Genomic prediction in multi-environment trials in maize using statistical and machine learning methods

In the context of multi-environment trials (MET), genomic prediction is proposed as a tool that allows the prediction of the phenotype of single cross hybrids that were not tested in field trials. This approach saves time and costs compared to traditional breeding methods. Thus, this study aimed to evaluate the genomic prediction of single cross maize hybrids not tested in MET, grain yield and female flowering time. We also aimed to propose an application of machine learning methodologies in MET in the prediction of hybrids and compare their performance with Genomic best linear unbiased prediction (GBLUP) with non-additive effects. Our results highlight that both methodologies are efficient and can be used in maize breeding programs to accurately predict the performance of hybrids in specific environments. The best methodology is case-dependent, specifically, to explore the potential of GBLUP, it is important to perform accurate modeling of the variance components to optimize the prediction of new hybrids. On the other hand, machine learning methodologies can capture non-additive effects without making any assumptions at the outset of the model. Overall, predicting the performance of new hybrids that were not evaluated in any field trials was more challenging than predicting hybrids in sparse test designs.

Using visual scores for genomic prediction of complex traits in breeding programs

KEY MESSAGE

An approach for handling visual scores with potential errors and subjectivity in scores was evaluated in simulated and blueberry recurrent selection breeding schemes to assist breeders in their decision-making. Most genomic prediction methods are based on assumptions of normality due to their simplicity and ease of implementation. However, in plant and animal breeding, continuous traits are often visually scored as categorical traits and analyzed as a Gaussian variable, thus violating the normality assumption, which could affect the prediction of breeding values and the estimation of genetic parameters. In this study, we examined the main challenges of visual scores for genomic prediction and genetic parameter estimation using mixed models, Bayesian, and machine learning methods. We evaluated these approaches using simulated and real breeding data sets. Our contribution in this study is a five-fold demonstration: (i) collecting data using an intermediate number of categories (1-3 and 1-5) is the best strategy, even considering errors associated with visual scores; (ii) Linear Mixed Models and Bayesian Linear Regression are robust to the normality violation, but marginal gains can be achieved when using Bayesian Ordinal Regression Models (BORM) and Random Forest Classification; (iii) genetic parameters are better estimated using BORM; (iv) our conclusions using simulated data are also applicable to real data in autotetraploid blueberry; and (v) a comparison of continuous and categorical phenotypes found that investing in the evaluation of 600-1000 categorical data points with low error, when it is not feasible to collect continuous phenotypes, is a strategy for improving predictive abilities. Our findings suggest the best approaches for effectively using visual scores traits to explore genetic information in breeding programs and highlight the importance of investing in the training of evaluator teams and in high-quality phenotyping.

Genomic studies of the additive and dominant genetic control on production traits of Euterpe edulis fruits

In forest genetic improvement programs for non-domesticated species, limited knowledge of kinship can compromise or make the estimation of variance components and genetic parameters of traits of interest unfeasible. We used mixed models and genomics (in the latter, considering additive and non-additive effects) to evaluate the genetic architecture of 12 traits in juçaizeiro for fruit production. A population of 275 genotypes without genetic relationship knowledge was phenotyped over three years and genotyped by whole genome SNP markers. We have verified superiority in the quality of the fits, the prediction accuracy for unbalanced data, and the possibility of unfolding the genetic effects into their additive and non-additive terms in the genomic models. Estimates of the variance components and genetic parameters obtained by the additive models may be overestimated since, when considering the dominance effect in the model, there are substantial reductions in them. The number of bunches, fresh fruit mass of bunch, rachis length, fresh mass of 25 fruits, and amount of pulp were strongly influenced by the dominance effect, showing that genomic models with such effect should be considered for these traits, which may result in selective improvements by being able to return more accurate genomic breeding values. The present study reveals the additive and non-additive genetic control of the evaluated traits and highlights the importance of genomic information-based approaches for populations without knowledge of kinship and experimental design. Our findings underscore the critical role of genomic data in elucidating the genetic control architecture of quantitative traits, thereby providing crucial insights for driving species' genetic improvement.

Population size in QTL detection using quantile regression in genome-wide association studies

The aim of this study was to evaluate the performance of Quantile Regression (QR) in Genome-Wide Association Studies (GWAS) regarding the ability to detect QTLs (Quantitative Trait Locus) associated with phenotypic traits of interest, considering different population sizes. For this, simulated data was used, with traits of different levels of heritability (0.30 and 0.50), and controlled by 3 and 100 QTLs. Populations of 1,000 to 200 individuals were defined, with a random reduction of 100 individuals for each population. The power of detection of QTLs and the false positive rate were obtained by means of QR considering three different quantiles (0.10, 0.50 and 0.90) and also by means of the General Linear Model (GLM). In general, it was observed that the QR models showed greater power of detection of QTLs in all scenarios evaluated and a relatively low false positive rate in scenarios with a greater number of individuals. The models with the highest detection power of true QTLs at the extreme quantils (0.10 and 0.90) were the ones with the highest detection power of true QTLs. In contrast, the analysis based on the GLM detected few (scenarios with larger population size) or no QTLs in the evaluated scenarios. In the scenarios with low heritability, QR obtained a high detection power. Thus, it was verified that the use of QR in GWAS is effective, allowing the detection of QTLs associated with traits of interest even in scenarios with few genotyped and phenotyped individuals.

