The Predicted Cross Value for Genetic Introgression of Multiple Alleles

Development and optimization of expected cross value for mate selection problems

In this study, we address the mate selection problem in the hybridization stage of a breeding pipeline, which constitutes the multi-objective breeding goal key to the performance of a variety development program. The solution framework we formulate seeks to ensure that individuals with the most desirable genomic characteristics are selected to cross in order to maximize the likelihood of the inheritance of desirable genetic materials to the progeny. Unlike approaches that use phenotypic values for parental selection and evaluate individuals separately, we use a criterion that relies on the genetic architecture of traits and evaluates combinations of genomic information of the pairs of individuals. We introduce the expected cross value (ECV) criterion that measures the expected number of desirable alleles for gametes produced by pairs of individuals sampled from a population of potential parents. We use the ECV criterion to develop an integer linear programming formulation for the parental selection problem. The formulation is capable of controlling the inbreeding level between selected mates. We evaluate the approach or two applications: (i) improving multiple target traits simultaneously, and (ii) finding a multi-parental solution to design crossing blocks. We evaluate the performance of the ECV criterion using a simulation study. Finally, we discuss how the ECV criterion and the proposed integer linear programming techniques can be applied to improve breeding efficiency while maintaining genetic diversity in a breeding program.

Evolutionary computing to assemble standing genetic diversity and achieve long-term genetic gain

Loss of genetic diversity in elite crop breeding pools can severely limit long-term genetic gains and limit ability to make gains in new traits, like heat tolerance, that are becoming important as the climate changes. Here, we investigate and propose potential breeding program applications of optimal haplotype stacking (OHS), a selection method that retains useful diversity in the population. OHS selects sets of candidates containing, between them, haplotype segments with very high segment breeding values for the target trait. We compared the performance of OHS, a similar method called optimal population value (OPV), truncation selection on genomic estimated breeding values (GEBVs), and optimal contribution selection (OCS) in stochastic simulations of recurrent selection on founder wheat genotypes. After 100 generations of intercrossing and selection, OCS and truncation selection had exhausted the genetic diversity, while considerable diversity remained in the OHS population. Gain under OHS in these simulations ultimately exceeded that from truncation selection or OCS. OHS achieved faster gains when the population size was small, with many progeny per cross. A promising hybrid strategy, involving a single cycle of OHS in the first generation followed by recurrent truncation selection, substantially improved long-term gain compared with truncation selection and performed similarly to OCS. The results of this study provide initial insights into where OHS could be incorporated into breeding programs.

Assessing the potential of genetic resource introduction into elite germplasm: a collaborative multiparental population for flint maize

KEY MESSAGE

Implementing a collaborative pre-breeding multi-parental population efficiently identifies promising donor x elite pairs to enrich the flint maize elite germplasm. Genetic diversity is crucial for maintaining genetic gains and ensuring breeding programs' long-term success. In a closed breeding program, selection inevitably leads to a loss of genetic diversity. While managing diversity can delay this loss, introducing external sources of diversity is necessary to bring back favorable genetic variation. Genetic resources exhibit greater diversity than elite materials, but their lower performance levels hinder their use. This is the case for European flint maize, for which elite germplasm has incorporated only a limited portion of the diversity available in landraces. To enrich the diversity of this elite genetic pool, we established an original cooperative maize bridging population that involves crosses between private elite materials and diversity donors to create improved genotypes that will facilitate the incorporation of original favorable variations. Twenty donor × elite BC1S2 families were created and phenotyped for hybrid value for yield related traits. Crosses showed contrasted means and variances and therefore contrasted potential in terms of selection as measured by their usefulness criterion (UC). Average expected mean performance gain over the initial elite material was 5%. The most promising donor for each elite line was identified. Results also suggest that one more generation, i.e., 3 in total, of crossing to the elite is required to fully exploit the potential of a donor. Altogether, our results support the usefulness of incorporating genetic resources into elite flint maize. They call for further effort to create fixed diversity donors and identify those most suitable for each elite program.

