Hybrid maize breeding with doubled haploids: I. One-stage versus two-stage selection for testcross performance

Optimization of breeding program design through stochastic simulation with kernel regression

In recent years, breeding programs have increased significantly in size and complexity, with various highly interdependent parameters and many contrasting breeding goals. As a result, resource allocation in these programs has become more complex, and deriving an optimal breeding strategy has become increasingly challenging. To address this, a common practice is to reduce the optimization problem to a set of scenarios that differ only in a few parameters and can therefore be analyzed in detail. The goal of this article is to provide a framework for the numerical optimization of breeding programs that goes beyond the simple comparison of scenarios. For this, we first determine the space of potential breeding programs only limited by basic constraints like the budget and housing capacities. Subsequently, the goal is to identify the optimal breeding program by finding the parametrization that maximizes the target function by combining different breeding goals. To assess the value of the target function for a parametrization, we propose using stochastic simulations and the subsequent use of a kernel regression method to cope with the stochasticity of simulation outcomes. This procedure is performed iteratively to narrow down the most promising areas of the search space and perform more and more simulations in these areas of interest. In a simplified example applied to a dairy cattle program, our proposed framework has shown its ability to identify an optimal breeding strategy that aligns with a target function aiming at genetic gain and genetic diversity conservation limited by budget constraints.

Optimal implementation of genomic selection in clone breeding programs-Exemplified in potato: I. Effect of selection strategy, implementation stage, and selection intensity on short-term genetic gain

Genomic selection (GS) is used in many animal and plant breeding programs to enhance genetic gain for complex traits. However, its optimal integration in clone breeding programs, for example potato, that up to now relied on phenotypic selection (PS) requires further research. In this study, we performed computer simulations based on an empirical genomic dataset of tetraploid potato to (i) investigate under a fixed budget how the weight of GS relative to PS, the stage of implementing GS, the correlation between an auxiliary trait and the target trait, the variance components, and the prediction accuracy affect the genetic gain of the target trait, (ii) determine the optimal allocation of resources maximizing the genetic gain of the target trait, and (iii) make recommendations to breeders how to implement GS in clone and especially potato breeding programs. In our simulation results, any selection strategy involving GS had a higher short-term genetic gain for the target trait than Standard-PS. In addition, we showed that implementing GS in consecutive selection stages can largely enhance short-term genetic gain and recommend the breeders to implement GS at single hills and A clone stages. Furthermore, we observed for selection strategies involving GS that the optimal allocation of resources maximizing the genetic gain of the target trait differed considerably from those typically used in potato breeding programs and, thus, require the adjustment of the selection and phenotyping intensities. The trends are described in our study. Therefore, our study provides new insight for breeders regarding how to optimally implement GS in a commercial potato breeding program to improve the short-term genetic gain for their target trait.

Applications of Doubled Haploids in Plant Breeding and Applied Research

Manifold and diverse applications of doubled haploid (DH) plants have emerged in academy and in the plant breeding industry since the first discovery of a haploid mutant in the Jimson Weed (Datura stramonium), followed by the first reports about anther culture in the same species, maternal haploids by wide crosses in tobacco (Nicotiana tabacum L.) and barley (Hordeum vulgare L.), interspecific hybridization, ovary culture (gynogenesis), isolated microspore culture, and more recently the CENH3 approach in thale cress (Arabidopsis thaliana L.) and other species. Research and development efforts were and are still significant in both user groups. Luckily, often academic and industrial partners cooperate in challenging and sometimes voluminous projects worldwide. Not only to develop innovative DH protocols and technologies per se, but also to exploit the advantages of DH plants in a huge variety of research and development experiments. This review concentrates not on the DH technologies per se, but on the application of DHs in plant-related research and development projects.

