A comparison of experimental designs for selection in breeding trials with nested treatment structure

Relationships Among Arsenic-Related Traits, Including Rice Grain Arsenic Concentration and Straighthead Resistance, as Revealed by Genome-Wide Association

There is global concern that rice grains and foods can contain harmful amounts of arsenic (As), motivating breeders to produce cultivars that restrict As accumulation in grains to protect human health. Arsenic is also toxic to plants, with straighthead disorder (StHD), causing panicle sterility, being observed in rice. The genetic variation in StHD resistance suggests that plants have evolved mechanisms that reduce As toxicity, possibly via regulation of As uptake, transport, or detoxification/sequestration. Because these mechanisms could also underlie the wide (3- to 100-fold) differences in grain As concentration (grain-As) observed among diverse rice genotypes, it was hypothesized that some genes reduce both grain-As content and StHD susceptibility and may be detectable as co-located StDH and As quantitative trait loci (QTL). We used a machine-learning Bayesian network approach plus high-resolution genome-wide association study (GWAS) to identify QTL for grain-As and StHD resistance within the USDA Rice Minicore Collection (RMC). Arsenic enters roots through phosphorus (P) and silica (Si) transporters, As detoxification involves sulfur (S), and cell signaling to activate stress tolerance mechanisms is impacted by Si, calcium (Ca), and copper (Cu). Therefore, concentrations of Si, P, S, Ca, and Cu were included in this study to elucidate physiological mechanisms underlying grain-As and StHD QTL. Multiple QTL (from 9 to 33) were identified for each of the investigated As-associated traits. Although the QTL for StHD, Si, and grain-As did not overlap as heavily as our hypothesis predicted (4/33 StHD and 4/15 As QTL co-located), they do provide useful guidance to future research. Furthermore, these are the first StHD and Si QTL to be identified using high-density mapping, resulting in their being mapped to shorter, more precise genomic regions than previously reported QTL. The candidate genes identified provide guidance for future research, such as gene editing or mutation studies to further investigate the role of antioxidants and ROS scavenging to StHD resistance, as indicated by candidate genes around the commonly reported qStHD8-2 QTL. Other genes indicated for future study for improving grain-As and StHD include several multidrug and toxic compound extrusion (MATE) genes, F-box genes, and NIPs not documented to date to transport As.

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

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.

Genome-enabled prediction for sparse testing in multi-environmental wheat trials

Sparse testing in genome-enabled prediction in plant breeding can be emulated throughout different line allocations where some lines are observed in all environments (overlap) and others are observed in only one environment (nonoverlap). We studied three general cases of the composition of the sparse testing allocation design for genome-enabled prediction of wheat (Triticum aestivum L.) breeding: (a) completely nonoverlapping wheat lines in environments, (b) completely overlapping wheat lines in all environments, and (c) a proportion of nonoverlapping/overlapping wheat lines allocated in the environments. We also studied several cases in which the size of the testing population was systematically decreased. The study used three extensive wheat data sets (W1, W2, and W3). Three different genome-enabled prediction models (M1-M3) were used to study the effect of the sparse testing in terms of the genomic prediction accuracy. Model M1 included only main effects of environments and lines; M2 included main effects of environments, lines, and genomic effects; whereas the remaining model (M3) also incorporated the genomic × environment interaction (GE). The results show that the GE component of the genome-based model M3 captures a larger genetic variability than the main genomic effects term from models M1 and M2. In addition, model M3 provides higher prediction accuracy than models M1 and M2 for the same allocation designs (different combinations of nonoverlapping/overlapping lines in environments and training set sizes). Overlapped sets of 30-50 lines in all the environments provided stable genomic-enabled prediction accuracy. Reducing the size of the testing populations under all allocation designs decreases the prediction accuracy, which recovers when more lines are tested in all environments. Model M3 offers the possibility of maintaining the prediction accuracy throughout both extreme situations of all nonoverlapping lines and all overlapping lines.

The Design of Early-Stage Plant Breeding Trials Using Genetic Relatedness

The use of appropriate statistical methods has a key role in improving the accuracy of selection decisions in a plant breeding program. This is particularly important in the early stages of testing in which selections are based on data from a limited number of field trials that include large numbers of breeding lines with minimal replication. The method of analysis currently recommended for early-stage trials in Australia involves a linear mixed model that includes genetic relatedness via ancestral information: non-genetic effects that reflect the experimental design and a residual model that accommodates spatial dependence. Such analyses have been widely accepted as they have been found to produce accurate predictions of both additive and total genetic effects, the latter providing the basis for selection decisions. In this paper, we present the results of a case study of 34 early-stage trials to demonstrate this type of analysis and to reinforce the importance of including information on genetic relatedness. In addition to the application of a superior method of analysis, it is also critical to ensure the use of sound experimental designs. Recently, model-based designs have become popular in Australian plant breeding programs. Within this paradigm, the design search would ideally be based on a linear mixed model that matches, as closely as possible, the model used for analysis. Therefore, in this paper, we propose the use of models for design generation that include information on genetic relatedness and also include non-genetic and residual models based on the analysis of historic data for individual breeding programs. At present, the most commonly used design generation model omits genetic relatedness information and uses non-genetic and residual models that are supplied as default models in the associated software packages. The major reasons for this are that preexisting software is unacceptably slow for designs incorporating genetic relatedness and the accuracy gains resulting from the use of genetic relatedness have not been quantified. Both of these issues are addressed in the current paper. An updating scheme for calculating the optimality criterion in the design search is presented and is shown to afford prodigious computational savings. An in silico study that compares three types of design function across a range of ancillary treatments shows the gains in accuracy for the prediction of total genetic effects (and thence selection) achieved from model-based designs using genetic relatedness and program specific non-genetic and residual models.