Natural and artificial selection of multiple alleles revealed through genomic analyses

Genome-to-phenome research in agriculture aims to improve crops through in silico predictions. Genome-wide association study (GWAS) is potent in identifying genomic loci that underlie important traits. As a statistical method, increasing the sample quantity, data quality, or diversity of the GWAS dataset positively impacts GWAS power. For more precise breeding, concrete candidate genes with exact functional variants must be discovered. Many post-GWAS methods have been developed to narrow down the associated genomic regions and, ideally, to predict candidate genes and causative mutations (CMs). Historical natural selection and breeding-related artificial selection both act to change the frequencies of different alleles of genes that control phenotypes. With higher diversity and more extensive GWAS datasets, there is an increased chance of multiple alleles with independent CMs in a single causal gene. This can be caused by the presence of samples from geographically isolated regions that arose during natural or artificial selection. This simple fact is a complicating factor in GWAS-driven discoveries. Currently, none of the existing association methods address this issue and need to identify multiple alleles and, more specifically, the actual CMs. Therefore, we developed a tool that computes a score for a combination of variant positions in a single candidate gene and, based on the highest score, identifies the best number and combination of CMs. The tool is publicly available as a Python package on GitHub, and we further created a web-based Multiple Alleles discovery (MADis) tool that supports soybean and is hosted in SoyKB (https://soykb.org/SoybeanMADisTool/). We tested and validated the algorithm and presented the utilization of MADis in a pod pigmentation L1 gene case study with multiple CMs from natural or artificial selection. Finally, we identified a candidate gene for the pod color L2 locus and predicted the existence of multiple alleles that potentially cause loss of pod pigmentation. In this work, we show how a genomic analysis can be employed to explore the natural and artificial selection of multiple alleles and, thus, improve and accelerate crop breeding in agriculture.

Genetic basis of maize maternal haploid induction beyond MATRILINEAL and ZmDMP

In maize, doubled haploid (DH) lines are created in vivo through crosses with maternal haploid inducers. Their induction ability, usually expressed as haploid induction rate (HIR), is known to be under polygenic control. Although two major genes (MTL and ZmDMP) affecting this trait were recently described, many others remain unknown. To identify them, we designed and performed a SNP based (~9007) genome-wide association study using a large and diverse panel of 159 maternal haploid inducers. Our analyses identified a major gene near MTL, which is present in all inducers and necessary to disrupt haploid induction. We also found a significant quantitative trait loci (QTL) on chromosome 10 using a case-control mapping approach, in which 793 noninducers were used as controls. This QTL harbors a kokopelli ortholog, whose role in maternal haploid induction was recently described in Arabidopsis. QTL with smaller effects were identified on six of the ten maize chromosomes, confirming the polygenic nature of this trait. These QTL could be incorporated into inducer breeding programs through marker-assisted selection approaches. Further improving HIR is important to reduce the cost of DH line production.

A simulation framework for reciprocal recurrent selection-based hybrid breeding under transparent and opaque simulators

Hybrid breeding is an established and effective process to improve offspring performance, while it is resource-intensive and time-consuming for the recurrent process in reality. To enable breeders and researchers to evaluate the effectiveness of competing decision-making strategies, we present a modular simulation framework for reciprocal recurrent selection-based hybrid breeding. Consisting of multiple modules such as heterotic separation, genomic prediction, and genomic selection, this simulation framework allows breeders to efficiently simulate the hybrid breeding process with multiple options of simulators and decision-making strategies. We also integrate the recently proposed concepts of transparent and opaque simulators into the framework in order to reflect the breeding process more realistically. Simulation results show the performance comparison among different breeding strategies under the two simulators.

Identification of Disease Resistance Parents and Genome-Wide Association Mapping of Resistance in Spring Wheat