Single and multi-trait genomic prediction for agronomic traits in Euterpe edulis

Popularly known as juçaizeiro, Euterpe edulis has been gaining prominence in the fruit growing sector and has demanded the development of superior genetic materials. Since it is a native species and still little studied, the application of more sophisticated techniques can result in higher gains with less time. Until now, there are no studies that apply genomic prediction for this crop, especially in multi-trait analysis. In this sense, this study aimed to apply new methods and breeding techniques for the juçaizeiro, to optimize this breeding program through the application of genomic prediction. This data consisted of 275 juçaizeiro genotypes from a population of Rio Novo do Sul-ES, Brazil. The genomic prediction was performed using the multi-trait (G-BLUP MT) and single-trait (G-BLUP ST) models and the selection of superior genotypes was based on a selection index. Similar results for predictive ability were observed for both models. However, the G-BLUP ST model provided greater selection gains when compared to the G-BLUP MT. For this reason, the genomic estimated breeding values (GEBVs) from the G-BLUP ST, were used to select the six superior genotypes (UFES.A.RN.390, UFES.A.RN.386, UFES.A.RN.080, UFES.A.RN.383, UFES.S.RN.098, and UFES.S.RN.093). This was intended to provide superior genetic materials for the development of seedlings and implantation of productive orchards, which will meet the demands of the productive, industrial and consumer market.

Increasing cassava root yield: Additive-dominant genetic models for selection of parents and clones

Genomic selection has been promising in situations where phenotypic assessments are expensive, laborious, and/or inefficient. This work evaluated the efficiency of genomic prediction methods combined with genetic models in clone and parent selection with the goal of increasing fresh root yield, dry root yield, as well as dry matter content in cassava roots. The bias and predictive ability of the combinations of prediction methods Genomic Best Linear Unbiased Prediction (G-BLUP), Bayes B, Bayes Cπ, and Reproducing Kernel Hilbert Spaces with additive and additive-dominant genetic models were estimated. Fresh and dry root yield exhibited predominantly dominant heritability, while dry matter content exhibited predominantly additive heritability. The combination of prediction methods and genetic models did not show significant differences in the predictive ability for dry matter content. On the other hand, the prediction methods with additive-dominant genetic models had significantly higher predictive ability than the additive genetic models for fresh and dry root yield, allowing higher genetic gains in clone selection. However, higher predictive ability for genotypic values did not result in differences in breeding value predictions between additive and additive-dominant genetic models. G-BLUP with the classical additive-dominant genetic model had the best predictive ability and bias estimates for fresh and dry root yield. For dry matter content, the highest predictive ability was obtained by G-BLUP with the additive genetic model. Dry matter content exhibited the highest heritability, predictive ability, and bias estimates compared with other traits. The prediction methods showed similar selection gains with approximately 67% of the phenotypic selection gain. By shortening the breeding cycle time by 40%, genomic selection may overcome phenotypic selection by 10%, 13%, and 18% for fresh root yield, dry root yield, and dry matter content, respectively, with a selection proportion of 15%. The most suitable genetic model for each trait allows for genomic selection optimization in cassava with high selection gains, thereby accelerating the release of new varieties.

Microbiome of rehydrated corn and sorghum grain silages treated with microbial inoculants in different fermentation periods

Due to the co-evolved intricate relationships and mutual influence between changes in the microbiome and silage fermentation quality, we explored the effects of Lactobacillus plantarum and Propionibacterium acidipropionici (Inoc1) or Lactobacillus buchneri (Inoc2) inoculants on the diversity and bacterial and fungal community succession of rehydrated corn (CG) and sorghum (SG) grains and their silages using Illumina Miseq sequencing after 0, 3, 7, 21, 90, and 360 days of fermentation. The effects of inoculants on bacterial and fungal succession differed among the grains. Lactobacillus and Weissella species were the main bacteria involved in the fermentation of rehydrated corn and sorghum grain silage. Aspergillus spp. mold was predominant in rehydrated CG fermentation, while the yeast Wickerhamomyces anomalus was the major fungus in rehydrated SG silages. The Inoc1 was more efficient than CTRL and Inoc2 in promoting the sharp growth of Lactobacillus spp. and maintaining the stability of the bacterial community during long periods of storage in both grain silages. However, the bacterial and fungal communities of rehydrated corn and sorghum grain silages did not remain stable after 360 days of storage.

