for computing the genomic relationship matrix (by SNP or runs of homozygosity (ROH)). The outcomes were compared to three traditional mating schemes (random, positive assortative or negative assortative matings). In addition, the performance of the GM approach was tested on real datasets obtained from a Large White pig breeding population. RESULTS: Genomic mating outperforms other approaches in limiting the inbreeding accumulation for the same expected genetic gain. The use of ROH-based genealogical relatedness in GM achieved faster genetic gains than using relatedness based on individual SNPs. The GROH-based GM schemes with the maximum genetic gain resulted in 0.9%-2.6% higher rates of genetic gain ΔG, and 13%-83.3% lower ΔF than positive assortative mating regardless of heritability. The rates of inbreeding were always the fastest with positive assortative mating. Results from a purebred Large White pig population, confirmed that GM with ROH-based GRM was more efficient than traditional mating schemes. CONCLUSION: Compared with traditional mating schemes, genomic mating can not only achieve sustainable genetic progress but also effectively control the rates of inbreeding accumulation in the population. Our findings demonstrated that breeders should consider using genomic mating for genetic improvement of pigs.

A comparison of methods for training population optimization in genomic selection.

KEY MESSAGE: Maximizing CDmean and Avg_GRM_self were the best criteria for training set optimization. A training set size of 50-55% (targeted) or 65-85% (untargeted) is needed to obtain 95% of the accuracy.  With the advent of genomic selection (GS) as a widespread breeding tool, mechanisms to efficiently design an optimal training set for GS models became more relevant, since they allow maximizing the accuracy while minimizing the phenotyping costs. The literature described many training set optimization methods, but there is a lack of a comprehensive comparison among them. This work aimed to provide an extensive benchmark among optimization methods and optimal training set size by testing a wide range of them in seven datasets, six different species, different genetic architectures, population structure, heritabilities, and with several GS models to provide some guidelines about their application in breeding programs. Our results showed that targeted optimization (uses information from the test set) performed better than untargeted (does not use test set data), especially when heritability was low. The mean coefficient of determination was the best targeted method, although it was computationally intensive. Minimizing the average relationship within the training set was the best strategy for untargeted optimization. Regarding the optimal training set size, maximum accuracy was obtained when the training set was the entire candidate set. Nevertheless, a 50-55% of the candidate set was enough to reach 95-100% of the maximum accuracy in the targeted scenario, while we needed a 65-85% for untargeted optimization. Our results also suggested that a diverse training set makes GS robust against population structure, while including clustering information was less effective. The choice of the GS model did not have a significant influence on the prediction accuracies.

Genome-wide association study and genomic prediction of resistance to stripe rust in current Central and Northern European winter wheat germplasm.

KEY MESSAGE: We found two loci on chromosomes 2BS and 6AL that significantly contribute to stripe rust resistance in current European winter wheat germplasm. Stripe or yellow rust, caused by the fungus Puccinia striiformis Westend f. sp. tritici, is one of the most destructive wheat diseases. Sustainable management of wheat stripe rust can be achieved through the deployment of rust resistant cultivars. To detect effective resistance loci for use in breeding programs, an association mapping panel of 230 winter wheat cultivars and breeding lines from Northern and Central Europe was employed. Genotyping with the Illumina® iSelect® 25 K Infinium® single nucleotide polymorphism (SNP) genotyping array yielded 8812 polymorphic markers. Structure analysis revealed two subpopulations with 92 Austrian breeding lines and cultivars, which were separated from the other 138 genotypes from Germany, Norway, Sweden, Denmark, Poland, and Switzerland. Genome-wide association study for adult plant stripe rust resistance identified 12 SNP markers on six wheat chromosomes which showed consistent effects over several testing environments. Among these, two marker loci on chromosomes 2BS (RAC875_c1226_652) and 6AL (Tdurum_contig29607_413) were highly predictive in three independent validation populations of 1065, 1001, and 175 breeding lines. Lines with the resistant haplotype at both loci were nearly free of stipe rust symptoms. By using mixed linear models with those markers as fixed effects, we could increase predictive ability in the three populations by 0.13-0.46 compared to a standard genomic best linear unbiased prediction approach. The obtained results facilitate an efficient selection for stripe rust resistance against the current pathogen population in the Northern and Central European winter wheat gene pool.