Doubled haploid technology for line development in maize: technical advances and prospects

KEY MESSAGE

Increased efficiencies achieved in different steps of DH line production offer greater benefits to maize breeding programs. Doubled haploid (DH) technology has become an integral part of many commercial maize breeding programs as DH lines offer several economic, logistic and genetic benefits over conventional inbred lines. Further, new advances in DH technology continue to improve the efficiency of DH line development and fuel its increased adoption in breeding programs worldwide. The established method for maize DH production covered in this review involves in vivo induction of maternal haploids by a male haploid inducer genotype, identification of haploids from diploids at the seed or seedling stage, chromosome doubling of haploid (D0) seedlings and finally, selfing of fertile D0 plants. Development of haploid inducers with high haploid induction rates and adaptation to different target environments have facilitated increased adoption of DH technology in the tropics. New marker systems for haploid identification, such as the red root marker and high oil marker, are being increasingly integrated into new haploid inducers and have the potential to make DH technology accessible in germplasm such as some Flint, landrace, or tropical material, where the standard R1-nj marker is inhibited. Automation holds great promise to further reduce the cost and time in haploid identification. Increasing success rates in chromosome doubling protocols and/or reducing environmental and human toxicity of chromosome doubling protocols, including research on genetic improvement in spontaneous chromosome doubling, have the potential to greatly reduce the production costs per DH line.

Parent-progeny imputation from pooled samples for cost-efficient genotyping in plant breeding

The increased usage of whole-genome selection (WGS) and other molecular evaluation methods in plant breeding relies on the ability to genotype a very large number of untested individuals in each breeding cycle. Many plant breeding programs evaluate large biparental populations of homozygous individuals derived from homozygous parent inbred lines. This structure lends itself to parent-progeny imputation, which transfers the genotype scores of the parents to progeny individuals that are genotyped for a much smaller number of loci. Here we introduce a parent-progeny imputation method that infers individual genotypes from non-barcoded pooled samples of DNA of multiple individuals using a Hidden Markov Model (HMM). We demonstrate the method for pools of simulated maize double haploids (DH) from biparental populations, genotyped using a genotyping by sequencing (GBS) approach for 3,000 loci at 0.125x to 4x coverage. We observed high concordance between true and imputed marker scores and the HMM produced well-calibrated genotype probabilities that correctly reflected the uncertainty of the imputed scores. Genomic estimated breeding values (GEBV) calculated from the imputed scores closely matched GEBV calculated from the true marker scores. The within-population correlation between these sets of GEBV approached 0.95 at 1x and 4x coverage when pooling two or four individuals, respectively. Our approach can reduce the genotyping cost per individual by a factor up to the number of pooled individuals in GBS applications without the need for extra sequencing coverage, thereby enabling cost-effective large scale genotyping for applications such as WGS in plant breeding.

Optimum breeding strategies using genomic selection for hybrid breeding in wheat, maize, rye, barley, rice and triticale

A breeding strategy with moderate nursery selection followed by genomic selection and one-stage phenotypic selection maximizes annual selection gain for grain yield across a wide range of hybrid breeding scenarios. Genomic selection (GS) is a promising method for the selection of quantitatively inherited traits but its most effective implementation in routine hybrid breeding schemes requires further research. We compared five breeding strategies and varied their available budget, the costs for doubled haploid (DH) line and hybrid seed production as well as variance components for grain yield in a wide range. In contrast to previous studies, we included a nursery selection for disease resistance just before GS on grain yield. The breeding strategy GSrapid with moderate nursery selection followed by one stage GS and one final stage with phenotypic selection on grain yield had the highest annual selection gain across all strategies, budgets, costs and variance components considered and we, therefore, highly recommend its use in hybrid breeding of cereals. Although selecting on traits not correlated with grain yield in the observation nursery, this selection reduced the selection gain of grain yield, especially in the breeding schemes with GS and for selected fractions smaller than 0.3. Owing to the very high number of test candidates entering breeding strategies with GS, the costs for DH line production had a larger impact on the annual selection gain than the hybrid seed production costs. The optimum allocation of test resources maximizing annual selection gain in classical two-stage phenotypic selection on grain yield and for the recommended breeding strategy GSrapid is finally explored for maize, wheat, rye, barley, rice and triticale.

