Whole-genome versus per-chromosome targeted recombination: Simulations and predicted gains in maize with an integer programming model.

Per-chromosome targeted recombination, with one to two recombinations at specific marker intervals on each chromosome, doubles the predicted genetic gains in biparental populations. We developed an integer programing model to identify where a fixed number of targeted recombinations should occur across the whole genome, without restrictions on the number of targeted recombinations on each chromosome. We compared whole-genome and per-chromosome targeted recombination in 392 biparental maize (Zea mays L.) populations and in simulation experiments. For yield, moisture, test weight, and a simulated trait controlled by 2000 quantitative trait loci (QTL), predicted gains were 8%-9% larger with 10 targeted recombinations across the entire genome than with one targeted recombination on each of the 10 chromosomes. With whole-genome targeted recombination, the number of recombinations on a given chromosome was correlated (r = 0.76-0.91) with the chromosome size (in cM). Simulation results suggested that previous results on gains from targeted recombination relative to nontargeted recombination were too optimistic by around 20%. Because the underlying QTL are unknown, studies on targeted recombination have relied on genomewide marker effects as proxies for QTL information. The simulation results indicated a 25% (for 10 recombinations) to 33% (for 20 recombinations) reduction in response due to the use of genomewide marker effects as proxies for QTL information. Overall, the results indicated that the integer programming model we developed is useful for increasing both the predicted and true gains from targeted recombination, but the predicted gains are likely to overestimate the true gains.

Reciprocal testcross design for genome-wide prediction of maize single-cross performance.

KEY MESSAGE: A reciprocal testcross design increases the relatedness among single crosses and testcrosses, thereby increasing the effectiveness of genome-wide prediction in maize. A reciprocal testcross design uses parental inbreds in an opposite heterotic group as testers in maize (Zea mays L.) inbred development. In particular, doubled haploids from the A × B cross are testcrossed with inbreds Y and Z, and doubled haploids from Y × Z are testcrossed with inbreds A and B. Our objective was to determine if a reciprocal testcross design is superior to a traditional, non-reciprocal testcross design. A total of 700 Iowa Stiff Stalk Synthetic (BSSS) doubled haploids and 231 non-BSSS doubled haploids were developed from 10 breeding populations and had data on 11,032 single nucleotide polymorphism markers. Each doubled haploid was testcrossed to one to five testers from the opposite heterotic group, and the resulting 1642 testcrosses were evaluated in multilocation yield trials in 2019. Divergent selection for yield/moisture, on the basis of genome-wide predictions according to a reciprocal testcross design, led to significant responses (in 2020) in all 10 populations for yield/moisture and moisture and in three populations for yield. Predictive ability for yield/moisture and moisture was 0.11 to 0.26 higher with a reciprocal testcross design than with a testcross design. This higher predictive ability was attributed to a stronger relatedness between the training and test populations. No significant difference in predictive ability was found for yield, for which predictive ability was lower. Differences among genetic models that included and excluded specific combining ability were small. Overall, the empirical results supported the usefulness of a reciprocal testcross design in maize breeding.

Genomewide selection for fruit quality traits in apple: breeding insights gained from prediction and postdiction.

Many fruit quality traits in apple (Malus domestica Borkh.) are controlled by multiple small-effect quantitative trait loci (QTLs). Genomewide selection (genomic selection) might be an effective breeding approach for highly quantitative traits in woody perennial crops with long generation times like apple. The goal of this study was to determine if genomewide prediction is an effective breeding approach for fruit quality traits in an apple scion breeding program. Representative apple scion breeding germplasm (nindividuals = 955), high-quality single nucleotide polymorphism (SNP) data (nSNPs = 977), and breeding program fruit quality trait data at harvest were analyzed. Breeding parents `Honeycrisp' and `Minneiska' were highly represented. Moderate to high predictive abilities were observed for most fruit quality traits at harvest. For example, when 25% random subsets of the germplasm set were used as training sets, mean predictive abilities ranged from 0.35 to 0.54 across traits. Trait, training and test sets, family size for within family prediction, and number of SNPs per chromosome affected model predictive ability. Inclusion of large-effect QTLs as fixed effects resulted in higher predictive abilities for some traits (e.g. percent red overcolor). Postdiction (i.e. retrospective) analyses demonstrated the impact of culling threshold on selection decisions. The results of this study demonstrate that genomewide selection is a useful breeding approach for certain fruit quality traits in apple.