Assessment of genomic prediction reliability and optimization of experimental designs in multi-environment trials.

KEY MESSAGE: New forms of the coefficient of determination can help to forecast the accuracy of genomic prediction and optimize experimental designs in multi-environment trials with genotype-by-environment interactions. In multi-environment trials, the relative performance of genotypes may vary depending on the environmental conditions, and this phenomenon is commonly referred to as genotype-by-environment interaction (G[Formula: see text]E). With genomic prediction, G[Formula: see text]E can be accounted for by modeling the genetic covariance between trials, even when the overall experimental design is highly unbalanced between trials, thanks to the genomic relationship between genotypes. In this study, we propose new forms of the coefficient of determination (CD, i.e., the expected model-based square correlation between a genetic value and its corresponding prediction) that can be used to forecast the genomic prediction reliability of genotypes, both for their trial-specific performance and their mean performance. As the expected prediction reliability based on these new CD criteria is generally a good approximation of the observed reliability, we demonstrate that they can be used to optimize multi-environment trials in the presence of G[Formula: see text]E. In addition, this reliability may be highly variable between genotypes, especially in unbalanced designs with complex pedigree relationships between genotypes. Therefore, it can be useful for breeders to assess it before selecting genotypes based on their predicted genetic values. Using a wheat population evaluated both for simulated and phenology traits, and two maize populations evaluated for grain yield, we illustrate this approach and confirm the value of our new CD criteria.

Texture features of primary tumor on 18F-FDG PET images in non-small cell lung cancer: The relationship between imaging and histopathological parameters.

PURPOSE: The aims of this study were to evaluate the relationships between textural features of the primary tumor on FDG PET images and clinical-histopathological parameters which are useful in predicting prognosis in newly diagnosed non-small cell lung cancer (NSCLC) patients. METHODS: PET/CT images of ninety (90) patients with NSCLC prior to surgery were analyzed retrospectively. All patients had resectable tumors. From the images we acquired data related to metabolism (SUVmax, MTV, TLG) and texture features of primary tumors. Histopathological tumor types and subgroups, degree of Ki-67 expression and necrosis rates of the primary tumor, mediastinal lymph node (MLN) status and nodal stages were recorded. RESULTS: Among the two histologic tumor types (adenocarcinoma and squamous cell carcinoma) significant differences were present regarding metabolic parameters, Ki-67 index with higher values and kurtosis with lower values in the latter group. Textural heterogeneity was found to be higher in poorly differentiated tumors compared to moderately differentiated tumors in patients with adenocarcinoma. While Ki-67 index had significant correlations with metabolic parameters and kurtosis, tumor necrosis rate was only significantly correlated with textural features. By univariate and multivariate analyses of the imaging and histopathological factors examined, only gradient variance was significant predictive factor for the presence of MLN metastasis. CONCLUSIONS: Textural features had significant associations with histologic tumor types, degree of pathological differentiation, tumor proliferation and necrosis rates. Texture analysis has potential to differentiate tumor types and subtypes and to predict MLN metastasis in patients with NSCLC.

Linkage and QTL mapping for tuber shape and specific gravity in a tetraploid mapping population of potato representing the russet market class.