Multi-trait and multi-environment Bayesian analysis to predict the G x E interaction in flood-irrigated rice

The biggest challenge for the reproduction of flood-irrigated rice is to identify superior genotypes that present development of high-yielding varieties with specific grain qualities, resistance to abiotic and biotic stresses in addition to superior adaptation to the target environment. Thus, the objectives of this study were to propose a multi-trait and multi-environment Bayesian model to estimate genetic parameters for the flood-irrigated rice crop. To this end, twenty-five rice genotypes belonging to the flood-irrigated rice breeding program were evaluated. Grain yield and flowering were evaluated in the agricultural year 2017/2018. The experimental design used in all experiments was a randomized block design with three replications. The Markov Chain Monte Carlo algorithm was used to estimate genetic parameters and genetic values. The flowering is highly heritable by the Bayesian credibility interval: h2 = 0.039-0.80, and 0.02-0.91, environment 1 and 2, respectively. The genetic correlation between traits was significantly different from zero in the two environments (environment 1: -0.80 to 0.74; environment 2: -0.82 to 0.86. The relationship of CVe and CVg higher for flowering in the reduced model (CVg/CVe = 5.83 and 13.98, environments 1 and 2, respectively). For the complete model, this trait presented an estimate of the relative variation index of: CVe = 4.28 and 4.21, environments 1 and 2, respectively. In summary, the multi-trait and multi-environment Bayesian model allowed a reliable estimate of the genetic parameter of flood-irrigated rice. Bayesian analyzes provide robust inference of genetic parameters. Therefore, we recommend this model for genetic evaluation of flood-irrigated rice genotypes, and their generalization, in other crops. Precise estimates of genetic parameters bring new perspectives on the application of Bayesian methods to solve modeling problems in the genetic improvement of flood-irrigated rice.

Factor analysis applied in genomic selection studies in the breeding of Coffea canephora

Brazil stands out worldwide in the production of coffee. The observed increases in its productivity and morpho agronomic traits are the results of the improvement of several methodologies applied in obtaining improved cultivars, among which the predictive methods of genetic value stand out. These contribute significantly to the selection of higher genotypes, increasing the genetic gain per unit time. In this context, genomic-wide selection (GWS) is a tool that stands out, since it allows predicting the future phenotype of an individual based only on molecular information. Performing joint selection of traits is the interest of most breeding programs, and factor analysis (FA) has been used to assist in this end. The aim of this study was to evaluate the use of FA in the context of GWS, in genotypes of Coffea canephora. It was found that FA was efficient to elucidate the relationships between the traits and generate new variables. The factors formed can assist in the selection, as in addition to allowing joint interpretations, they present good estimates of predictive capacity, heritability and accuracy. Furthermore, high agreement was observed between the individuals selected based on the factors and those selected considering the individual traits. Additionally, it was observed agreement between the top 10% individuals selected based on the "vigor factor" and each variable individually. However, the selection based on "vigor factor" presented individuals with more suitable size from the phytotechnical point of view.

Marker effects and heritability estimates using additive-dominance genomic architectures via artificial neural networks in Coffea canephora

Many methodologies are used to predict the genetic merit in animals and plants, but some of them require priori assumptions that may increase the complexity of the model. Artificial neural network (ANN) has advantage to not require priori assumptions about the relationships between inputs and the output allowing great flexibility to handle different types of complex non-additive effects, such as dominance and epistasis. Despite this advantage, the biological interpretability of ANNs is still limited. The aim of this research was to estimate the heritability and markers effects for two traits in Coffea canephora using an additive-dominance architecture ANN and to compare it with genomic best linear unbiased prediction (GBLUP). The data used consists of 51 clones of C. canephora varietal Conilon, 32 of varietal group Robusta and 82 intervarietal hybrids. From this, 165 phenotyped individuals were genotyped for 14,387 SNPs. Due to the high computational cost of ANNs, we used Bagging decision tree to reduce the dimensionality of the data, selecting the markers that accumulated 70% of the total importance. An ANN with three hidden layers was run, each varying from 1 to 40 neurons summing 64,000 neural networks. The network architectures with the best predictive ability were selected. The best architectures were composed by 4, 15, and 33 neurons in the first, second and third hidden layers, respectively, for yield, and by 13, 20, and 24 neurons, respectively for rust resistance. The predictive ability was greater when using ANN with three hidden layers than using one hidden layer and GBLUP, with 0.72 and 0.88 for yield and coffee leaf rust resistance, respectively. The concordance rate (CR) of the 10% larger markers effects among the methods varied between 10% and 13.8%, for additive effects and between 5.4% and 11.9% for dominance effects. The narrow-sense ([Formula: see text]) and dominance-only ([Formula: see text]) heritability estimates were 0.25 and 0.06, respectively, for yield, and 0.67 and 0.03, respectively for rust resistance. The ANN was able to estimate the heritabilities from an additive-dominance genomic architectures and the ANN with three hidden layers obtained best predictive ability when compared with those obtained from GBLUP and ANN with one hidden layer.

Phenotypic and molecular characterization of a set of tropical maize inbred lines from a public breeding program in Brazil

Background

The characterization of genetic diversity and population differentiation for maize inbred lines from breeding programs is of great value in assisting breeders in maintaining and potentially increasing the rate of genetic gain. In our study, we characterized a set of 187 tropical maize inbred lines from the public breeding program of the Universidade Federal de Viçosa (UFV) in Brazil based on 18 agronomic traits and 3,083 single nucleotide polymorphisms (SNP) markers to evaluate whether this set of inbred lines represents a panel of tropical maize inbred lines for association mapping analysis and investigate the population structure and patterns of relationships among the inbred lines from UFV for better exploitation in our maize breeding program.