Genomic selection in wheat: optimum allocation of test resources and comparison of breeding strategies for line and hybrid breeding

The implementation of genomic selection in breeding programs can be recommended for hybrid and line breeding in wheat. High prediction accuracies from genomic selection (GS) were reported for grain yield in wheat asking for the elaboration of efficient breeding strategies applying GS. Our objectives were therefore, (1) to optimize the number of lines, locations and testers in different multi-stage breeding strategies with and without GS, (2) to elaborate the most efficient breeding strategy based on the selection gain and its standard deviation, and (3) to investigate the potential of GS to improve the relative efficiency of hybrid versus line breeding in wheat. We used the open source software package "selectiongain" to optimize the allocation of resources in different breeding strategies by predicting the expected selection gain for a fixed budget. Classical two-stage phenotypic selection was compared with three GS breeding strategies for line and hybrid breeding in wheat. The ranking of the alternative breeding strategies varied largely in dependence of the GS prediction accuracy. Fast-track breeding strategies based solely on GS were only advantageous for high GS prediction accuracies that is >0.50 and >0.65 for hybrid and line breeding, respectively. However, a GS prediction accuracy across breeding cycles of 0.3 or even less must be assumed as realistic for grain yield in wheat. For this low GS prediction accuracy, the use of GS is advantageous for line but especially for hybrid breeding in wheat. Furthermore, the use of GS in hybrid wheat breeding increased the relative efficiency of hybrid versus line breeding and, thus, might be an important pillar for the establishment of hybrid wheat.

Optimum allocation of test resources and comparison of breeding strategies for hybrid wheat

The use of a breeding strategy combining the evaluation of line per se with testcross performance maximizes annual selection gain for hybrid wheat breeding. Recent experimental studies confirmed a high commercial potential for hybrid wheat requiring the design of optimum breeding strategies. Our objectives were to (1) determine the optimum allocation of the type and number of testers, the number of test locations and the number of doubled haploid lines for different breeding strategies, (2) identify the best breeding strategy and (3) elaborate key parameters for an efficient hybrid wheat breeding program. We performed model calculations using the selection gain for grain yield as target variable to optimize the number of lines, testers and test locations in four different breeding strategies. A breeding strategy (BS2) combining the evaluation of line per se performance and general combining ability (GCA) had a far larger annual selection gain across all considered scenarios than a breeding strategy (BS1) focusing only on GCA. In the combined strategy, the production of testcross seed conducted in parallel with the first yield trial for line per se performance (BS2rapid) resulted in a further increase of the annual selection gain. For the current situation in hybrid wheat, this relative superiority of the strategy BS2rapid amounted to 67 % in annual selection gain compared to BS1. Varying a large number of parameters, we identified the high costs for hybrid seed production and the low variance of GCA in hybrid wheat breeding as key parameters limiting selection gain in BS2rapid.

Long-term perspective of hybrid versus line breeding in wheat based on quantitative genetic theory

The predicted future yield potential of hybrids was competitive with lines in the near future, but on a long term the competitiveness of hybrids depends on a number of factors. The change from line to hybrid breeding in autogamous crops is a recent controversial discussion among scientists and breeders. Our objectives were to employ wheat as a model to: (1) deliver a theoretical framework for the comparison of the selection gain of hybrid versus line breeding; (2) elaborate key parameters affecting selection gain in this comparison; (3) and evaluate the potential to modify these parameters in applied breeding programs. We developed a prediction model for future yield potential in both breeding methods as the sum of the population mean and the expected selection gain. The expected selection gain was smaller in hybrid than in line breeding and depended strongly on the hybrid seed production costs and the genetic variance available in hybrid versus line breeding. Owing to heterosis, the predicted future yield potential of hybrids was competitive with lines in the near future. On a long term, however, the competitiveness of hybrid compared to line breeding is questionable and depends on a number of factors. However, market specifications and political reasons might justify the current high interest in hybrid wheat breeding.