Covariance between nonrelatives in maize.

The covariance between relatives is a tenet in quantitative genetics, but the covariance between nonrelatives in crops has not been studied. My objective was to determine if a covariance between nonrelatives is present in maize (Zea mays L.). The germplasm comprised 272 maize lines that were previously genotyped with 28,626 single nucleotide polymorphism (SNP) markers. Pairs of unrelated lines were identified on the basis of their membership probabilities in five subpopulations. The covariance between nonrelatives was assessed as the regression of phenotypic similarity on SNP similarity between unrelated lines. Out of 77 regressions, seven were significant at a 5% false discovery rate: anthesis and silking dates in unrelated B73 and Oh43 lines; plant height and ear height in unrelated Oh43 and PH207 lines; oil in unrelated A321 and Mo17 lines; starch in unrelated B73 and PH207 lines; and protein in unrelated B73 and Mo17 lines. The latter covariance was negative, and this negative covariance between nonrelatives was attributed to the subpopulations having different linkage phases between the markers and underlying causal variants. Overall, the results indicated that a covariance between nonrelatives in maize is not ubiquitous but is sometimes present for specific traits and for certain groups of unrelated individuals. I propose that the covariance between nonrelatives and the covariance between relatives be combined into a generalized covariance between individuals, thus giving a unified framework for expressing the resemblance regardless of the degree of relatedness.

Linear, funnel, and multiple funnel schemes for stacking chromosomes that carry targeted recombinations in plants.

KEY MESSAGE: Up to five chromosomes that carry targeted recombinations can be stacked via a multiple funnel scheme, provided that the probabilities of inheriting intact chromosomes from donor parents are high. Targeted recombination involves inducing or selecting for recombination events at specific points in the genome to maximize genetic gain. Practical application of targeted recombination requires efficient breeding strategies to stack multiple chromosomes that carry such recombinations. Our objectives were to determine how many chromosomes with targeted recombinations can be feasibly stacked in a breeding program, and how the feasibility of stacking is affected by the crossing design, homozygosity versus heterozygosity of the donor lines, size of the chromosomal segment showing recombination, and probability of an intact chromosome being inherited. Based on a genetic model for maize (Zea mays L.) with 10 pairs of chromosomes, we examined different crossing schemes by simulation experiments and analytical studies with the goal of minimizing the number of generations and population sizes required for stacking. We found that targeted recombinations on up to five chromosomes can be stacked within practical constraints on time and resources. Linear and funnel schemes were less efficient than a multiple funnel scheme, which involved making all possible crosses in the first generation and stacking two additional chromosomes across multiple lines in subsequent generations. Homozygosity versus heterozygosity of the donor lines did not affect stacking efficiency. Population sizes and stacking efficiency were largely determined by the probability of intact chromosomal transfer from a donor parent to offspring. Such probability increased as the size of the chromosome segment from the donor decreased. When the probability of inheriting an intact chromosome was less than 0.15, population sizes needed for stacking became infeasibly large.

Reinventing quantitative genetics for plant breeding: something old, something new, something borrowed, something BLUE.

The goals of quantitative genetics differ according to its field of application. In plant breeding, the main focus of quantitative genetics is on identifying candidates with the best genotypic value for a target population of environments. Keeping quantitative genetics current requires keeping old concepts that remain useful, letting go of what has become archaic, and introducing new concepts and methods that support contemporary breeding. The core concept of continuous variation being due to multiple Mendelian loci remains unchanged. Because the entirety of germplasm available in a breeding program is not in Hardy-Weinberg equilibrium, classical concepts that assume random mating, such as the average effect of an allele and additive variance, need to be retired in plant breeding. Doing so is feasible because with molecular markers, mixed-model approaches that require minimal genetic assumptions can be used for best linear unbiased estimation (BLUE) and prediction. Plant breeding would benefit from borrowing approaches found useful in other disciplines. Examples include reliability as a new measure of the influence of genetic versus nongenetic effects, and operations research and simulation approaches for designing breeding programs. The genetic entities in such simulations should not be generic but should be represented by the pedigrees, marker data, and phenotypic data for the actual germplasm in a breeding program. Over the years, quantitative genetics in plant breeding has become increasingly empirical and computational and less grounded in theory. This trend will continue as the amount and types of data available in a breeding program increase.