Results

Our results showed that there was large phenotypic and genotypic variation in the set of tropical maize inbred lines from the UFV maize breeding program. We also found high genetic diversity (GD = 0.34) and low pairwise kinship coefficients among the maize inbred lines (only approximately 4.00 % of the pairwise relative kinship was above 0.50) in the set of inbred lines. The LD decay distance over all ten chromosomes in the entire set of maize lines with r² = 0.1 was 276,237 kb. Concerning the population structure, our results from the model-based STRUCTURE and principal component analysis methods distinguished the inbred lines into three subpopulations, with high consistency maintained between both results. Additionally, the clustering analysis based on phenotypic and molecular data grouped the inbred lines into 14 and 22 genetic divergence clusters, respectively.

Conclusions

Our results indicate that the set of tropical maize inbred lines from UFV maize breeding programs can comprise a panel of tropical maize inbred lines suitable for a genome-wide association study to dissect the variation of complex quantitative traits in maize, mainly in tropical environments. In addition, our results will be very useful for assisting us in the assignment of heterotic groups and the selection of the best parental combinations for new breeding crosses, mapping populations, mapping synthetic populations, guiding crosses that target highly heterotic and yielding hybrids, and predicting untested hybrids in the public breeding program UFV.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12864-021-08127-7.

Can Cross-Country Genomic Predictions Be a Reasonable Strategy to Support Germplasm Exchange? - A Case Study With Hydrogen Cyanide in Cassava

Genomic prediction (GP) offers great opportunities for accelerated genetic gains by optimizing the breeding pipeline. One of the key factors to be considered is how the training populations (TP) are composed in terms of genetic improvement, kinship/origin, and their impacts on GP. Hydrogen cyanide content (HCN) is a determinant trait to guide cassava's products usage and processing. This work aimed to achieve the following objectives: (i) evaluate the feasibility of using cross-country (CC) GP between germplasm's of Embrapa Mandioca e Fruticultura (Embrapa, Brazil) and The International Institute of Tropical Agriculture (IITA, Nigeria) for HCN; (ii) provide an assessment of population structure for the joint dataset; (iii) estimate the genetic parameters based on single nucleotide polymorphisms (SNPs) and a haplotype-approach. Datasets of HCN from Embrapa and IITA breeding programs were analyzed, separately and jointly, with 1,230, 590, and 1,820 clones, respectively. After quality control, ∼14K SNPs were used for GP. The genomic estimated breeding values (GEBVs) were predicted based on SNP effects from analyses with TP composed of the following: (i) Embrapa genotypic and phenotypic data, (ii) IITA genotypic and phenotypic data, and (iii) the joint datasets. Comparisons on GEBVs' estimation were made considering the hypothetical situation of not having the phenotypic characterization for a set of clones for a certain research institute/country and might need to use the markers' effects that were trained with data from other research institutes/country's germplasm to estimate their clones' GEBV. Fixation index (F_ST) among the genetic groups identified within the joint dataset ranged from 0.002 to 0.091. The joint dataset provided an improved accuracy (0.8-0.85) compared to the prediction accuracy of either germplasm's sources individually (0.51-0.67). CC GP proved to have potential use under the present study's scenario, the correlation between GEBVs predicted with TP from Embrapa and IITA was 0.55 for Embrapa's germplasm, whereas for IITA's it was 0.1. This seems to be among the first attempts to evaluate the CC GP in plants. As such, a lot of useful new information was provided on the subject, which can guide new research on this very important and emerging field.

Prediction of the importance of auxiliary traits using computational intelligence and machine learning: A simulation study

The present study evaluated the importance of auxiliary traits of a principal trait based on phenotypic information and previously known genetic structure using computational intelligence and machine learning to develop predictive tools for plant breeding. Data of an F₂ population represented by 500 individuals, obtained from a cross between contrasting homozygous parents, were simulated. Phenotypic traits were simulated based on previously established means and heritability estimates (30%, 50%, and 80%); traits were distributed in a genome with 10 linkage groups, considering two alleles per marker. Four different scenarios were considered. For the principal trait, heritability was 50%, and 40 control loci were distributed in five linkage groups. Another phenotypic control trait with the same complexity as the principal trait but without any genetic relationship with it and without pleiotropy or a factorial link between the control loci for both traits was simulated. These traits shared a large number of control loci with the principal trait, but could be distinguished by the differential action of the environment on them, as reflected in heritability estimates (30%, 50%, and 80%). The coefficient of determination were considered to evaluate the proposed methodologies. Multiple regression, computational intelligence, and machine learning were used to predict the importance of the tested traits. Computational intelligence and machine learning were superior in extracting nonlinear information from model inputs and quantifying the relative contributions of phenotypic traits. The R² values ranged from 44.0% - 83.0% and 79.0% - 94.0%, for computational intelligence and machine learning, respectively. In conclusion, the relative contributions of auxiliary traits in different scenarios in plant breeding programs can be efficiently predicted using computational intelligence and machine learning.

