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We used chessboard-like experimental series I, II, and III and random fivefold cross-validations experimental series IV, V, and VI to evaluate the prediction ability of genomic prediction within experimental series fig. They tend to privilege people of their own group, lineage or family.

The lines were divided into 13 to 18 individual trials connected through five to six common checks.

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But even online, Prostitutes Leopoldshohe penetrates to have an dating. This was also observed when inspecting the results across experimental series: hybrids 9. Because each of the parents in experimental series I, II, and III was tested in several hybrid combinations, we investigated the ability to predict hybrid grain yield performance using a genomic-based unbiased prediction model incorporating Prostitutes Leopoldshohe additive Prostitutes Leopoldshohe dominance genomic relationships and a chessboard-like cross-validation with three different level of relatedness: T 2T 1and T 0 fig.

The Prostitutes Leopoldshohe in test set T 2Prostitutes Leopoldshohe included only hybrids originating from the same group of parents as the hybrids in the training set, showed the highest prediction ability of 0.

Prostitutes Leopoldshohe value decreased to 0. Thus, the decreasing trend in prediction ability reflected the diminishing relatedness from the T 2 to the T 0 scenario.

Using the combined phenotypic data, we selected a genotype that was common in at least one of the pairs of experimental sets described above I versus II—V and VI versus II—V and coded it differently in the two sets.

The declines in prediction ability observed Prostitutes Leopoldshohe our wheat experiments were more pronounced than in maize This can be explained by a lower effective population size for a single maize breeding program compared with the diversity panels sampled across multiple wheat breeding programs in our Prostitutes Leopoldshohe. A Prediction ability within experimental series Exp. B Prediction abilities across different experimental series. For each of the training populations shown on the x axis, the prediction abilities for the different test populations are displayed as colored bars.

C Increase in prediction ability combining incremental data across experimental series. The lengths of Prostitutes Leopoldshohe colored boxes in each bar represent the proportions of the genotypes of the different experimental series used as training sets. D Prostitutes Leopoldshohe population size within and across the experimental series.

The different experimental series Prostitutes Leopoldshohe color coded according to the key in A. The topcross mating design of experimental series IV with only four tester lines fig. S3 and of experimental series V with an average of two tester lines Prostitutes Leopoldshohe. S4 prevented chessboard-like cross-validation, and we, therefore, applied random fivefold cross-validation fig. The prediction ability was 0. This, as expected, corresponds to the values observed for the T Prostitutes Leopoldshohe scenario in experimental series I, II, and III and Prostitutes Leopoldshohe again that within—experimental series relatedness is the driving force of the prediction ability for hybrid grain yield in our study.

Experimental series VI was the most comprehensive series in our study, with lines being genotyped and phenotyped table S2. It represented grain Prostitutes Leopoldshohe data from a commercial line breeding program. The fivefold cross-validation showed a high prediction ability of 0.

Thus, the prediction ability in experimental series I, II, and III might have Prostitutes Leopoldshohe suppressed due to range restriction, a phenomenon that the correlation is reduced when the sample has a restricted range of scores In addition, the degrees of freedom to estimate the additive effects of SNPs in the inbred population depend on the number of lines, but in the case of hybrids, on the number of parents.

Thus, the increased degrees of freedom allowed a more precise estimation of the additive effects to predict grain yields in experimental series VI compared with the other series. This, together, explains why the prediction ability of 0. This decrease cannot be explained by an Prostitutes Leopoldshohe genetic distance between the parental lines of experimental series I, II, III, and IV compared with the distance of the T 0 scenarios within experimental series Prostitutes Leopoldshohe S5 and fig.

The prediction Prostitutes Leopoldshohe from one experimental Prostitutes Leopoldshohe to another varied Prostitutes Leopoldshohe fold 0. In several instances, values for the prediction abilities across experimental series outperformed the mean value of 0.

Instead, the lower prediction Prostitutes Leopoldshohe across two experimental series table S6 and Fig. To assess this in more detail, only experimental series II Prostitutes Leopoldshohe used as training set to predict the performance of previously untested hybrids that had both parental lines in common with experimental series II T 2 Prostitutes Leopoldshohe.

These hybrids were phenotyped in a separate validation experiment for grain yield in eight environments, which Prostitutes Leopoldshohe not been used for experimental series II. The prediction ability for these previously untested T 2 hybrids tested in a Prostitutes Leopoldshohe set of environments reached only 0.

S7whereas within experimental series II, a prediction ability of 0. This demonstrates the pronounced impact of interaction between genotypes and experimental series on the prediction ability. By using experimental series VI as the training population and the remaining experimental series as test populations, the prediction ability for the parental lines 0. The use of a comprehensive population of inbred lines as training set, as experimental series VI, cannot account for the general heterosis effect observed in hybrids Fig.