Impact of selective genotyping in the training population on accuracy and bias of genomic selection

Estimating marker effects based on routinely generated phenotypic data of breeding programs is a cost-effective strategy to implement genomic selection. Truncation selection in breeding populations, however, could have a strong impact on the accuracy to predict genomic breeding values. The main objective of our study was to investigate the influence of phenotypic selection on the accuracy and bias of genomic selection. We used experimental data of 788 testcross progenies from an elite maize breeding program. The testcross progenies were evaluated in unreplicated field trials in ten environments and fingerprinted with 857 SNP markers. Random regression best linear unbiased prediction method was used in combination with fivefold cross-validation based on genotypic sampling. We observed a substantial loss in the accuracy to predict genomic breeding values in unidirectional selected populations. In contrast, estimating marker effects based on bidirectional selected populations led to only a marginal decrease in the prediction accuracy of genomic breeding values. We concluded that bidirectional selection is a valuable approach to efficiently implement genomic selection in applied plant breeding programs.

Gene stacking strategies with doubled haploids derived from biparental crosses: theory and simulations assuming a finite number of loci

Recent progress in genotyping and doubled haploid (DH) techniques has created new opportunities for development of improved selection methods in numerous crops. Assuming a finite number of unlinked loci (ℓ) and a given total number (n) of individuals to be genotyped, we compared, by theory and simulations, three methods of marker-assisted selection (MAS) for gene stacking in DH lines derived from biparental crosses: (1) MAS for high values of the marker score (T, corresponding to the total number of target alleles) in the F(2) generation and subsequently among DH lines derived from the selected F(2) individual (Method 1), (2) MAS for augmented F(2) enrichment and subsequently for T among DH lines from the best carrier F(2) individual (Method 2), and (3) MAS for T among DH lines derived from the F(1) generation (Method 3). Our objectives were to (a) determine the optimum allocation of resources to the F(2) ([Formula: see text]) and DH generations [Formula: see text] for Methods 1 and 2 by simulations, (b) compare the efficiency of all three methods for gene stacking by simulations, and (c) develop theory to explain the general effect of selection on the segregation variance and interpret our simulation results. By theory, we proved that for smaller values of ℓ, the segregation variance of T among DH lines derived from F(2) individuals, selected for high values of T, can be much smaller than expected in the absence of selection. This explained our simulation results, showing that for Method 1, it is best to genotype more F(2) individuals than DH lines ([Formula: see text]), whereas under Method 2, the optimal ratio [Formula: see text] was close to 0.5. However, for ratios deviating moderately from the optimum, the mean [Formula: see text] of T in the finally selected DH line ([Formula: see text]) was hardly reduced. Method 3 had always the lowest mean [Formula: see text] of [Formula: see text] except for small numbers of loci (ℓ = 4) and is favorable only if a small number of loci are to be stacked in one genotype and/or saving one generation is of crucial importance in cultivar development. Method 2 is under most circumstances the superior method, because it generally showed the highest mean [Formula: see text] and lowest SD of [Formula: see text] for the finally selected DH.

Hybrid maize breeding with doubled haploids: V. Selection strategies for testcross performance with variable sizes of crosses and S(1) families