The likelihood of success in developing modern cultivars depend on multiple factors, including the identification of suitable parents to initiate new crosses, and characterizations of genomic regions associated with target traits. The objectives of the present study were to (a) determine the best economic weights of four major wheat diseases (leaf spot, common bunt, leaf rust, and stripe rust) and grain yield for multi-trait restrictive linear phenotypic selection index (RLPSI), (b) select the top 10% cultivars and lines (hereafter referred as genotypes) with better resistance to combinations of the four diseases and acceptable grain yield as potential parents, and (c) map genomic regions associated with resistance to each disease using genome-wide association study (GWAS). A diversity panel of 196 spring wheat genotypes was evaluated for their reaction to stripe rust at eight environments, leaf rust at four environments, leaf spot at three environments, common bunt at two environments, and grain yield at five environments. The panel was genotyped with the Wheat 90K SNP array and a few KASP SNPs of which we used 23,342 markers for statistical analyses. The RLPSI analysis performed by restricting the expected genetic gain for yield displayed significant (p < 0.05) differences among the 3125 economic weights. Using the best four economic weights, a subset of 22 of the 196 genotypes were selected as potential parents with resistance to the four diseases and acceptable grain yield. GWAS identified 37 genomic regions, which included 12 for common bunt, 13 for leaf rust, 5 for stripe rust, and 7 for leaf spot. Each genomic region explained from 6.6 to 16.9% and together accounted for 39.4% of the stripe rust, 49.1% of the leaf spot, 94.0% of the leaf rust, and 97.9% of the common bunt phenotypic variance combined across all environments. Results from this study provide valuable information for wheat breeders selecting parental combinations for new crosses to develop improved germplasm with enhanced resistance to the four diseases as well as the physical positions of genomic regions that confer resistance, which facilitates direct comparisons for independent mapping studies in the future.

Benefit of Introgression Depends on Level of Genetic Trait Variation in Cereal Breeding Programmes

We investigated the benefit from introgression of external lines into a cereal breeding programme and strategies that accelerated introgression of the favourable alleles while minimising linkage drag using stochastic computer simulation. We simulated genomic selection for disease resistance and grain yield in two environments with a high level of genotype-by-environment interaction (G × E) for the latter trait, using genomic data of a historical barley breeding programme as the base generation. Two populations (existing and external) were created from this base population with different allele frequencies for few (N = 10) major and many (N ~ 990) minor simulated disease quantitative trait loci (QTL). The major disease QTL only existed in the external population and lines from the external population were introgressed into the existing population which had minor disease QTL with low, medium and high allele frequencies. The study revealed that the benefit of introgression depended on the level of genetic variation for the target trait in the existing cereal breeding programme. Introgression of external resources into the existing population was beneficial only when the existing population lacked variation in disease resistance or when minor disease QTL were already at medium or high frequency. When minor disease QTL were at low frequencies, no extra genetic gain was achieved from introgression. More benefit in the disease trait was obtained from the introgression if the major disease QTL had larger effect sizes, more selection emphasis was applied on disease resistance, or more external lines were introgressed. While our strategies to increase introgression of major disease QTL were generally successful, most were not able to completely avoid negative impacts on selection for grain yield with the only exception being when major introgression QTL effects were very large. Breeding programmes are advised to carefully consider the level of genetic variation in a trait available in their breeding programme before deciding to introgress germplasms.

Deep scoping: a breeding strategy to preserve, reintroduce and exploit genetic variation

The deep scoping method incorporates the use of a gene bank together with different population layers to reintroduce genetic variation into the breeding population, thus maximizing the long-term genetic gain without reducing the short-term genetic gain or increasing the total financial cost. Genomic prediction is often combined with truncation selection to identify superior parental individuals that can pass on favorable quantitative trait locus (QTL) alleles to their offspring. However, truncation selection reduces genetic variation within the breeding population, causing a premature convergence to a sub-optimal genetic value. In order to also increase genetic gain in the long term, different methods have been proposed that better preserve genetic variation. However, when the genetic variation of the breeding population has already been reduced as a result of prior intensive selection, even those methods will not be able to avert such premature convergence. Pre-breeding provides a solution for this problem by reintroducing genetic variation into the breeding population. Unfortunately, as pre-breeding often relies on a separate breeding population to increase the genetic value of wild specimens before introducing them in the elite population, it comes with an increased financial cost. In this paper, on the basis of a simulation study, we propose a new method that reintroduces genetic variation in the breeding population on a continuous basis without the need for a separate pre-breeding program or a larger population size. This way, we are able to introduce favorable QTL alleles into an elite population and maximize the genetic gain in the short as well as in the long term without increasing the financial cost.

Dynamic Programming for Resource Allocation in Multi-Allelic Trait Introgression

Trait introgression is a complex process that plant breeders use to introduce desirable alleles from one variety or species to another. Two of the major types of decisions that must be made during this sophisticated and uncertain workflow are: parental selection and resource allocation. We formulated the trait introgression problem as an engineering process and proposed a Markov Decision Processes (MDP) model to optimize the resource allocation procedure. The efficiency of the MDP model was compared with static resource allocation strategies and their trade-offs among budget, deadline, and probability of success are demonstrated. Simulation results suggest that dynamic resource allocation strategies from the MDP model significantly improve the efficiency of the trait introgression by allocating the right amount of resources according to the genetic outcome of previous generations.