Nonetheless, the highest average prediction ability Prostitutes Leopoldshohe hybrid performance from one experiment to another was observed using the comprehensive line training data 0. This finding illustrates the potential to increase the predictive power for hybrids by exploiting the precision of estimating additive effects in the large population of inbred lines.

One of the important tasks in hybrid wheat breeding is to predict for new environments the single-cross performance of parental lines that have not yet been evaluated in other hybrids. Despite the large number of hybrids evaluated in each experimental series in our study table S2Prostitutes Leopoldshohe average prediction ability was low 0.

We assessed the relevance of N : N e in more detail by randomly sampling subpopulations out of experimental series VI Prostitutes Leopoldshohe a range of N : N e from 2 Prostitutes Leopoldshohe 60 Fig.

We used a nonlinear regression based on data from experimental series VI, estimated relevant parameters, and extrapolated the prediction abilities for N from to 20, and N e from 2 to Fig. The trend not only highlights the potential to increase substantially the prediction ability by accumulating Prostitutes Leopoldshohe data but also shows the limit determined by the heritability of the phenotypic data of the training population.

The latter represents a major obstacle, as plant breeding programs use multistage selection: In the first stages, a large number of individuals are phenotyped in few environments to maximize the selection intensity, and only in the last stage are a small number of individuals evaluated in a large number of environments to maximize heritability.

Thus, to assemble a large training population that has been intensively phenotyped, data must be collected across years or even across breeding programs. B Association between observed and estimated prediction accuracies in subsamples drawn randomly out of experimental series VI.

C Projection of prediction ability for population size N from to 20, and N e from 2 to Prostitutes Leopoldshohe the red line corresponds to the square root of heritability, which represents the upper limit of the prediction ability. We further studied whether marker density is a major limiting factor for the prediction ability by resampling subsets of markers in the entire dataset comprising experimental series I to VI.

The Prostitutes Leopoldshohe density, therefore, is not Prostitutes Leopoldshohe major limiting factor in our Prostitutes Leopoldshohe. In summary, the compilation and integration of comprehensive datasets for the training of models for hybrid prediction not only have the potential to improve out-of-sample hybrid prediction ability but also challenge current breeding practices.

The characteristics of big data differ between crop and animal breeding in comparison to human genetics.

Unlocking big data doubled the accuracy in predicting the grain yield in hybrid wheat

In crop and Prostitutes Leopoldshohe breeding, heritability can be increased by massive phenotyping of progenies 3031the effective Prostitutes Leopoldshohe sizes are much smaller compared with human genetics 2032and genetic variance among offspring is the key source exploited in selection programs 8.

In human genetics, on the other hand, the heritability of a particular trait often depends on nonrepeated observations and can hardly be influenced by the experimenter, populations with large effective size and unrelated individuals Prostitutes Leopoldshohe often used, while genetic variance within families is considered as noise 8 The latter assumption is now also relevant for crop breeding when recurrent speed-breeding programs with several selection cycles per year are implemented, resulting in a decrease in relatedness between training and test populations Recent results in not only human genetics but also animal breeding 8 have shown that big data lead to a substantial reduction in the gap between trait heritability and the genotypic variance, which can be explained with a Prostitutes Leopoldshohe predictor.

The prediction abilities that were achieved in our study exceeded those expected based on studies simulating individual breeding programs This can be explained by the higher heritability and the larger training population in our study compared with the simulation study. However, the assumed heritability in the simulation study is based on the optimal allocation of resources in multistage selection programs, and thus, much higher heritabilities in individual breeding programs are unlikely.

This suggests that it is a particular adequate strategy to combine data across individual breeding programs to fully exploit the potential of predictive plant breeding. Likewise, increasing the ratio between the number of Prostitutes Leopoldshohe tested on grain yield in hybrid backgrounds and the effective population size is a promising approach to improve the prediction ability of the hybrid performance.

In this context, incomplete factorial mating designs with balanced missing hybrid patterns, as used in experimental series II and III fig. S3Prostitutes Leopoldshohe topcross designs, as used in experimental series IV and V, are efficient and can be optimized by Prostitutes Leopoldshohe the connectivity and diversity between training and test populations Prostitutes Leopoldshohe Moreover, comprehensive line datasets such as experimental series VI can also provide valuable data for increasing the prediction abilities of Prostitutes Leopoldshohe at least in the transitional phase from line to hybrid breeding.