In hybrid maize (Zea mays L.) breeding, doubled haploids (DH) are increasingly replacing inbreds developed by recurrent selfing. Doubled haploids may be developed directly from S(0) plants in the parental cross or via S(1) families. In both these breeding schemes, we examined 2 two-stage selecting strategies, i.e., considering or ignoring cross and family structure while selection among and within parental crosses and S(1) families. We examined the optimum allocation of resources to maximize the selection gain DeltaG and the probability P(q) of identifying the q% best genotypes. Our specific objectives were to (1) determine the optimum number and size of crosses and S(1) families, as well as the optimum number of test environments and (2) identify the superior selection strategy. Selection was based on the evaluation of testcross progenies of (1) DH lines in both stages (DHTC) and (2) S(1) families in the first stage and of DH lines within S(1) families in the second stage (S(1)TC-DHTC) with uniform and variable sizes of crosses and S(1) families. We developed and employed simulation programs for selection with variable sizes of crosses and S(1) families within crosses. The breeding schemes and selection strategies showed similar relative efficiency for both optimization criteria DeltaG and P (0.1%). As compared with DHTC, S(1)TC-DHTC had larger DeltaG and P (0.1%), but a higher standard deviation of DeltaG. The superiority of S(1)TC-DHTC was increased when the selection was done among all DH lines ignoring their cross and family structure and using variable sizes of crosses and S(1) families. In DHTC, the best selection strategy was to ignore cross structures and use uniform size of crosses.

Optimum allocation of resources for QTL detection using a nested association mapping strategy in maize

In quantitative trait locus (QTL) mapping studies, it is mandatory that the available financial resources are spent in such a way that the power for detection of QTL is maximized. The objective of this study was to optimize for three different fixed budgets the power of QTL detection 1 - beta* in recombinant inbred line (RIL) populations derived from a nested design by varying (1) the genetic complexity of the trait, (2) the costs for developing, genotyping, and phenotyping RILs, (3) the total number of RILs, and (4) the number of environments and replications per environment used for phenotyping. Our computer simulations were based on empirical data of 653 single nucleotide polymorphism markers of 26 diverse maize inbred lines which were selected on the basis of 100 simple sequence repeat markers out of a worldwide sample of 260 maize inbreds to capture the maximum genetic diversity. For the standard scenario of costs, the optimum number of test environments (E (opt)) ranged across the examined total budgets from 7 to 19 in the scenarios with 25 QTL. In comparison, the E (opt) values observed for the scenarios with 50 and 100 QTL were slightly higher. Our finding of differences in 1 - beta* estimates between experiments with optimally and sub-optimally allocated resources illustrated the potential to improve the power for QTL detection without increasing the total resources necessary for a QTL mapping experiment. Furthermore, the results of our study indicated that also in studies using the latest genomics tools to dissect quantitative traits, it is required to evaluate the individuals of the mapping population in a high number of environments with a high number of replications per environment.

Hybrid maize breeding with doubled haploids. IV. Number versus size of crosses and importance of parental selection in two-stage selection for testcross performance

Parental selection influences the gain from selection and the optimum allocation of test resources in breeding programs. We compared two hybrid maize (Zea mays L.) breeding schemes with evaluation of testcross progenies: (a) doubled haploid (DH) lines in both stages (DHTC) and (b) S(1) families in the first stage and DH lines within S(1) families in the second stage (S(1)TC-DHTC). Our objectives were to (1) determine the optimum allocation regarding the number of crosses, S(1) families, DH lines, and test locations, (2) investigate the impact of parental selection on the optimum allocation and selection gain (DeltaG), and (3) compare the maximum DeltaG achievable with each breeding scheme. Selection gain was calculated by numerical integration. Different assumptions were made regarding the budget, variance components, correlation between the mean phenotypic performance of the parents and the mean genotypic value of the testcross performance of their progenies (rho( P )), and the composition of the finally selected test candidates. In comparison with randomly chosen crosses, maximum DeltaG was largely increased with parental selection in both breeding schemes. With an increasing correlation rho( P ), this superiority increased strongly, while the optimum number of crosses decreased in favor of an increased number of test candidates within crosses. Thus, concentration on few crosses among the best parental lines might be a promising approach for short-term success in advanced cycle breeding. Breeding scheme S(1)TC-DHTC led to a larger DeltaG but had a longer cycle length than DHTC. However, with further improvements in the DH technique and the realization of more than two generations per year, early testing of S(1) families prior to production of DH lines would become very attractive in hybrid maize breeding.