Predicted genetic gains from introgressing chromosome segments from exotic germplasm into an elite soybean cultivar.

KEY MESSAGE: To improve an elite soybean line, introgress longer chromosome segments instead of QTL alleles from exotic germplasm. Broadening the diversity of cultivated soybean [Glycine max (L.) Merrill] through introgression of exotic germplasm has been difficult. Our objectives were to (1) determine if introgressing specific chromosome segments (instead of quantitative trait locus alleles) from exotic soybean germplasm has potential for improving an elite cultivar, and (2) identify strategies to introgress and pyramid exotic chromosome segments into an elite cultivar. We estimated genomewide marker effects for yield and other traits in seven crosses between the elite line IA3023 and seven soybean plant introductions (PIs). We then predicted genetic gains from having ≤ 2 targeted recombinations per linkage group. When introgression was modeled for yield while controlling maturity in the seven PI × IA3023 populations, the predicted yield was 8-25% over the yield of IA3023. Correlated changes in maturity, seed traits, lodging, and plant height were generally small but were in the favorable direction. In contrast, selecting the best recombinant inbred (without targeted recombination) in each of the PI × IA3023 populations led to negative or minimal yield gains over IA3023. In one PI × IA3023 population, introgressing and pyramiding only two linkage groups from recombinant inbreds into IA3023 was predicted to achieve an 8% yield gain over IA3023 without sacrificing the performance for other traits. The probability of inheriting intact chromosomes was high enough to allow introgression and pyramiding of chromosome segments in 5-6 generations. Overall, our study suggested that introgressing specific chromosome segments is an effective way to introduce exotic soybean germplasm into an elite cultivar.

Assessing by Modeling the Consequences of Increased Recombination in Recurrent Selection of Oryza sativa and Brassica rapa.

Meiotic recombination generates genetic diversity but in most species the number of crossovers per meiosis is limited. Previous modeling studies showed that increasing recombination can enhance response to selection. However, such studies did not assume a specific method of modifying recombination. Our objective was to test whether two methods used to increase recombination in plants could increase genetic gain in a population undergoing recurrent selection such as in genomic selection programs. The first method, in Oryza sativa, used a mutant of anti-crossover genes, increasing global recombination without affecting the recombination landscape shape. The second one used the ploidy level of a cross between Brassica rapa and Brassica napus, increasing recombination especially in pericentromeric regions. Our modeling framework used these recombination landscapes and sampled quantitative trait loci positions from the actual gene distributions. We simulated selection programs with initially a cross between two inbred lines, for two species. Increased recombination enhanced the response to selection. The amount of enhancement in the cumulative gain largely depended on the species and the number of quantitative trait loci (2, 10, 20, 50, 200 or 1000 per chromosome). Genetic gains were increased up to 30% after 20 generations. Furthermore, increasing recombination in cold regions was the most effective: the gain was larger by 25% with the first method and 34% with the second one in B. rapa, and 12% compared to 16% in O. sativa In summary, increased recombination enhances the genetic gain in long-term selection programs, with visible effects after four to five generations.

Predicted Genetic Gains from Targeted Recombination in Elite Biparental Maize Populations.

Targeted recombination is the ability to induce or select for specific recombination points on chromosomes. A first study with the intermated B73 × Mo17 maize ( L.) population showed that targeted recombination doubles the predicted gains for yield and other agronomic traits. Our objective was to assess the predicted gains from targeted recombination for quantitative traits in multiple, elite maize populations. A total of 969 biparental maize populations were phenotyped at four to 12 environments in the United States from 2000 to 2008. Positions of one and two targeted recombinations per chromosome were determined from genomewide marker effects for 2911 single nucleotide polymorphism (SNP) loci. Relative efficiency (RE) was calculated as the predicted response to targeted recombination divided by the predicted response to nontargeted recombination. On average, targeted recombination doubled the predicted genetic gains for yield, moisture, and test weight. For each trait, RE ranged from around 60 to 400% among the populations, and targeted recombination did not increase gains in around 4% of the populations. The RE tended to decrease as the similarity between the parents increased. Having targeted recombination on three chromosomes (for yield and test weight) to seven chromosomes (for moisture) led to the same or greater predicted gain than nontargeted recombination. Marker intervals for targeted recombination varied across populations and traits. Overall, our results for multiple, elite maize populations indicated that targeted recombination is a most promising breeding approach.