Quantile regression in genomic selection for oligogenic traits in autogamous plants: A simulation study

This study assessed the efficiency of Genomic selection (GS) or genome-wide selection (GWS), based on Regularized Quantile Regression (RQR), in the selection of genotypes to breed autogamous plant populations with oligogenic traits. To this end, simulated data of an F2 population were used, with traits with different heritability levels (0.10, 0.20 and 0.40), controlled by four genes. The generations were advanced (up to F6) at two selection intensities (10% and 20%). The genomic genetic value was computed by RQR for different quantiles (0.10, 0.50 and 0.90), and by the traditional GWS methods, specifically RR-BLUP and BLASSO. A second objective was to find the statistical methodology that allows the fastest fixation of favorable alleles. In general, the results of the RQR model were better than or equal to those of traditional GWS methodologies, achieving the fixation of favorable alleles in most of the evaluated scenarios. At a heritability level of 0.40 and a selection intensity of 10%, RQR (0.50) was the only methodology that fixed the alleles quickly, i.e., in the fourth generation. Thus, it was concluded that the application of RQR in plant breeding, to simulated autogamous plant populations with oligogenic traits, could reduce time and consequently costs, due to the reduction of selfing generations to fix alleles in the evaluated scenarios.

Cassava yield traits predicted by genomic selection methods

Genomic selection (GS) has been used to optimize genetic gains when phenotypic selection is considered costly and difficult to measure. The objective of this work was to evaluate the efficiency and consistency of GS prediction for cassava yield traits (Manihot esculenta Crantz) using different methods, taking into account the effect of population structure. BLUPs and deregressed BLUPs were obtained for 888 cassava accessions and evaluated for fresh root yield, dry root yield and dry matter content in roots in 21 trials conducted from 2011 to 2016. The deregressed BLUPs obtained for the accessions from a 48K single nucleotide polymorphism dataset were used for genomic predictions based on the BayesB, BLASSO, RR-BLUP, G-BLUP and RKHS methods. The accessions’ BLUPs were used in the validation step using four cross-validation strategies, taking into account population structure and different GS methods. Similar estimates of predictive ability and bias were identified for the different genomic selection methods in the first cross-validation strategy. Lower predictive ability was observed for fresh root yield (0.4569 –RR-BLUP to 0.4756—RKHS) and dry root yield (0.4689 –G-BLUP to 0.4818—RKHS) in comparison with dry matter content (0.5655 –BLASSO to 0.5670 –RKHS). However, the RKHS method exhibited higher efficiency and consistency in most of the validation scenarios in terms of prediction ability for fresh root yield and dry root yield. The correlations of the genomic estimated breeding values between the genomic selection methods were quite high (0.99–1.00), resulting in high coincidence of clone selection regardless of the genomic selection method. The deviance analyses within and between the validation clusters formed by the discriminant analysis of principal components were significant for all traits. Therefore, this study indicated that i) the prediction of dry matter content was more accurate compared to that of yield traits, possibly as a result of the smaller influence of non-additive genetic effects; ii) the RKHS method resulted in high and stable prediction ability in most of the validation scenarios; and iii) some kinship between the validation and training populations is desirable in order for genomic selection to succeed due to the significant effect of population structure on genomic selection predictions.

Multi-trait multi-environment Bayesian model reveals G x E interaction for nitrogen use efficiency components in tropical maize

Identifying maize inbred lines that are more efficient in nitrogen (N) use is an important strategy and a necessity in the context of environmental and economic impacts attributed to the excessive N fertilization. N-uptake efficiency (NUpE) and N-utilization efficiency (NUtE) are components of N-use efficiency (NUE). Despite the most maize breeding data have a multi-trait structure, they are often analyzed under a single-trait framework. We aimed to estimate the genetic parameters for NUpE and NUtE in contrasting N levels, in order to identify superior maize inbred lines, and to propose a Bayesian multi-trait multi-environment (MTME) model. Sixty-four tropical maize inbred lines were evaluated in two experiments: at high (HN) and low N (LN) levels. The MTME model was compared to single-trait multi-environment (STME) models. Based on deviance information criteria (DIC), both multi- and single-trait models revealed genotypes x environments (G x E) interaction. In the MTME model, NUpE was found to be weakly heritable with posterior modes of heritability of 0.016 and 0.023 under HN and LN, respectively. NUtE at HN was found to be highly heritable (0.490), whereas under LN condition it was moderately heritable (0.215). We adopted the MTME model, since combined analysis often presents more accurate breeding values than single models. Superior inbred lines for NUpE and NUtE were identified and this information can be used to plan crosses to obtain maize hybrids that have superior nitrogen use efficiency.