The look ahead trace back optimizer for genomic selection under transparent and opaque simulators

Recent advances in genomic selection (GS) have demonstrated the importance of not only the accuracy of genomic prediction but also the intelligence of selection strategies. The look ahead selection algorithm, for example, has been found to significantly outperform the widely used truncation selection approach in terms of genetic gain, thanks to its strategy of selecting breeding parents that may not necessarily be elite themselves but have the best chance of producing elite progeny in the future. This paper presents the look ahead trace back algorithm as a new variant of the look ahead approach, which introduces several improvements to further accelerate genetic gain especially under imperfect genomic prediction. Perhaps an even more significant contribution of this paper is the design of opaque simulators for evaluating the performance of GS algorithms. These simulators are partially observable, explicitly capture both additive and non-additive genetic effects, and simulate uncertain recombination events more realistically. In contrast, most existing GS simulation settings are transparent, either explicitly or implicitly allowing the GS algorithm to exploit certain critical information that may not be possible in actual breeding programs. Comprehensive computational experiments were carried out using a maize data set to compare a variety of GS algorithms under four simulators with different levels of opacity. These results reveal how differently a same GS algorithm would interact with different simulators, suggesting the need for continued research in the design of more realistic simulators. As long as GS algorithms continue to be trained in silico rather than in planta, the best way to avoid disappointing discrepancy between their simulated and actual performances may be to make the simulator as akin to the complex and opaque nature as possible.

A look-ahead Monte Carlo simulation method for improving parental selection in trait introgression

Multiple trait introgression is the process by which multiple desirable traits are converted from a donor to a recipient cultivar through backcrossing and selfing. The goal of this procedure is to recover all the attributes of the recipient cultivar, with the addition of the specified desirable traits. A crucial step in this process is the selection of parents to form new crosses. In this study, we propose a new selection approach that estimates the genetic distribution of the progeny of backcrosses after multiple generations using information of recombination events. Our objective is to select the most promising individuals for further backcrossing or selfing. To demonstrate the effectiveness of the proposed method, a case study has been conducted using maize data where our method is compared with state-of-the-art approaches. Simulation results suggest that the proposed method, look-ahead Monte Carlo, achieves higher probability of success than existing approaches. Our proposed selection method can assist breeders to efficiently design trait introgression projects.

Application of multi-trait Bayesian decision theory for parental genomic selection

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback–Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best-performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for the posterior expected loss (PEL). For both data sets, the KL LF gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave a better performance in three of four traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm.

Origin Specific Genomic Selection: A Simple Process To Optimize the Favorable Contribution of Parents to Progeny

Modern crop breeding is in constant demand for new genetic diversity as part of the arms race with genetic gain. The elite gene pool has limited genetic variation and breeders are trying to introduce novelty from unadapted germplasm, landraces and wild relatives. For polygenic traits, currently available approaches to introgression are not ideal, as there is a demonstrable bias against exotic alleles during selection. Here, we propose a partitioned form of genomic selection, called Origin Specific Genomic Selection (OSGS), where we identify and target selection on favorable exotic alleles. Briefly, within a population derived from a bi-parental cross, we isolate alleles originating from the elite and exotic parents, which then allows us to separate out the predicted marker effects based on the allele origins. We validated the usefulness of OSGS using two nested association mapping (NAM) datasets: barley NAM (elite-exotic) and maize NAM (elite-elite), as well as by computer simulation. Our results suggest that OSGS works well in its goal to increase the contribution of favorable exotic alleles in bi-parental crosses, and it is possible to extend the approach to broader multi-parental populations.

Optimized breeding strategies to harness genetic resources with different performance levels

Background

The narrow genetic base of elite germplasm compromises long-term genetic gain and increases the vulnerability to biotic and abiotic stresses in unpredictable environmental conditions. Therefore, an efficient strategy is required to broaden the genetic base of commercial breeding programs while not compromising short-term variety release. Optimal cross selection aims at identifying the optimal set of crosses that balances the expected genetic value and diversity. We propose to consider genomic selection and optimal cross selection to recurrently improve genetic resources (i.e. pre-breeding), to bridge the improved genetic resources with elites (i.e. bridging), and to manage introductions into the elite breeding population. Optimal cross selection is particularly adapted to jointly identify bridging, introduction and elite crosses to ensure an overall consistency of the genetic base broadening strategy.