Small ad hoc versus large general training populations for genomewide selection in maize biparental crosses.

KEY MESSAGE: For genomewide selection in each biparental population, it is better to use a smaller ad hoc training population than a single, large training population. In genomewide selection, different types of training populations can be used for a biparental population made from homozygous parents (A and B). Our objective was to determine whether the response to selection (R) and predictive ability (rMP) in an A/B population are higher with a large training population that is used for all biparental crosses, or with a smaller ad hoc training population highly related to the A/B population. We studied 969 biparental maize (Zea mays L.) populations phenotyped at four to 12 environments. Parent-offspring marker imputation was done for 2911 single nucleotide polymorphism loci. For 27 A/B populations, training populations were constructed by pooling: (1) all prior populations with A as one parent (A/*, where * is a related inbred) and with B as one parent (*/B) [general combining ability (GCA) model]; (2) A/* or */B crosses only; (3) all */* crosses (same background model, SB); and (4) all */*, A/*, and */B crosses (SB + GCA model). The SB model training population was 450-6000% as large as the GCA model training populations, but the mean coefficient of coancestry between the training population and A/B population was lower for the SB model (0.44) than for the GCA model (0.71). The GCA model had the highest R and rMP for all traits. For yield, R was 0.22 Mg ha-1 with the GCA model and 0.15 Mg ha-1 with the SB model. We concluded that it is best to use an ad hoc training population for each A/B population.

Targeted recombination to increase genetic gain in self-pollinated species.

KEY MESSAGE: If we can induce or select for recombination at targeted marker intervals, genetic gains for quantitative traits in self-pollinated species may be doubled. Targeted recombination refers to inducing or selecting for a recombination event at genomic positions that maximize genetic gain in a cross. A previous study indicated that targeted recombination could double the rate of genetic gains in maize (Zea mays L.), a cross-pollinated crop for which historical genetic gains have been large. Our objectives were to determine whether targeted recombination can sufficiently increase predicted gains in self-pollinated species, and whether prospective gains from targeted recombination vary across crops, populations, traits, and chromosomes. Genomewide marker effects were estimated from previously published marker and phenotypic data on 21 biparental populations of soybean [Glycine max (L.) Merr.], wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), and pea (Pisum sativum L.). With the predicted gain from nontargeted recombination as the baseline, the relative gains from creating a doubled haploid with up to one targeted recombination [RG(x ≤ 1)] and two targeted recombinations [RG(x ≤ 2)] per chromosome or linkage group were calculated. Targeted recombination significantly (P = 0.05) increased the predicted genetic gain compared to nontargeted recombination for all traits and all populations, except for plant height in barley. The mean RG(x ≤ 1) was 211%, whereas the mean RG(x ≤ 2) was 243%. The predicted gain varied among traits and populations. For most traits and populations, having targeted recombination on less than a third of all the chromosomes led to the same or higher predicted gain than nontargeted recombination. Together with previous findings in maize, our results suggested that targeted recombination could double the genetic gains in both self- and cross-pollinated crops.

Prospective Targeted Recombination and Genetic Gains for Quantitative Traits in Maize.