Reliable genome-wide prediction models based on extensive training populations allow the exploration of a large potential Prostitutes Leopoldshohe space by predicting the performance of millions of single-cross hybrids 4 — 6 For example, this is fundamental for genome-based establishment of heterotic groups Prostitutes Leopoldshohe. Moreover, genome-wide predictions can boost the selection intensity in Prostitutes Leopoldshohe breeding and, thus, the selection Prostitutes Leopoldshohe 5.

We have illustrated the latter point by predicting the grain yield of all 10, potential single hybrids of the lines of experimental series I to V fig.

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In total, untested single-cross hybrids had a predicted yield higher than that of the best predicted parental line. The best predicted hybrid not tested to Prostitutes Leopoldshohe is expected to exceed with The era of genome-wide selection using big data could further benefit from a revision of the genetic 635 as well as experimental designs of Prostitutes Leopoldshohe yield trials presently in use. The current medium-sized datasets in plant breeding often reflect sequential experimental phenotyping series that lead to a block experiment —wise missing value structure in the integrated Prostitutes Leopoldshohe dataset: A subset of genotypes is evaluated in Prostitutes Leopoldshohe subset of environments with a small number of overlapping entries table S3.

The latter allow Prostitutes Leopoldshohe estimation of the main effects of the environments but do not allow separation of the genotype main effects Prostitutes Leopoldshohe the interaction effects between genotype and environmental series for those genotypes, which have not been evaluated across series. A key challenge in further improving Prostitutes Leopoldshohe ability is, therefore, to reduce the influence of interaction effects between genotypes and experimental series.

The pronounced interaction effects between genotypes and experimental series are Prostitutes Leopoldshohe likely the result of a reduced representation of the environmental diversity in the different experimental series during phenotyping.

On the basis of data of experimental series II, a simple approach to increase the environmental diversity while keeping the number of plots in a very similar range is shown Fig. As a baseline, we randomly sampled grain yield data of all lines and hybrids for 3 of the Prostitutes Leopoldshohe environments, corresponding to plots, and estimated the correlation between grain yield estimates for the data of the subsets and the total 12 environments Fig.

Reducing the variation of correlations at a comparable mean value to the base line model is, however, possible by dividing the lines and hybrids into 10 subgroups, each of which is tested in only three environments, with the restriction that two environments overlap with those of the next Prostitutes Leopoldshohe.

All environments are linked with 11 check varieties, giving a total of plots Fig. Further improvement may be possible by selecting the subgroups of hybrids in such a way that a close relationship T 2 scenario between the different subgroups is ensured, and this relationship is taken into account in the phenotypic data analyses.

Alternatively, innovations in phenotyping can be used to identify environmental drivers for interaction effects between genotypes and environments The information on the environmental drivers can then be integrated as covariables Prostitutes Leopoldshohe the statistical analyses to obtain more accurate estimates of Prostitutes Leopoldshohe genotype main effects, thus reducing the estimation bias caused by interaction effects between genotypes and experimental series 38 Prostitutes Leopoldshohe summary, an optimized design of multienvironment yield trials in the era of genomic selection coupled with innovations in an integrated analysis of field trials promises to increase the accuracy of predictive plant breeding based on big data.

A In scenario I, all lines and hybrids are tested in a subset of three environments Env. C In scenario Prostitutes Leopoldshohe, the lines Prostitutes Leopoldshohe hybrids are divided into 10 subgroups, each of which is tested in only three environments, with the restriction that two environments overlap with those of the next group. All 12 environments are linked with 11 check varieties yellow color.

The study includes plant material and phenotypic data Prostitutes Leopoldshohe six experimental series. Experimental series I was Prostitutes Leopoldshohe on elite winter bread Prostitutes Leopoldshohe lines and their single-cross hybrid progenies.

Details of the plant material and phenotypic data have been published in a previous study 6. Parental lines have been Prostitutes Leopoldshohe to reflect a wide range of the diversity that exists in Central Europe.

The lines were divided into a female pool of lines and a male pool of 15 lines, depending on pollination capacity, plant height, and flowering time. A factorial mating design was used to produce single-cross hybrids fig. In each environment, the experimental design consisted of three trials. Prostitutes Leopoldshohe each trial, a partially replicated Prostitutes Leopoldshohe lattice design was used.

Different genotypes were Prostitutes Leopoldshohe in different trials linked by 10 common checks. Plot sizes ranged from 5 to 7. Experimental series II was based on elite winter bread wheat lines and their single-cross hybrid progenies.

Details of the plant material and phenotypic data have been published in a previous study Briefly, parental lines have been chosen Prostitutes Leopoldshohe reflect a wide range of the diversity that exists in Central Europe.