BACKGROUND: Tuber shape and specific gravity (dry matter) are important agronomic traits in potato processing and impact production costs, quality, and consistency of the final processed food products such as French fries and potato chips. In this study, linkage and QTL mapping were performed for these two traits to allow for the implementation of marker-assisted selection to facilitate breeding efforts in the russet market class. Two parents, Rio Grande Russet (female) and Premier Russet (male) and their 205 F1 progenies were initially phenotyped for tuber shape and specific gravity in field trials conducted in Idaho and North Carolina in 2010 and 2011, with specific gravity also being measured in Minnesota in 2011. Progenies and parents were previously genotyped using the Illumina SolCAP Infinium 8303 Potato SNP array, with ClusterCall and MAPpoly (R-packages) subsequently used for autotetraploid SNP calling and linkage mapping in this study. The 12 complete linkage groups and phenotypic data were then imported into QTLpoly, an R-package designed for polyploid QTL analyses. RESULTS: Significant QTL for tuber shape were detected on chromosomes 4, 7, and 10, with heritability estimates ranging from 0.09 to 0.36. Significant tuber shape QTL on chromosomes 4 and 7 were specific to Idaho and North Carolina environments, respectively, whereas the QTL on chromosome 10 was significant regardless of growing environment. Single marker analyses identified alleles in the parents associated with QTL on chromosomes 4, 7, and 10 that contributed to significant differences in tuber shape among progenies. Significant QTL were also identified for specific gravity on chromosomes 1 and 5 with heritability ranging from 0.12 to 0.21 and were reflected across environments. CONCLUSION: Fully automated linkage mapping and QTL analysis were conducted to identify significant QTL for tuber shape and dry matter in a tetraploid mapping population representing the russet market class. The findings are important for the development of molecular markers useful to potato breeders for marker-assisted selection for the long tuber shape and acceptable dry matter required by the potato industry within this important market class.

Training Set Optimization for Sparse Phenotyping in Genomic Selection: A Conceptual Overview.

Genomic selection (GS) is becoming an essential tool in breeding programs due to its role in increasing genetic gain per unit time. The design of the training set (TRS) in GS is one of the key steps in the implementation of GS in plant and animal breeding programs mainly because (i) TRS optimization is critical for the efficiency and effectiveness of GS, (ii) breeders test genotypes in multi-year and multi-location trials to select the best-performing ones. In this framework, TRS optimization can help to decrease the number of genotypes to be tested and, therefore, reduce phenotyping cost and time, and (iii) we can obtain better prediction accuracies from optimally selected TRS than an arbitrary TRS. Here, we concentrate the efforts on reviewing the lessons learned from TRS optimization studies and their impact on crop breeding and discuss important features for the success of TRS optimization under different scenarios. In this article, we review the lessons learned from training population optimization in plants and the major challenges associated with the optimization of GS including population size, the relationship between training and test set (TS), update of TRS, and the use of different packages and algorithms for TRS implementation in GS. Finally, we describe general guidelines to improving the rate of genetic improvement by maximizing the use of the TRS optimization in the GS framework.

TrainSel: An R Package for Selection of Training Populations.

A major barrier to the wider use of supervised learning in emerging applications, such as genomic selection, is the lack of sufficient and representative labeled data to train prediction models. The amount and quality of labeled training data in many applications is usually limited and therefore careful selection of the training examples to be labeled can be useful for improving the accuracies in predictive learning tasks. In this paper, we present an R package, TrainSel, which provides flexible, efficient, and easy-to-use tools that can be used for the selection of training populations (STP). We illustrate its use, performance, and potentials in four different supervised learning applications within and outside of the plant breeding area.

Combining Partially Overlapping Multi-Omics Data in Databases Using Relationship Matrices.