Results

We compared simulated breeding programs introducing donors with different performance levels, directly or indirectly after bridging. We also evaluated the effect of the training set composition on the success of introductions. We observed that with recurrent introductions of improved donors, it is possible to maintain the genetic diversity and increase mid- and long-term performances with only limited penalty at short-term. Considering a bridging step yielded significantly higher mid- and long-term genetic gain when introducing low performing donors. The results also suggested to consider marker effects estimated with a broad training population including donor by elite and elite by elite progeny to identify bridging, introduction and elite crosses.

Conclusion

Results of this study provide guidelines on how to harness polygenic variation present in genetic resources to broaden elite germplasm.

Genomic prediction with a maize collaborative panel: identification of genetic resources to enrich elite breeding programs

Collaborative diversity panels and genomic prediction seem relevant to identify and harness genetic resources for polygenic trait-specific enrichment of elite germplasms. In plant breeding, genetic diversity is important to maintain the pace of genetic gain and the ability to respond to new challenges in a context of climatic and social expectation changes. Many genetic resources are accessible to breeders but cannot all be considered for broadening the genetic diversity of elite germplasm. This study presents the use of genomic predictions trained on a collaborative diversity panel, which assembles genetic resources and elite lines, to identify resources to enrich an elite germplasm. A maize collaborative panel (386 lines) was considered to estimate genome-wide marker effects. Relevant predictive abilities (0.40-0.55) were observed on a large population of private elite materials, which supported the interest of such a collaborative panel for diversity management perspectives. Grain-yield estimated marker effects were used to select a donor that best complements an elite recipient at individual loci or haplotype segments, or that is expected to give the best-performing progeny with the elite. Among existing and new criteria that were compared, some gave more weight to the donor-elite complementarity than to the donor value, and appeared more adapted to long-term objective. We extended this approach to the selection of a set of donors complementing an elite population. We defined a crossing plan between identified donors and elite recipients. Our results illustrated how collaborative projects based on diversity panels including both public resources and elite germplasm can contribute to a better characterization of genetic resources in view of their use to enrich elite germplasm.

Optimizing Selection and Mating in Genomic Selection with a Look-Ahead Approach: An Operations Research Framework

New genotyping technologies have made large amounts of genotypic data available for plant breeders to use in their efforts to accelerate the rate of genetic gain. Genomic selection (GS) techniques allow breeders to use genotypic data to identify and select, for example, plants predicted to exhibit drought tolerance, thereby saving expensive and limited field-testing resources relative to phenotyping all plants within a population. A major limitation of existing GS approaches is the trade-off between short-term genetic gain and long-term potential. Some approaches focus on achieving short-term genetic gain at the cost of reduced genetic diversity necessary for long-term gains. In contrast, others compromise short-term progress to preserve long-term potential without consideration of the time and resources required to achieve it. Our contribution is to define a new “look-ahead” metric for assessing selection decisions, which evaluates the probability of achieving high genetic gains by a specific time with limited resources. Moreover, we propose a heuristic algorithm to identify optimal selection decisions that maximize the look-ahead metric. Simulation results demonstrate that look-ahead selection outperforms other published selection methods.

Usefulness Criterion and Post-selection Parental Contributions in Multi-parental Crosses: Application to Polygenic Trait Introgression