The Prostitutes Leopoldshohe were divided into a female pool of lines and a male pool of 41 lines, depending on pollination capacity, plant height, and flowering time. In each trial, an unreplicated alpha lattice design was used. Different genotypes were evaluated in different trials linked by the 11 common checks.

Plot sizes ranged from 5. Experimental series III was based on elite winter bread wheat lines and their single-cross hybrid progenies. The lines Prostitutes Leopoldshohe divided into Prostitutes Leopoldshohe female pool of lines and a male pool of 40 lines, depending on pollination capability, plant height, and flowering time.

Experiment IV was based on elite winter bread wheat lines and their single-cross hybrid progenies.

The lines were divided Prostitutes Leopoldshohe a female pool of 8 lines and a Prostitutes Leopoldshohe pool of lines, depending on pollination capability, plant height, and flowering time. The parental lines and hybrids were split into two series linked by 16 common checks.

An unreplicated alpha lattice design was used. Experimental series V included hybrids between elite lines and historic varieties or accessions obtained from the gene bank of the IPK Gatersleben. Six hundred sixty-seven hybrids were produced by crossing 45 elite winter bread wheat lines adapted to the growing conditions of Central Europe Prostitutes Leopoldshohe diverse accessions.

Here, the elite lines were used as females in hybrid seed production. The accessions were used as male parents and were selected by screening a sample of gene bank accessions from the gene bank of IPK Gatersleben for pronounced Prostitutes Leopoldshohe extrusion.

In addition, hybrids were produced by crossing historic varieties with plants originating from four different seed mixtures, each including either two or three elite male lines fig. Elite lines with good anther extrusion but which showed different flowering times were combined in the four mixtures and used as male crossing partners to optimize the hybrid seed production by an almost perfect match of flowering time between male and female lines Prostitutes Leopoldshohe to guarantee the unambiguous identification of hybrids.

The historic varieties originated from all over Europe from the past four decades and were characterized by a short plant height. Trials 1, 2, and 3 included, and entries evaluated in the years, andrespectively. Plot sizes ranged from 6 to 9 m 2. Part of the phenotypic data of the lines evaluated in it have been published in a previous study Briefly, the lines were evaluated in the years,and for grain yield in up to 10 sites in Germany.

Prostitutes Leopoldshohe lines were divided into 13 to 18 individual trials connected through five to six common checks. The experimental design for each trial followed an alpha design with one to Prostitutes Leopoldshohe replications per site, with the number of entries per trial ranging from 30 to Plot size ranged from 6.

A linear mixed model was used including the Prostitutes Leopoldshohe of genotypes, trials, replications nested within trials, and blocks nested within Prostitutes Leopoldshohe and replications. All data were screened for outliers fig. Outliers were removed, and best linear unbiased estimations BLUEs of the genotypes in each environment were obtained as outlined in detail elsewhere Prostitutes Leopoldshohe and served as the Prostitutes Leopoldshohe for the subsequent analyses.

All linear mixed models were implemented using the software ASReml-R 3. The genomic profiles of lines were determined using 15, or 90, SNP arrays based on an Illumina Infinium assay The number of markers in each experimental series ranged from 11, to 81, To reduce the risk of a high proportion of missing values in the integrated data, we used only common SNP markers across all six experiments.

After imputation, we removed the monomorphic markers, and the remaining 10, SNP markers were Prostitutes Leopoldshohe for subsequent analyses. Marker profiles of the hybrids were deduced from the corresponding parental Prostitutes Leopoldshohe. LD between all pairs of SNP markers within each chromosome was calculated as the squared Pearson correlation coefficient r 2 between vectors of SNP alleles using the lines.

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The persistence of linkage phase between the experiments was inferred by analyzing how similar or dissimilar the correlations between pairs of markers were following the approach suggested previously The squared correlation between r values of two different experiments was defined as LD phase and plotted against Prostitutes Leopoldshohe physical map distance to fit natural smoothing splines. A two-step procedure was applied to analyze the grain yield data across environments In the first step, the data for each environment were analyzed separately.

BLUEs of the genotypes in each environment were Prostitutes Leopoldshohe and served Prostitutes Leopoldshohe the input of the second step, where a linear mixed model was applied including the effects of Prostitutes Leopoldshohe and genotypes.

Fixed genotypic effects were assumed to obtain the BLUEs of the genotypic values of the Prostitutes Leopoldshohe and their parents. Within each experimental series, broad-sense heritability was calculated with a one-step model.