Independent Component Analysis (ICA) based-clustering of temporal RNA-seq data

Gene expression time series (GETS) analysis aims to characterize sets of genes according to their longitudinal patterns of expression. Due to the large number of genes evaluated in GETS analysis, an useful strategy to summarize biological functional processes and regulatory mechanisms is through clustering of genes that present similar expression pattern over time. Traditional cluster methods usually ignore the challenges in GETS, such as the lack of data normality and small number of temporal observations. Independent Component Analysis (ICA) is a statistical procedure that uses a transformation to convert raw time series data into sets of values of independent variables, which can be used for cluster analysis to identify sets of genes with similar temporal expression patterns. ICA allows clustering small series of distribution-free data while accounting for the dependence between subsequent time-points. Using temporal simulated and real (four libraries of two pig breeds at 21, 40, 70 and 90 days of gestation) RNA-seq data set we present a methodology (ICAclust) that jointly considers independent components analysis (ICA) and a hierarchical method for clustering GETS. We compare ICAclust results with those obtained for K-means clustering. ICAclust presented, on average, an absolute gain of 5.15% over the best K-means scenario. Considering the worst scenario for K-means, the gain was of 84.85%, when compared with the best ICAclust result. For the real data set, genes were grouped into six distinct clusters with 89, 51, 153, 67, 40, and 58 genes each, respectively. In general, it can be observed that the 6 clusters presented very distinct expression patterns. Overall, the proposed two-step clustering method (ICAclust) performed well compared to K-means, a traditional method used for cluster analysis of temporal gene expression data. In ICAclust, genes with similar expression pattern over time were clustered together.

Regularized quantile regression for SNP marker estimation of pig growth curves

Background

Genomic growth curves are generally defined only in terms of population mean; an alternative approach that has not yet been exploited in genomic analyses of growth curves is the Quantile Regression (QR). This methodology allows for the estimation of marker effects at different levels of the variable of interest. We aimed to propose and evaluate a regularized quantile regression for SNP marker effect estimation of pig growth curves, as well as to identify the chromosome regions of the most relevant markers and to estimate the genetic individual weight trajectory over time (genomic growth curve) under different quantiles (levels).

Results

The regularized quantile regression (RQR) enabled the discovery, at different levels of interest (quantiles), of the most relevant markers allowing for the identification of QTL regions. We found the same relevant markers simultaneously affecting different growth curve parameters (mature weight and maturity rate): two (ALGA0096701 and ALGA0029483) for RQR(0.2), one (ALGA0096701) for RQR(0.5), and one (ALGA0003761) for RQR(0.8). Three average genomic growth curves were obtained and the behavior was explained by the curve in quantile 0.2, which differed from the others.

Conclusions

RQR allowed for the construction of genomic growth curves, which is the key to identifying and selecting the most desirable animals for breeding purposes. Furthermore, the proposed model enabled us to find, at different levels of interest (quantiles), the most relevant markers for each trait (growth curve parameter estimates) and their respective chromosomal positions (identification of new QTL regions for growth curves in pigs). These markers can be exploited under the context of marker assisted selection while aiming to change the shape of pig growth curves.

Assessing the expected response to genomic selection of individuals and families in Eucalyptus breeding with an additive-dominant model

We report a genomic selection (GS) study of growth and wood quality traits in an outbred F₂ hybrid Eucalyptus population (n=768) using high-density single-nucleotide polymorphism (SNP) genotyping. Going beyond previous reports in forest trees, models were developed for different selection targets, namely, families, individuals within families and individuals across the entire population using a genomic model including dominance. To provide a more breeder-intelligible assessment of the performance of GS we calculated the expected response as the percentage gain over the population average expected genetic value (EGV) for different proportions of genomically selected individuals, using a rigorous cross-validation (CV) scheme that removed relatedness between training and validation sets. Predictive abilities (PAs) were 0.40-0.57 for individual selection and 0.56-0.75 for family selection. PAs under an additive+dominance model improved predictions by 5 to 14% for growth depending on the selection target, but no improvement was seen for wood traits. The good performance of GS with no relatedness in CV suggested that our average SNP density (~25 kb) captured some short-range linkage disequilibrium. Truncation GS successfully selected individuals with an average EGV significantly higher than the population average. Response to GS on a per year basis was ~100% more efficient than by phenotypic selection and more so with higher selection intensities. These results contribute further experimental data supporting the positive prospects of GS in forest trees. Because generation times are long, traits are complex and costs of DNA genotyping are plummeting, genomic prediction has good perspectives of adoption in tree breeding practice.

Regional heritability mapping and genome-wide association identify loci for complex growth, wood and disease resistance traits in Eucalyptus

Although genome-wide association studies (GWAS) have provided valuable insights into the decoding of the relationships between sequence variation and complex phenotypes, they have explained little heritability. Regional heritability mapping (RHM) provides heritability estimates for genomic segments containing both common and rare allelic effects that individually contribute too little variance to be detected by GWAS. We carried out GWAS and RHM for seven growth, wood and disease resistance traits in a breeding population of 768 Eucalyptus hybrid trees using EuCHIP60K. Total genomic heritabilities accounted for large proportions (64-89%) of pedigree-based trait heritabilities, providing additional evidence that complex traits in eucalypts are controlled by many sequence variants across the frequency spectrum, each with small contributions to the phenotypic variance. RHM detected 26 quantitative trait loci (QTLs) encompassing 2191 single nucleotide polymorphisms (SNPs), whereas GWAS detected 13 single SNP-trait associations. RHM and GWAS QTLs individually explained 5-15% and 4-6% of the genomic heritability, respectively. RHM was superior to GWAS in capturing larger proportions of genomic heritability. Equated to previously mapped QTLs, our results highlighted genomic regions for further examination towards gene discovery. RHM-QTLs bearing a combination of common and rare variants could be useful enhancements to incorporate prior knowledge of the underlying genetic architecture in genomic prediction models.