Supplementary materials accompanying this paper appear online.

Multi-trait multi-environment models in the genetic selection of segregating soybean progeny

At present, single-trait best linear unbiased prediction (BLUP) is the standard method for genetic selection in soybean. However, when genetic selection is performed based on two or more genetically correlated traits and these are analyzed individually, selection bias may arise. Under these conditions, considering the correlation structure between the evaluated traits may provide more-accurate genetic estimates for the evaluated parameters, even under environmental influences. The present study was thus developed to examine the efficiency and applicability of multi-trait multi-environment (MTME) models by the residual maximum likelihood (REML/BLUP) and Bayesian approaches in the genetic selection of segregating soybean progeny. The study involved data pertaining to 203 soybean F2:4 progeny assessed in two environments for the following traits: number of days to maturity (DM), 100-seed weight (SW), and average seed yield per plot (SY). Variance components and genetic and non-genetic parameters were estimated via the REML/BLUP and Bayesian methods. The variance components estimated and the breeding values and genetic gains predicted with selection through the Bayesian procedure were similar to those obtained by REML/BLUP. The frequentist and Bayesian MTME models provided higher estimates of broad-sense heritability per plot (or heritability of total effects of progeny; [Formula: see text]) and mean accuracy of progeny than their respective single-trait versions. Bayesian analysis provided the credibility intervals for the estimates of [Formula: see text]. Therefore, MTME led to greater predicted gains from selection. On this basis, this procedure can be efficiently applied in the genetic selection of segregating soybean progeny.

Phenotypic Selection in Ornamental Breeding: It's Better to Have the BLUPs Than to Have the BLUEs

Plant breeders always face the challenge to select the best individuals. Selection methods are required that maximize selection gain based on available data. When several crosses have been made, the BLUP procedure achieves this by combining phenotypic data with information on pedigree relationships via an index, known as family-index selection. The index, estimated based on the intra-class correlation coefficient, exploits the relationship among individuals within a family relative to other families in the population. An intra-class correlation coefficient of one indicates that the individual performance can be fully explained based on the family background, whereas an intra-class correlation coefficient of zero indicates the performance of individuals is independent of the family background. In the case the intra-class correlation coefficient is one, family-index selection is considered. In the case the intra-class correlation coefficient is zero, individual selection is considered. The main difference between individual and family-index selection lies in the adjustment in estimating the individual's effect depending on the intra-class correlation coefficient afforded by the latter. Two examples serve to illustrate the application of the BLUP method. The efficiency of individual and family-index selection was evaluated in terms of the heritability obtained from linear mixed models implementing the selection methods by suitably defining the treatment factor as the sum of individual and family effect. Family-index selection was found to be at least as efficient as individual selection in Dianthus caryophyllus L., except for flower size in standard carnation and vase life in mini carnation for which traits family-index selection outperformed individual selection. Family-index selection was superior to individual selection in Pelargonium zonale in cases when the heritability was low. Hence, the pedigree-based BLUP procedure can enhance selection efficiency in production-related traits in P. zonale or shelf-life related in D. caryophyllus L.

Optimization of multi-environment trials for genomic selection based on crop models

We propose a statistical criterion to optimize multi-environment trials to predict genotype × environment interactions more efficiently, by combining crop growth models and genomic selection models. Genotype × environment interactions (GEI) are common in plant multi-environment trials (METs). In this context, models developed for genomic selection (GS) that refers to the use of genome-wide information for predicting breeding values of selection candidates need to be adapted. One promising way to increase prediction accuracy in various environments is to combine ecophysiological and genetic modelling thanks to crop growth models (CGM) incorporating genetic parameters. The efficiency of this approach relies on the quality of the parameter estimates, which depends on the environments composing this MET used for calibration. The objective of this study was to determine a method to optimize the set of environments composing the MET for estimating genetic parameters in this context. A criterion called OptiMET was defined to this aim, and was evaluated on simulated and real data, with the example of wheat phenology. The MET defined with OptiMET allowed estimating the genetic parameters with lower error, leading to higher QTL detection power and higher prediction accuracies. MET defined with OptiMET was on average more efficient than random MET composed of twice as many environments, in terms of quality of the parameter estimates. OptiMET is thus a valuable tool to determine optimal experimental conditions to best exploit MET and the phenotyping tools that are currently developed.

Marker-based estimation of heritability in immortal populations

Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within- and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.

Breeding drought-tolerant maize hybrids for the US corn-belt: discovery to product

Germplasm, genetics, phenotyping, and selection, combined with a clear definition of product targets, are the foundation of successful hybrid maize breeding. Breeding maize hybrids with superior yield for the drought-prone regions of the US corn-belt involves integration of multiple drought-specific technologies together with all of the other technology components that comprise a successful maize hybrid breeding programme. Managed-environment technologies are used to enable scaling of precision phenotyping in appropriate drought environmental conditions to breeding programme level. Genomics and other molecular technologies are used to study trait genetic architecture. Genetic prediction methodology was used to breed for improved yield performance for drought-prone environments. This was enabled by combining precision phenotyping for drought performance with genetic understanding of the traits contributing to successful hybrids in the target drought-prone environments and the availability of molecular markers distributed across the maize genome. Advances in crop growth modelling methodology are being used to evaluate the integrated effects of multiple traits for their combined effects and evaluate drought hybrid product concepts and guide their development and evaluation. Results to date, lessons learned, and future opportunities for further improving the drought tolerance of maize for the US corn-belt are discussed.