Private and public breeding programs, as well as companies and universities, have developed different genomics technologies that have resulted in the generation of unprecedented amounts of sequence data, which bring new challenges in terms of data management, query, and analysis. The magnitude and complexity of these datasets bring new challenges but also an opportunity to use the data available as a whole. Detailed phenotype data, combined with increasing amounts of genomic data, have an enormous potential to accelerate the identification of key traits to improve our understanding of quantitative genetics. Data harmonization enables cross-national and international comparative research, facilitating the extraction of new scientific knowledge. In this paper, we address the complex issue of combining high dimensional and unbalanced omics data. More specifically, we propose a covariance-based method for combining partial datasets in the genotype to phenotype spectrum. This method can be used to combine partially overlapping relationship/covariance matrices. Here, we show with applications that our approach might be advantageous to feature imputation based approaches; we demonstrate how this method can be used in genomic prediction using heterogeneous marker data and also how to combine the data from multiple phenotypic experiments to make inferences about previously unobserved trait relationships. Our results demonstrate that it is possible to harmonize datasets to improve available information across gene-banks, data repositories, or other data resources.

Genetic Correlation, Genome-Wide Association and Genomic Prediction of Portable NIRS Predicted Carotenoids in Cassava Roots.

Random forests (RF) was used to correlate spectral responses to known wet chemistry carotenoid concentrations including total carotenoid content (TCC), all-trans ß-carotene (ATBC), violaxanthin (VIO), lutein (LUT), 15-cis beta-carotene (15CBC), 13-cis beta-carotene (13CBC), alpha-carotene (AC), 9-cis beta-carotene (9CBC), and phytoene (PHY) from laboratory analysis of 173 cassava root samples in Columbia. The cross-validated correlations between the actual and estimated carotenoid values using RF ranged from 0.62 in PHY to 0.97 in ATBC. The developed models were used to evaluate the carotenoids of 594 cassava clones with spectral information collected across three locations in a national breeding program (NRCRI, Umudike), Nigeria. Both populations contained cassava clones characterized as white and yellow. The NRCRI evaluated phenotypes were used to assess the genetic correlations, conduct genome-wide association studies (GWAS), and genomic predictions. Estimates of genetic correlation showed various levels of the relationship among the carotenoids. The associations between TCC and the individual carotenoids were all significant (P < 0.001) with high positive values (r > 0.75, except in LUT and PHY where r < 0.3). The GWAS revealed significant genomic regions on chromosomes 1, 2, 4, 13, 14, and 15 associated with variation in at least one of the carotenoids. One of the identified candidate genes, phytoene synthase (PSY) has been widely reported for variation in TCC in cassava. On average, genomic prediction accuracies from the single-trait genomic best linear unbiased prediction (GBLUP) and RF as well as from a multiple-trait GBLUP model ranged from ∼0.2 in LUT and PHY to 0.52 in TCC. The multiple-trait GBLUP model gave slightly higher accuracies than the single trait GBLUP and RF models. This study is one of the initial attempts in understanding the genetic basis of individual carotenoids and demonstrates the usefulness of NIRS in cassava improvement.

Genome wide association study of 5 agronomic traits in olive (Olea europaea L.).

Olive (Olea europaea L.) is one of the most economically and historically important fruit crops worldwide. Genetic progress for valuable agronomic traits has been slow in olive despite its importance and benefits. Advances in next generation sequencing technologies provide inexpensive and highly reproducible genotyping approaches such as Genotyping by Sequencing, enabling genome wide association study (GWAS). Here we present the first comprehensive GWAS study on olive using GBS. A total of 183 accessions (FULL panel) were genotyped using GBS, 94 from the Turkish Olive GenBank Resource (TOGR panel) and 89 from the USDA-ARS National Clonal Germplasm Repository (NCGR panel) in the USA. After filtering low quality and redundant markers, GWAS was conducted using 24,977 SNPs in FULL, TOGR and NCGR panels. In total, 52 significant associations were detected for leaf length, fruit weight, stone weight and fruit flesh to pit ratio using the MLM_K. Significant GWAS hits were mapped to their positions and 19 candidate genes were identified within a 10-kb distance of the most significant SNP. Our findings provide a framework for the development of markers and identification of candidate genes that could be used in olive breeding programs.

Design of training populations for selective phenotyping in genomic prediction.