Using artificial neural networks to select upright cowpea (Vigna unguiculata) genotypes with high productivity and phenotypic stability

Cowpea (Vigna unguiculata) is grown in three Brazilian regions: the Midwest, North, and Northeast, and is consumed by people on low incomes. It is important to investigate the genotype x environment (GE) interaction to provide accurate recommendations for farmers. The aim of this study was to identify cowpea genotypes with high adaptability and phenotypic stability for growing in the Brazilian Cerrado, and to compare the use of artificial neural networks with the Eberhart and Russell (1966) method. Six trials with upright cowpea genotypes were conducted in 2005 and 2006 in the States of Mato Grosso do Sul and Mato Grosso. The data were subjected to adaptability and stability analysis by the Eberhart and Russell (1966) method and artificial neural networks. The genotypes MNC99-537F-4 and EVX91-2E-2 provided grain yields above the overall environment means, and exhibited high stability according to both methods. Genotype IT93K-93-10 was the most suitable for unfavorable environments. There was a high correlation between the results of both methods in terms of classifying the genotypes by their adaptability and stability. Therefore, this new approach would be effective in quantifying the GE interaction in upright cowpea breeding programs.

Genome wide selection in Citrus breeding

Genome wide selection (GWS) is essential for the genetic improvement of perennial species such as Citrus because of its ability to increase gain per unit time and to enable the efficient selection of characteristics with low heritability. This study assessed GWS efficiency in a population of Citrus and compared it with selection based on phenotypic data. A total of 180 individual trees from a cross between Pera sweet orange (Citrus sinensis Osbeck) and Murcott tangor (Citrus sinensis Osbeck x Citrus reticulata Blanco) were evaluated for 10 characteristics related to fruit quality. The hybrids were genotyped using 5287 DArT_seq^TM (diversity arrays technology) molecular markers and their effects on phenotypes were predicted using the random regression - best linear unbiased predictor (rr-BLUP) method. The predictive ability, prediction bias, and accuracy of GWS were estimated to verify its effectiveness for phenotype prediction. The proportion of genetic variance explained by the markers was also computed. The heritability of the traits, as determined by markers, was 16-28%. The predictive ability of these markers ranged from 0.53 to 0.64, and the regression coefficients between predicted and observed phenotypes were close to unity. Over 35% of the genetic variance was accounted for by the markers. Accuracy estimates with GWS were lower than those obtained by phenotypic analysis; however, GWS was superior in terms of genetic gain per unit time. Thus, GWS may be useful for Citrus breeding as it can predict phenotypes early and accurately, and reduce the length of the selection cycle. This study demonstrates the feasibility of genomic selection in Citrus.

Genomic prediction for additive and dominance effects of censored traits in pigs

Age at the time of slaughter is a commonly used trait in animal breeding programs. Since studying this trait involves incomplete observations (censoring), analysis can be performed using survival models or modified linear models, for example, by sampling censored data from truncated normal distributions. For genomic selection, the greatest genetic gains can be achieved by including non-additive genetic effects like dominance. Thus, censored traits with effects on both survival models have not yet been studied under a genomic selection approach. We aimed to predict genomic values using the Cox model with dominance effects and compare these results with the linear model with and without censoring. Linear models were fitted via the maximum likelihood method. For censored data, sampling through the truncated normal distribution was used, and the model was called the truncated normal linear via Gibbs sampling (TNL). We used an F₂ pig population; the response variable was time (days) from birth to slaughter. Data were previously adjusted for fixed effects of sex and contemporary group. The model predictive ability was calculated based on correlation of predicted genomic values with adjusted phenotypic values. The results showed that both with and without censoring, there was high agreement between Cox and linear models in selection of individuals and markers. Despite including the dominance effect, there was no increase in predictive ability. This study showed, for the first time, the possibility of performing genomic prediction of traits with censored records while using the Cox survival model with additive and dominance effects.

New accuracy estimators for genomic selection with application in a cassava (Manihot esculenta) breeding program

Genomic selection is the main force driving applied breeding programs and accuracy is the main measure for evaluating its efficiency. The traditional estimator (TE) of experimental accuracy is not fully adequate. This study proposes and evaluates the performance and efficiency of two new accuracy estimators, called regularized estimator (RE) and hybrid estimator (HE), which were applied to a practical cassava breeding program and also to simulated data. The simulation study considered two individual narrow sense heritability levels and two genetic architectures for traits. TE, RE, and HE were compared under four validation procedures: without validation (WV), independent validation, ten-fold validation through jacknife allowing different markers, and with the same markers selected in each cycle. RE presented accuracies closer to the parametric ones and less biased and more precise ones than TE. HE proved to be very effective in the WV procedure. The estimators were applied to five traits evaluated in a cassava experiment, including 358 clones genotyped for 390 SNPs. Accuracies ranged from 0.67 to 1.12 with TE and from 0.22 to 0.51 with RE. These results indicated that TE overestimated the accuracy and led to one accuracy estimate (1.12) higher than one, which is outside of the parameter space. Use of RE turned the accuracy into the parameter space. Cassava breeding programs can be more realistically implemented using the new estimators proposed in this study, providing less risky practical inferences.