Advances in clustered regularly interspaced short palindromic repeats (CRISPR) technology have allowed targeted recombination in specific DNA sequences in yeast (). My objective was to determine if the selection gains from targeted recombination are large enough to warrant the development of targeted recombination technology in plants. Genomewide marker effects for quantitative traits in two maize ( L.) experiments were used to identify targeted recombination points that would maximize the per-chromosome genetic gains in a given cross. With nontargeted recombination in the intermated B73 × Mo17 population, selecting the best out of 180 recombinant inbreds led to a 7.1% gain for testcross yield. Having one targeted recombination on each of the 10 maize chromosomes led to a predicted gain of 15.3% for yield. Targeted recombination therefore led to a predicted relative efficiency () of (0.153 ÷ 0.071) = 212% of targeted recombination compared with nontargeted recombination. For the five other traits in the intermated B73 × Mo17 population and for four traits in 45 other maize crosses, the values ranged from 105 to 600%. The targeted recombination points differed among traits and crosses. Predicted gains increased when the number of targeted recombinations per chromosome increased from one to two. Overall, the results suggested that targeted recombination could double the selection gains for quantitative traits in maize and that the development of targeted recombination technology is worthwhile. Empirical experiments with current marker-assisted breeding procedures are needed to validate the per-chromosome predicted gains.

Germplasm Architecture Revealed through Chromosomal Effects for Quantitative Traits in Maize.

Germplasm architecture refers to how favorable alleles for a given trait are distributed across the genome in a germplasm collection. Our objective was to assess germplasm architecture for quantitative traits among US maize ( L.) inbreds. A total of 271 inbreds were genotyped at 28,626 single nucleotide polymorphism (SNP) loci and phenotyped for anthesis date, plant height, starch and protein concentration, and resistance to northern corn leaf blight (NCLB, caused by ). Chromosomal effects were calculated as the sum of the trait effects of SNP alleles carried on a specific chromosome by an inbred. The chromosomal effects were further decomposed into the mean effects of chromosomes, mean effects of inbreds, and chromosome × inbred effects. On average, none of the 10 maize chromosomes was particularly rich or poor in favorable quantitative trait locus (QTL) alleles. However, extreme values of chromosome × inbred effects often involved chromosomes 5 and 8 for anthesis date, chromosomes 1 and 5 for plant height, and chromosome 9 for protein concentration. Inbreds with one or two chromosomes deficient in favorable alleles were candidates for improvement via chromosome-substitution lines. Specific chromosomes for which each of five genetic backgrounds (B73, Mo17, Oh43, A321, and PH207) were rich or poor for unknown favorable alleles were also identified. Chromosomal effects varied widely even when prior association mapping in the same germplasm collection had failed to identify any QTL. Genomewide marker effects, particularly when partitioned into chromosomal effects, provide a simple way to dissect germplasm architecture for quantitative traits.

Genomic prediction contributing to a promising global strategy to turbocharge gene banks.

The 7.4 million plant accessions in gene banks are largely underutilized due to various resource constraints, but current genomic and analytic technologies are enabling us to mine this natural heritage. Here we report a proof-of-concept study to integrate genomic prediction into a broad germplasm evaluation process. First, a set of 962 biomass sorghum accessions were chosen as a reference set by germplasm curators. With high throughput genotyping-by-sequencing (GBS), we genetically characterized this reference set with 340,496 single nucleotide polymorphisms (SNPs). A set of 299 accessions was selected as the training set to represent the overall diversity of the reference set, and we phenotypically characterized the training set for biomass yield and other related traits. Cross-validation with multiple analytical methods using the data of this training set indicated high prediction accuracy for biomass yield. Empirical experiments with a 200-accession validation set chosen from the reference set confirmed high prediction accuracy. The potential to apply the prediction model to broader genetic contexts was also examined with an independent population. Detailed analyses on prediction reliability provided new insights into strategy optimization. The success of this project illustrates that a global, cost-effective strategy may be designed to assess the vast amount of valuable germplasm archived in 1,750 gene banks.

Bandwagons I, too, have known.