Phenotyping is the current bottleneck in plant breeding, especially because next-generation sequencing has decreased genotyping cost more than 100.000 fold in the last 20 years. Therefore, the cost of phenotyping needs to be optimized within a breeding program. When designing the implementation of genomic selection scheme into the breeding cycle, breeders need to select the optimal method for (1) selecting training populations that maximize genomic prediction accuracy and (2) to reduce the cost of phenotyping while improving precision. In this article, we compared methods for selecting training populations under two scenarios: Firstly, when the objective is to select a training population set (TRS) to predict the remaining individuals from the same population (Untargeted), and secondly, when a test set (TS) is first defined and genotyped, and then the TRS is optimized specifically around the TS (Targeted). Our results show that optimization methods that include information from the test set (targeted) showed the highest accuracies, indicating that apriori information from the TS improves genomic predictions. In addition, predictive ability enhanced especially when population size was small which is a target to decrease phenotypic cost within breeding programs.

Multi-objective optimized genomic breeding strategies for sustainable food improvement.

The purpose of breeding programs is to obtain sustainable gains in multiple traits while controlling the loss of genetic variation. The decisions at each breeding cycle involve multiple, usually competing, objectives; these complex decisions can be supported by the insights that are gained by applying multi-objective optimization principles to breeding. The discussion in this manuscript includes the definition of several multi-objective optimized breeding approaches within the phenotypic or genomic breeding frameworks and the comparison of these approaches with the standard multi-trait breeding schemes such as tandem selection, independent culling and index selection. Proposed methods are demonstrated with two empirical data sets and simulations. In addition, we have described several graphical tools that can aid breeders in arriving at a compromise decision. The results show that the proposed methodology is a viable approach to answer several real breeding problems. In simulations, the newly proposed methods resulted in gains larger than the methods previously proposed including index selection: Compared to the best alternative breeding strategy, the gains from multi-objective optimized parental proportions approaches were about 20-30% higher at the end of long-term simulations of breeding cycles. In addition, the flexibility of the multi-objective optimized breeding strategies were displayed with methods and examples covering non-dominated selection, assignment of optimal parental proportions, using genomewide marker effects in producing optimal mating designs, and finally in selection of training populations for genomic prediction.

Correction to: Accuracy of genomic selection to predict maize single-crosses obtained through different mating designs.

Unfortunately, the first author name of the above-mentioned article was incorrectly published in the original publication. The complete correct name should read as follows.

Regional Heritability Mapping Provides Insights into Dry Matter Content in African White and Yellow Cassava Populations.

The HarvestPlus program for cassava ( Crantz) fortifies cassava with ß-carotene by breeding for carotene-rich tubers (yellow cassava). However, a negative correlation between yellowness and dry matter (DM) content has been identified. We investigated the genetic control of DM in white and yellow cassava. We used regional heritability mapping (RHM) to associate DM with genomic segments in both subpopulations. Significant segments were subjected to candidate gene analysis and candidates were validated with prediction accuracies. The RHM procedure was validated via a simulation approach and revealed significant hits for white cassava on chromosomes 1, 4, 5, 10, 17, and 18, whereas hits for the yellow were on chromosome 1. Candidate gene analysis revealed genes in the carbohydrate biosynthesis pathway including plant serine-threonine protein kinases (SnRKs), UDP (uridine diphosphate)-glycosyltransferases, UDP-sugar transporters, invertases, pectinases, and regulons. Validation using 1252 unique identifiers from the SnRK gene family genome-wide recovered 50% of the predictive accuracy of whole-genome single nucleotide polymorphisms for DM, whereas validation using 53 likely genes (extracted from the literature) from significant segments recovered 32%. Genes including an acid invertase, a neutral or alkaline invertase, and a glucose-6-phosphate isomerase were validated on the basis of an a priori list for the cassava starch pathway, and also a fructose-biphosphate aldolase from the Calvin cycle pathway. The power of the RHM procedure was estimated as 47% when the causal quantitative trait loci generated 10% of the phenotypic variance (sample size = 451). Cassava DM genetics are complex and RHM may be useful for complex traits.