For each experimental series, a submodel of the following general model was applied, and only those factors relevant to the experimental design and the population used in a certain experimental series were retained. The Prostitutes Leopoldshohe terms were genotype-by-environment interaction effects. For integrated analysis across experimental series, the broad-sense heritability was calculated on the basis of the BLUEs within each environment with model.

These included 78 groups of hybrids and Prostitutes Leopoldshohe of lines. The final genomic dataset comprised 10, unique lines and hybrids ; Prostitutes Leopoldshohe latter were derived by crossing male and female lines. This population of 10, genotypes for which 10, high-quality SNP markers had been assessed was used for the genome-wide prediction analyses.

We used a genomic best linear unbiased prediction model G-BLUP including additive and dominance effects. Details of the method can be found in Prostitutes Leopoldshohe. The above models were implemented using the R package BGLR 50 with 30, iterations, with the first iteration used as burn-in.

We used chessboard-like experimental series I, II, Prostitutes Leopoldshohe III and random fivefold cross-validations experimental series IV, V, and VI to evaluate the prediction ability of genomic prediction within experimental series fig. Basically, data were divided into two sets, a training set and a test set.

The genomic data of the Prostitutes Leopoldshohe set were used to predict the genetic values of hybrids and lines. The prediction ability for each test set was estimated as the Pearson correlation coefficient between the predictions and the observed phenotypic values. In addition, we tested the prediction ability across experimental series using different combinations of training sets. In the first scenario, we used one out of the six experimental series as training set.

Each of the other experimental series was used as test set. The prediction ability for each test set was estimated Prostitutes Leopoldshohe the Pearson correlation coefficient between the predicted and the observed hybrid performances. For the training sets, we incrementally added the experimental series except the one used as test set.

The prediction ability for each test set was estimated again as the Pearson correlation coefficient between the predicted and the observed hybrid performances. We estimated Prostitutes Leopoldshohe effective population size N e as.

The estimated prediction Prostitutes Leopoldshohe depends on the heritability of the trait and the ratio between the effective number of segments in the genome and the number of individuals in the training population From Eq. We also calculated the broad-sense heritability of each subpopulation and used Eq.

All the above analyses use software R version 3. On the basis of the data Prostitutes Leopoldshohe experimental series II, we tested in silico three scenarios of field designs, each requiring a similar number of plots. The full data of experimental series II included 11 checks, elite lines, and single-cross hybrid progenies. In scenario I, a balanced missing design was considered in which all lines and hybrids were tested in three randomly selected environments, corresponding to plots.

We analyzed all combinations of three environments and estimated the across environment BLUEs in each subset. The random sampling was run for times as in scenario I, and the average number of plots used in this scenario was In scenario III, all lines and hybrids were divided into 10 subgroups, each Prostitutes Leopoldshohe which was tested in Prostitutes Leopoldshohe three environments, with the restriction that two environments overlapped with those of the next group.

The 11 checks were tested in all environments to estimate the environmental effects, and the average number of plots used in this scenario corresponded to The Pearson correlation Prostitutes Leopoldshohe BLUEs from subsets Prostitutes Leopoldshohe scenarios I, II, and Prostitutes Leopoldshohe, and the total data including 12 environments were Prostitutes Leopoldshohe to estimate the precision of the estimates of the genotype effects.

To assess the role of Prostitutes Leopoldshohe between genotypes and experimental series, we generated previously untested T 2 hybrids that had both parental lines in common with experimental series II but were not tested Prostitutes Leopoldshohe experimental series II.

We selected the hybrids out of the 23, potential hybrids using the predicted grain yield performance and further information on producibility of single-cross hybrids, i. The yield of the other 22 hybrids is somewhere in between these two groups.

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The hybrids were phenotyped in a separate validation experiment for grain yield in eight environments in Germany in the year We estimated the BLUEs as outlined above and studied their correlation with the predicted hybrid performance using data from experimental series II. We used the complete dataset and Prostitutes Leopoldshohe ridge regression BLUP model with additive and dominance marker effects to predict the hybrid performance of all potential single-cross hybrids between the inbred lines.

The model is as follows. The elements of Z D are 0 and 1, while the two homozygote classes are coded as Prostitutes Leopoldshohe, and Prostitutes Leopoldshohe heterozygotes are coded as 1. We thank GFPi and proWeizen for project coordination.

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Author contributions: J. Competing interests: The authors declare that they Prostitutes Leopoldshohe no competing interests. Requests for the data of the experimental series VI should be submitted to Patrick Thorwarth moc. National Center for Biotechnology InformationU. Journal List Sci Adv v. Sci Adv. Published online Jun Schulthess1 Mario Gils4 Philipp Prostitutes Leopoldshohe.