Predicting the usefulness of crosses in terms of expected genetic gain and genetic diversity is of interest to secure performance in the progeny and to maintain long-term genetic gain in plant breeding. A wide range of crossing schemes are possible including large biparental crosses, backcrosses, four-way crosses, and synthetic populations. In silico progeny simulations together with genome-based prediction of quantitative traits can be used to guide mating decisions. However, the large number of multi-parental combinations can hinder the use of simulations in practice. Analytical solutions have been proposed recently to predict the distribution of a quantitative trait in the progeny of biparental crosses using information of recombination frequency and linkage disequilibrium between loci. Here, we extend this approach to obtain the progeny distribution of more complex crosses including two to four parents. Considering agronomic traits and parental genome contribution as jointly multivariate normally distributed traits, the usefulness criterion parental contribution (UCPC) enables to (i) evaluate the expected genetic gain for agronomic traits, and at the same time (ii) evaluate parental genome contributions to the selected fraction of progeny. We validate and illustrate UCPC in the context of multiple allele introgression from a donor into one or several elite recipients in maize (Zea mays L.). Recommendations regarding the interest of two-way, three-way, and backcrosses were derived depending on the donor performance. We believe that the computationally efficient UCPC approach can be useful for mate selection and allocation in many plant and animal breeding contexts.

Technological advances in maize breeding: past, present and future

Maize has for many decades been both one of the most important crops worldwide and one of the primary genetic model organisms. More recently, maize breeding has been impacted by rapid technological advances in sequencing and genotyping technology, transformation including genome editing, doubled haploid technology, parallelled by progress in data sciences and the development of novel breeding approaches utilizing genomic information. Herein, we report on past, current and future developments relevant for maize breeding with regard to (1) genome analysis, (2) germplasm diversity characterization and utilization, (3) manipulation of genetic diversity by transformation and genome editing, (4) inbred line development and hybrid seed production, (5) understanding and prediction of hybrid performance, (6) breeding methodology and (7) synthesis of opportunities and challenges for future maize breeding.

A Bayesian Decision Theory Approach for Genomic Selection

Plant and animal breeders are interested in selecting the best individuals from a candidate set for the next breeding cycle. In this paper, we propose a formal method under the Bayesian decision theory framework to tackle the selection problem based on genomic selection (GS) in single- and multi-trait settings. We proposed and tested three univariate loss functions (Kullback-Leibler, KL; Continuous Ranked Probability Score, CRPS; Linear-Linear loss, LinLin) and their corresponding multivariate generalizations (Kullback-Leibler, KL; Energy Score, EnergyS; and the Multivariate Asymmetric Loss Function, MALF). We derived and expressed all the loss functions in terms of heritability and tested them on a real wheat dataset for one cycle of selection and in a simulated selection program. The performance of each univariate loss function was compared with the standard method of selection (Std) that does not use loss functions. We compared the performance in terms of the selection response and the decrease in the population’s genetic variance during recurrent breeding cycles. Results suggest that it is possible to obtain better performance in a long-term breeding program using the single-trait scheme by selecting 30% of the best individuals in each cycle but not by selecting 10% of the best individuals. For the multi-trait approach, results show that the population mean for all traits under consideration had positive gains, even though two of the traits were negatively correlated. The corresponding population variances were not statistically different from the different loss function during the 10^th selection cycle. Using the loss function should be a useful criterion when selecting the candidates for selection for the next breeding cycle.

Selection on Expected Maximum Haploid Breeding Values Can Increase Genetic Gain in Recurrent Genomic Selection

Genomic selection (GS) offers the possibility to estimate the effects of genome-wide molecular markers, which can be used to calculate genomic estimated breeding values (GEBVs) for individuals without phenotypes. GEBVs can serve as a selection criterion in recurrent GS, maximizing single-cycle but not necessarily long-term genetic gain. As simple genome-wide sums, GEBVs do not take into account other genomic information, such as the map positions of loci and linkage phases of alleles. Therefore, we herein propose a novel selection criterion called expected maximum haploid breeding value (EMBV). EMBV predicts the expected performance of the best among a limited number of gametes that a candidate contributes to the next generation, if selected. We used simulations to examine the performance of EMBV in comparison with GEBV as well as the recently proposed criterion optimal haploid value (OHV) and weighted GS. We considered different population sizes, numbers of selected candidates, chromosome numbers and levels of dominant gene action. Criterion EMBV outperformed GEBV after about 5 selection cycles, achieved higher long-term genetic gain and maintained higher diversity in the population. The other selection criteria showed the potential to surpass both GEBV and EMBV in advanced cycles of the breeding program, but yielded substantially lower genetic gain in early to intermediate cycles, which makes them unattractive for practical breeding. Moreover, they were largely inferior in scenarios with dominant gene action. Overall, EMBV shows high potential to be a promising alternative selection criterion to GEBV for recurrent genomic selection.