KEY MESSAGE: Bandwagons come in waves. A plant breeder, just like a surfer, needs to carefully choose which waves to be on. A bandwagon is an idea, activity, or cause that becomes increasingly fashionable as more and more people adopt it. In a 1991 article entitled Bandwagons I Have Known, Professor N. W. Simmonds described several bandwagons that he encountered in his career, beginning with induced polyploidy and mutation breeding and ending with the then-new field of biotechnology. This article reviews and speculates about post-1990 bandwagons in plant improvement, including transgenic cultivars, quantitative trait locus (QTL) mapping, association mapping, genomewide (or genomic) selection, phenomics, envirotyping, and genome editing. The life cycle of a bandwagon includes an excitement phase of hype and funding; a realization phase when the initial hype is either tempered or the initial expectations are found to have been too low; and a reality phase when the useful aspects of a bandwagon become part of mainstream thinking and practice, or when an unsuccessful bandwagon is largely abandoned. During the realization phase, a new bandwagon that draws our attention and gives us renewed optimism typically arises. The most popular bandwagons, such as QTL mapping, are those for which the needed experimental resources are accessible, the required technical knowledge and skills can be easily learned, and the outputs can almost always be reported. The favorite bandwagon of any plant breeder has, in one way or another, resulted from Mendel's seminal discoveries 150 years ago. Our community of plant breeders needs to be continually diligent in welcoming new bandwagons, but also in hopping off from those that do not prove useful.

Recombination and genetic variance among maize doubled haploids induced from F1 and F2 plants.

KEY MESSAGE: Inducing maize doubled haploids from F 2 plants (DHF2) instead of F 1 plants (DHF1) led to more recombination events. However, the best DHF2 lines did not outperform the best DHF1 lines. Maize (Zea mays L.) breeders rely on doubled haploid (DH) technology for fast and efficient production of inbreds. Breeders can induce DH lines most quickly from F1 plants (DHF1), or induce DH lines from F2 plants (DHF2) to allow selection prior to DH induction and have more recombinations. Our objective was to determine if the additional recombinations in maize DHF2 lines lead to a larger genetic variance and a superior mean of the best lines. A total of 311 DHF1 and 241 DHF2 lines, derived from the same biparental cross, were crossed to two testers and evaluated in multilocation trials in Europe and the US. The mean number of recombinations per genome was 14.48 among the DHF1 lines and 21.38 among the DHF1 lines. The means of the DHF1 and DHF2 lines did not differ for yield, moisture, and plant height. The genetic variance was higher among DHF2 lines than among DHF1 lines for moisture, but not for yield and plant height. The ratio of repulsion to coupling linkages, which was estimated from genomewide marker effects, was higher among DHF1 lines than among DHF2 lines for moisture, but not for yield and plant height. The higher genetic variance for moisture among DHF2 lines did not lead to lower moisture of the best 10 % of the lines. Our results indicated that the decision of inducing DH lines from F1 or F2 plants needs to be made from considerations other than the performance of the resulting DHF1 or DHF2 lines.

Marker Imputation Before Genomewide Selection in Biparental Maize Populations.

Marker imputation can be used to increase the number of markers in genomewide selection. Our objectives were to determine (i) if marker imputation increases the response to selection (R) and prediction accuracy (rMP ) among the progeny of two maize (Zea mays L.) parental inbreds (A and B); (ii) the number of imputed single nucleotide polymorphism (SNP) markers needed to reach a plateau in rMP for grain yield, moisture, and test weight; and (iii) the lowest number of assayed SNP markers that can be used for imputation without a significant decrease in rMP . The progeny of 27 biparental crosses between A and B (A/B) were assayed with 49 to 100 SNP markers, and imputation was conducted to increase the number of markers to 2911. For each A/B test population, the training population in the general combining ability (GCA) model consisted of 4 to 26 maize crosses with A and B as one of the parents, whereas the training population in the A/B model was the A/B population itself. Marker imputation made the GCA model as good as or better than the A/B model in terms of R and rMP for all traits. The rMP values did not increase significantly beyond 500 imputed markers for grain yield and beyond 1000 imputed markers for moisture and test weight. We recommend that maize breeders assay an elite biparental cross with only around 50 polymorphic SNP markers, increase marker coverage to around 1000 markers by imputation, and use the GCA model with imputed markers for genomewide selection within the cross.

Genomewide predictions from maize single-cross data.