Potential causes of linkage disequilibrium in a European maize breeding program investigated with computer simulations

Knowledge about the forces generating and conserving linkage disequilibrium (LD) is important for drawing conclusions about the prospects and limitations of association mapping. The objectives of our research were to examine the importance of (1) selection, (2) mutation, and (3) genetic drift for generating LD in a typical maize breeding program. We conducted computer simulations based on genotypic data of Central European maize open-pollinated varieties which have played an important role as founders of the European flint heterotic group. The breeding scheme and the dimensioning underlying our simulations reflect essentially the maize breeding program of the University of Hohenheim. Results suggested that in a plant breeding program of the examined dimension and breeding scheme, genetic drift and selection are major forces generating LD. The currently used population-based association mapping tests do not explicitly correct for LD caused by these two forces. Therefore, increased type I error rates are expected if these tests are applied to plant breeding populations. As a consequence, we recommend to use family-based association tests for association mapping approaches in plant breeding populations.

Hybrid maize breeding with doubled haploids: III. Efficiency of early testing prior to doubled haploid production in two-stage selection for testcross performance

Early testing prior to doubled haploid (DH) production is a promising approach in hybrid maize breeding. We (1) determined the optimum allocation of the number of S(1) families, DH lines, and test locations for two different breeding schemes, (2) compared the maximum selection gain achievable under both breeding schemes, and (3) investigated limitations in the current method of DH production. Selection gain was calculated by numerical integration in two-stage breeding schemes with evaluation of testcross progenies of (1) DH lines in both stages (DHTC), or (2) S(1) families in the first and DH lines within S(1) families in the second stage (S(1)TC-DHTC). Different assumptions were made regarding the budget, variance components, and time of DH production within S(1) families. Maximum selection gain in S(1)TC-DHTC was about 10% larger than in DHTC, indicating the large potential of early testing prior to DH production. The optimum allocation of test resources in S(1)TC-DHTC involved similar numbers of test locations and test candidates in both stages resulting in a large optimum number of S(1) families in the first stage and DH lines within the best two S(1) families in the second stage. The longer cycle length of S(1)TC-DHTC can be compensated by haploid induction of individual S(1) plants instead of S(1) families. However, this reduces selection gain largely due to the current limitations in the DH technique. Substantial increases in haploid induction and chromosome doubling rates as well as reduction in costs of DH production would allow early testing of S(1) lines and subsequent production and testing of DH lines in a breeding scheme that combines high selection gain with a short cycle length.

Hybrid maize breeding with doubled haploids: II. Optimum type and number of testers in two-stage selection for general combining ability

Optimum allocation of test resources is of crucial importance for the efficiency of breeding programs. Our objectives were to (1) determine the optimum allocation of the number of lines, test locations, as well as number and type of testers in hybrid maize breeding using doubled haploids with two breeding strategies for improvement of general combining ability (GCA), (2) compare the maximum selection gain (DeltaG) achievable under both strategies, and (3) give recommendations for the optimum implementation of doubled haploids in commercial hybrid maize breeding. We calculated DeltaG by numerical integration for two two-stage selection strategies with evaluation of (1) testcross performance in both stages (BS1) or (2) line per se performance in the first stage followed by testcross performance in the second stage (BS2). Different assumptions were made regarding the budget, variance components (VCs), and the correlation between line per se performance and GCA. Selection gain for GCA increased with a broader genetic base of the tester. Hence, testers combining a large number of divergent lines are advantageous. However, in applied breeding programs, the use of single- or double-cross testers in the first and inbred testers in the second selection stage may be a good compromise between theoretical and practical requirements. With a correlation between line per se performance and GCA of 0.50, DeltaG for BS1 is about 5% higher than for BS2, if an economic weight of line per se performance is neglected. With increasing economic weight of line per se performance, relative efficiency of BS2 increased rapidly resulting in a superiority of BS2 over BS1 already for an economic weight for line per se performance larger than 0.1. Considering the importance of an economic seed production, an economic weight larger than 0.1 seems realistic indicating the necessity of separate breeding strategies for seed and pollen parent heterotic groups.