Accuracy of genomic selection to predict maize single-crosses obtained through different mating designs.

KEY MESSAGE: Testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Even though many papers have been published about genomic prediction (GP) in maize, the best mating design to build the training population has not been defined yet. Such design must maximize the accuracy given constraints on costs and on the logistics of the crosses to be made. Hence, the aims of this work were: (1) empirically evaluate the effect of the mating designs, used as training set, on genomic selection to predict maize single-crosses obtained through full diallel and North Carolina design II, (2) and identify the possibility of reducing the number of crosses and parents to compose these training sets. Our results suggest that testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Moreover, North Carolina design II is the best training set to predict hybrids taken from full diallel. However, hybrids from full diallel and North Carolina design II can be well predicted using optimized training sets, which also allow reducing the total number of crosses to be made. Nevertheless, the number of parents and the crosses per parent in the training sets should be maximized.

Accuracies of univariate and multivariate genomic prediction models in African cassava.

BACKGROUND: Genomic selection (GS) promises to accelerate genetic gain in plant breeding programs especially for crop species such as cassava that have long breeding cycles. Practically, to implement GS in cassava breeding, it is necessary to evaluate different GS models and to develop suitable models for an optimized breeding pipeline. In this paper, we compared (1) prediction accuracies from a single-trait (uT) and a multi-trait (MT) mixed model for a single-environment genetic evaluation (Scenario 1), and (2) accuracies from a compound symmetric multi-environment model (uE) parameterized as a univariate multi-kernel model to a multivariate (ME) multi-environment mixed model that accounts for genotype-by-environment interaction for multi-environment genetic evaluation (Scenario 2). For these analyses, we used 16 years of public cassava breeding data for six target cassava traits and a fivefold cross-validation scheme with 10-repeat cycles to assess model prediction accuracies. RESULTS: In Scenario 1, the MT models had higher prediction accuracies than the uT models for all traits and locations analyzed, which amounted to on average a 40% improved prediction accuracy. For Scenario 2, we observed that the ME model had on average (across all locations and traits) a 12% improved prediction accuracy compared to the uE model. CONCLUSIONS: We recommend the use of multivariate mixed models (MT and ME) for cassava genetic evaluation. These models may be useful for other plant species.

Locally epistatic models for genome-wide prediction and association by importance sampling.

BACKGROUND: In statistical genetics, an important task involves building predictive models of the genotype-phenotype relationship to attribute a proportion of the total phenotypic variance to the variation in genotypes. Many models have been proposed to incorporate additive genetic effects into prediction or association models. Currently, there is a scarcity of models that can adequately account for gene by gene or other forms of genetic interactions, and there is an increased interest in using marker annotations in genome-wide prediction and association analyses. In this paper, we discuss a hybrid modeling method which combines parametric mixed modeling and non-parametric rule ensembles. RESULTS: This approach gives us a flexible class of models that can be used to capture additive, locally epistatic genetic effects, gene-by-background interactions and allows us to incorporate one or more annotations into the genomic selection or association models. We use benchmark datasets that cover a range of organisms and traits in addition to simulated datasets to illustrate the strengths of this approach. CONCLUSIONS: In this paper, we describe a new strategy for incorporating genetic interactions into genomic prediction and association models. This strategy results in accurate models, with sometimes significantly higher accuracies than that of a standard additive model.

Genome-Wide Association Analysis Using R.

This chapter provides a practical overview of the statistical analysis using R [1] and genotype by sequencing (GBS) markers for genome-wide association studies (GWAS) in oats. Statistical analysis is performed by R package rrBLUP [2] and issues associated with the analysis are addressed along with the R code. The ultimate aim of this chapter is to provide a practical guideline to do GWAS analysis using R, rather than describe the theory in depth. For more details about the subject, readers are referred to the excellent resource book in GWAS [3]. A basic programming experience in R is assumed.