Genomic selection for slaughter age in pigs using the Cox frailty model

The aim of this study was to compare genomic selection methodologies using a linear mixed model and the Cox survival model. We used data from an F2 population of pigs, in which the response variable was the time in days from birth to the culling of the animal and the covariates were 238 markers [237 single nucleotide polymorphism (SNP) plus the halothane gene]. The data were corrected for fixed effects, and the accuracy of the method was determined based on the correlation of the ranks of predicted genomic breeding values (GBVs) in both models with the corrected phenotypic values. The analysis was repeated with a subset of SNP markers with largest absolute effects. The results were in agreement with the GBV prediction and the estimation of marker effects for both models for uncensored data and for normality. However, when considering censored data, the Cox model with a normal random effect (S1) was more appropriate. Since there was no agreement between the linear mixed model and the imputed data (L2) for the prediction of genomic values and the estimation of marker effects, the model S1 was considered superior as it took into account the latent variable and the censored data. Marker selection increased correlations between the ranks of predicted GBVs by the linear and Cox frailty models and the corrected phenotypic values, and 120 markers were required to increase the predictive ability for the characteristic analyzed.

Comparison of dimensionality reduction methods to predict genomic breeding values for carcass traits in pigs

A significant contribution of molecular genetics is the direct use of DNA information to identify genetically superior individuals. With this approach, genome-wide selection (GWS) can be used for this purpose. GWS consists of analyzing a large number of single nucleotide polymorphism markers widely distributed in the genome; however, because the number of markers is much larger than the number of genotyped individuals, and such markers are highly correlated, special statistical methods are widely required. Among these methods, independent component regression, principal component regression, partial least squares, and partial principal components stand out. Thus, the aim of this study was to propose an application of the methods of dimensionality reduction to GWS of carcass traits in an F2 (Piau x commercial line) pig population. The results show similarities between the principal and the independent component methods and provided the most accurate genomic breeding estimates for most carcass traits in pigs.

Ridge, Lasso and Bayesian additive-dominance genomic models

Background

A complete approach for genome-wide selection (GWS) involves reliable statistical genetics models and methods. Reports on this topic are common for additive genetic models but not for additive-dominance models. The objective of this paper was (i) to compare the performance of 10 additive-dominance predictive models (including current models and proposed modifications), fitted using Bayesian, Lasso and Ridge regression approaches; and (ii) to decompose genomic heritability and accuracy in terms of three quantitative genetic information sources, namely, linkage disequilibrium (LD), co-segregation (CS) and pedigree relationships or family structure (PR). The simulation study considered two broad sense heritability levels (0.30 and 0.50, associated with narrow sense heritabilities of 0.20 and 0.35, respectively) and two genetic architectures for traits (the first consisting of small gene effects and the second consisting of a mixed inheritance model with five major genes).

Results

G-REML/G-BLUP and a modified Bayesian/Lasso (called BayesA*B* or t-BLASSO) method performed best in the prediction of genomic breeding as well as the total genotypic values of individuals in all four scenarios (two heritabilities x two genetic architectures). The BayesA*B*-type method showed a better ability to recover the dominance variance/additive variance ratio. Decomposition of genomic heritability and accuracy revealed the following descending importance order of information: LD, CS and PR not captured by markers, the last two being very close.

Conclusions

Amongst the 10 models/methods evaluated, the G-BLUP, BAYESA*B* (−2,8) and BAYESA*B* (4,6) methods presented the best results and were found to be adequate for accurately predicting genomic breeding and total genotypic values as well as for estimating additive and dominance in additive-dominance genomic models.

Estimating additive and dominance variances for complex traits in pigs combining genomic and pedigree information

Knowledge of dominance effects should improve ge-netic evaluations, provide the accurate selection of purebred animals, and enable better breeding strategies, including the exploitation of het-erosis in crossbreeds. In this study, we combined genomic and pedi-gree data to study the relative importance of additive and dominance genetic variation in growth and carcass traits in an F2 pig population. Two GBLUP models were used, a model without a polygenic effect (ADM) and a model with a polygenic effect (ADMP). Additive effects played a greater role in the control of growth and carcass traits than did dominance effects. However, dominance effects were important for all traits, particularly in backfat thickness. The narrow-sense and broad-sense heritability estimates for growth (0.06 to 0.42, and 0.10 to 0.51, respectively) and carcass traits (0.07 to 0.37, and 0.10 to 0.76, respec-tively) exhibited a wide variation. The inclusion of a polygenic effect in the ADMP model changed the broad-sense heritability estimates only for birth weight and weight at 21 days of age.

Supervised independent component analysis as an alternative method for genomic selection in pigs

The objective of this work was to evaluate the efficiency of the supervised independent component regression (SICR) method for the estimation of genomic values and the SNP marker effects for boar taint and carcass traits in pigs. The methods were evaluated via the agreement between the predicted genetic values and the corrected phenotypes observed by cross-validation. These values were also compared with other methods generally used for the same purposes, such as RR-BLUP, SPCR, SPLS, ICR, PCR and PLS. The SICR method was found to have the most accurate prediction values.