Maize (Zea mays L.) breeders evaluate many single-cross hybrids each year in multiple environments. Our objective was to determine the usefulness of genomewide predictions, based on marker effects from maize single-cross data, for identifying the best untested single crosses and the best inbreds within a biparental cross. We considered 479 experimental maize single crosses between 59 Iowa Stiff Stalk Synthetic (BSSS) inbreds and 44 non-BSSS inbreds. The single crosses were evaluated in multilocation experiments from 2001 to 2009 and the BSSS and non-BSSS inbreds had genotypic data for 669 single nucleotide polymorphism (SNP) markers. Single-cross performance was predicted by a previous best linear unbiased prediction (BLUP) approach that utilized marker-based relatedness and information on relatives, and from genomewide marker effects calculated by ridge-regression BLUP (RR-BLUP). With BLUP, the mean prediction accuracy (r(MG)) of single-cross performance was 0.87 for grain yield, 0.90 for grain moisture, 0.69 for stalk lodging, and 0.84 for root lodging. The BLUP and RR-BLUP models did not lead to r(MG) values that differed significantly. We then used the RR-BLUP model, developed from single-cross data, to predict the performance of testcrosses within 14 biparental populations. The r(MG) values within each testcross population were generally low and were often negative. These results were obtained despite the above-average level of linkage disequilibrium, i.e., r(2) between adjacent markers of 0.35 in the BSSS inbreds and 0.26 in the non-BSSS inbreds. Overall, our results suggested that genomewide marker effects estimated from maize single crosses are not advantageous (cofmpared with BLUP) for predicting single-cross performance and have erratic usefulness for predicting testcross performance within a biparental cross.

Accuracy of genotypic value predictions for marker-based selection in biparental plant populations.

The availability of cheap and abundant molecular markers has led to plant-breeding methods that rely on the prediction of genotypic value from marker data, but published information is lacking on the accuracy of genotypic value predictions with empirical data in plants. Our objectives were to (1) determine the accuracy of genotypic value predictions from multiple linear regression (MLR) and genomewide selection via best linear unbiased prediction (BLUP) in biparental plant populations; (2) assess the accuracy of predictions for different numbers of markers (N(M)) and progenies (N(P)) used in estimation; and (3) determine if an empirical Bayes approach for modeling of the variances of individual markers and of epistatic effects leads to more accurate predictions in empirical data. We divided each of four maize (Zea mays L.) datasets, one Arabidopsis dataset, and two barley (Hordeum vulgare L.) datasets into an estimation set, where marker effects were calculated, and a test set, where genotypic values were predicted based on markers. Predictions were more accurate with BLUP than with MLR. Predictions became more accurate as N(P) and N(M) increased, until sufficient genome coverage was reached. Modeling marker variances with the empirical Bayes method sometimes led to slightly better predictions, but the accuracy with different variants of the empirical Bayes method was often inconsistent. In nearly all cases, the accuracy with BLUP was not significantly different from the highest accuracy across all methods. Accounting for epistasis in the empirical Bayes procedure led to poorer predictions. We concluded that among the methods considered, the quick and simple BLUP approach is the method of choice for predicting genotypic value in biparental plant populations.

Should maize doubled haploids be induced among F(1) or F (2) plants?

Maize (Zea mays L.) doubled haploid lines are typically produced from F(1) plants. Studies have suggested that the low frequency of recombinants in doubled haploids may reduce the response to selection. My objective was to determine if, for sustaining long-term response, doubled haploids should be induced in F(1) or F(2) plants during maize inbred development. In simulation experiments, I examined the response to multiple cycles of testcross selection among doubled haploid lines derived from F(1) plants (denoted by DH), doubled haploid lines derived from F(2) plants (DH(F2)), and recombinant inbred (RI) lines derived by single-seed descent. For a trait controlled by 100 or more quantitative trait loci (QTL), the cumulative responses to selection were up to 4-6% larger among DH(F2) lines than among DH lines. The cumulative responses were up to 5-8% larger among RI lines than among DH lines. The QTL become unlinked as the number of QTL in a finite genome decreases, and the responses among RI, DH, and DH(F2) lines were equal or nearly equal when only 20 QTL controlled the trait. Metabolic-flux epistasis reduced the differences in the response among RI, DH, and DH(F2) lines. Overall, the results indicated that doubled haploids should be induced from F(2) plants rather than from F(1) plants. If year-round nurseries are used and new F(1) crosses for inbred development are initially created on a speculative basis, the development of doubled haploids from F(2) rather than F(1) plants should not cause a delay in inbred development.