Prediction of Means and Variances of Crosses With Genome-Wide Marker Effects in Barley

Background: The expected genetic variance is an important criterion for the selection of crossing partners which will produce superior combinations of genotypes in their progeny. The advent of molecular markers has opened up new vistas for obtaining precise predictors for the genetic variance of a cross, but fast prediction methods that allow plant breeders to select crossing partners based on already available data from their breeding programs without complicated calculations or simulation of breeding populations are still lacking. The main objective of the present study was to demonstrate the practical applicability of an analytical approach for the selection of superior cross combinations with experimental data from a barley breeding program. We used genome-wide marker effects to predict the yield means and genetic variances of 14 DH families resulting from crosses of four donor lines with five registered elite varieties with the genotypic information of the parental lines. For the validation of the predicted parameters, the analytical approach was extended by the masking variance as a major component of phenotypic variance. The predicted parameters were used to fit normal distribution curves of the phenotypic values and to conduct an Anderson-Darling goodness-of-fit test for the observed phenotypic data of the 14 DH families from the field trial. Results: There was no evidence that the observed phenotypic values deviated from the predicted phenotypic normal distributions in 13 out of 14 crosses. The correlations between the observed and the predicted means and the observed and predicted variances were r = 0.95 and r = 0.34, respectively. After removing two crosses with downward outliers in the phenotypic data, the correlation between the observed and predicted variances increased to r = 0.76. A ranking of the 14 crosses based on the sum of predicted mean and genetic variance identified the 50% best crosses from the field trial correctly. Conclusions: We conclude that the prediction accuracy of the presented approach is sufficiently high to identify superior crosses even with limited phenotypic data. We therefore expect that the analytical approach based on genome-wide marker effects is applicable in a wide range of breeding programs.

Genetic Gain Increases by Applying the Usefulness Criterion with Improved Variance Prediction in Selection of Crosses

A crucial step in plant breeding is the selection and combination of parents to form new crosses. Genome-based prediction guides the selection of high-performing parental lines in many crop breeding programs which ensures a high mean performance of progeny. To warrant maximum selection progress, a new cross should also provide a large progeny variance. The usefulness concept as measure of the gain that can be obtained from a specific cross accounts for variation in progeny variance. Here, it is shown that genetic gain can be considerably increased when crosses are selected based on their genomic usefulness criterion compared to selection based on mean genomic estimated breeding values. An efficient and improved method to predict the genetic variance of a cross based on Markov chain Monte Carlo samples of marker effects from a whole-genome regression model is suggested. In simulations representing selection procedures in crop breeding programs, the performance of this novel approach is compared with existing methods, like selection based on mean genomic estimated breeding values and optimal haploid values. In all cases, higher genetic gain was obtained compared with previously suggested methods. When 1% of progenies per cross were selected, the genetic gain based on the estimated usefulness criterion increased by 0.14 genetic standard deviation compared to a selection based on mean genomic estimated breeding values. Analytical derivations of the progeny genotypic variance-covariance matrix based on parental genotypes and genetic map information make simulations of progeny dispensable, and allow fast implementation in large-scale breeding programs.

Improving Response in Genomic Selection with a Population-Based Selection Strategy: Optimal Population Value Selection

Genomic selection (GS) identifies individuals for inclusion in breeding programs based on the sum of their estimated marker effects or genomic estimated breeding values (GEBVs). Due to significant correlation between GEBVs and true breeding values, this has resulted in enhanced rates of genetic gain as compared to traditional methods of selection. Three extensions to GS, weighted genomic selection (WGS), optimal haploid value (OHV) selection, and genotype building (GB) selection have been proposed to improve long-term response, and to facilitate the efficient development of doubled haploids. In separate simulation studies, these methods were shown to outperform GS under various assumptions. However, further potential for improvement exists. In this paper, optimal population value (OPV) selection is introduced as selection based on the maximum possible haploid value in a subset of the population. Instead of evaluating the breeding merit of individuals as in GS, WGS, and OHV selection, the proposed method evaluates the breeding merit of a set of individuals as in GB. After testing these selection methods extensively, OPV and GB selection were found to achieve greater responses than GS, WGS, and OHV, with OPV outperforming GB across most percentiles. These results suggest a new paradigm for selection methods in which an individual's value is dependent upon its complementarity with others.