Matched pairs in factorial experiments with binary data

Two more models are proposed for the analysis of matched pairs in factorial experiments with binary data. They are applied to two-period crossover designs. Estimation and test procedures are derived both approximately and by maximizing likelihoods. Comparisons are made with previous methods of analysis and between the models proposed.     

Optimum prediction of three-way crosses from single crosses in forage maize (Zea mays L.)

Summary Three-way cross means were predicted with formulae involving linear functions of general (GCA) and specific combining ability (SCA) effects estimated from single-cross factorials between genetically divergent populations. Data from an experiment with 66 single-cross and 66 three-way cross forage maize (Zea mays L.) hybrids was used for comparing the prediction formulae. The genotypic correlation (r) between observed and predicted three-way crosses increased with increasing , the weighting factor of SCA effects, for plant height and ear dry matter (DM) content. It displayed slightly convex curves for total and stover DM yield, ear percentage, and metabolizable energy content of stover. For Jenkins' method B, r was considerably less than 1.0 for all traits, indicating the presence of epistasis. The square root of heritability (h) of the predicted means decreased with increasing , the reduction being small with a greater number of test environments. Using the product r·h as a criterion of efficiency, none of the prediction methods was consistently superior and the differences among them were rather small (< 7.5%) for all traits, irrespective of the number of test environments. We recommend evaluating the GCA of a greater number of lines from each parent population in testcrosses with a small number of elite lines from the opposite population. All possible three-way or double crosses between both sets of lines should be predicted by Jenkins's method C. This procedure allows one to select with a higher intensity among the predicted hybrids and thus should increase the genetic gain.Extended version of a paper (Geiger et al. 1986) read at the sixth meeting of the EUCARPIA Section Biometrics in Plant Breeding held at Birmingham, UK, July 28–August 1, 1986     

Support vector machine regression for the prediction of maize hybrid performance

Accurate prediction of the phenotypical performance of untested single-cross hybrids allows for a faster genetic progress of the breeding pool at a reduced cost. We propose a prediction method based on ɛ-insensitive support vector machine regression (ɛ-SVR). A brief overview of the theoretical background of this fairly new technique and the use of specific kernel functions based on commonly applied genetic similarity measures for dominant and co-dominant markers are presented. These different marker types can be integrated into a single regression model by means of simple kernel operations. Field trial data from the grain maize breeding programme of the private company RAGT R2n are used to assess the predictive capabilities of the proposed methodology. Prediction accuracies are compared to those of one of today’s best performing prediction methods based on best linear unbiased prediction. Results on our data indicate that both methods match each other’s prediction accuracies for several combinations of marker types and traits. The ɛ-SVR framework, however, allows for a greater flexibility in combining different kinds of predictor variables.     

Genomic prediction of hybrid performance in maize with models incorporating dominance and population specific marker effects

Identifying high performing hybrids is an essential part of every maize breeding program. Genomic prediction of maize hybrid performance allows to identify promising hybrids, when they themselves or other hybrids produced from their parents were not tested in field trials. Using simulations, we investigated the effects of marker density (10, 1, 0.3 marker per mega base pair, Mbp(-1)), convergent or divergent parental populations, number of parents tested in other combinations (2, 1, 0), genetic model (including population-specific and/or dominance marker effects or not), and estimation method (GBLUP or BayesB) on the prediction accuracy. We based our simulations on marker genotypes of Central European flint and dent inbred lines from an ongoing maize breeding program. To simulate convergent or divergent parent populations, we generated phenotypes by assigning QTL to markers with similar or very different allele frequencies in both pools, respectively. Prediction accuracies increased with marker density and number of parents tested and were higher under divergent compared with convergent parental populations. Modeling marker effects as population-specific slightly improved prediction accuracy under lower marker densities (1 and 0.3?Mbp(-1)). This indicated that modeling marker effects as population-specific will be most beneficial under low linkage disequilibrium. Incorporating dominance effects improved prediction accuracies considerably for convergent parent populations, where dominance results in major contributions of SCA effects to the genetic variance among inter-population hybrids. While the general trends regarding the effects of the aforementioned influence factors on prediction accuracy were similar for GBLUP and BayesB, the latter method produced significantly higher accuracies for models incorporating dominance.     

The agronomic performance of wheat doubled haploid lines derived from wheat x maize crosses

Summary The agronomic performance of 9 doubled haploid (DH) lines of Chinese Spring, 6 DH lines of Hope, 14 DH lines of the single chromosome substitution line Chinese Spring (Hope 5 A) and their respective parents was analyzed under field conditions. Seventeen Chinese Spring DH lines derived from wheat x Hordeum bulbosum crosses were also included for comparison. No significant variation was detected in either population of Chinese Spring DH lines and neither DH population differed from its parent. The Hope DH lines differed significantly for tiller biomass, spikelet number per ear, ear grain weight and 50-grain weight. However, all the variation could be attributed to the poor performance of only one line. Chinese Spring (Hope 5 A) DH lines showed significant variation for ear emergence time, but this was probably due to genetic heterogeneity in the parental stock. Overall, the results suggest that most DH lines produced by the wheat x maize method resemble their wheat parent, and that the variation induced in DH production is likely to be similar to that found in DHs from wheat x Hordeum bulbosum crosses.     

Meta-analysis of untargeted metabolomic data from multiple profiling experiments

metaXCMS is a software program for the analysis of liquid chromatography/mass spectrometry-based untargeted metabolomic data. It is designed to identify the differences between metabolic profiles across multiple sample groups (e.g., 'healthy' versus 'active disease' versus 'inactive disease'). Although performing pairwise comparisons alone can provide physiologically relevant data, these experiments often result in hundreds of differences, and comparison with additional biologically meaningful sample groups can allow for substantial data reduction. By performing second-order (meta-) analysis, metaXCMS facilitates the prioritization of interesting metabolite features from large untargeted metabolomic data sets before the rate-limiting step of structural identification. Here we provide a detailed step-by-step protocol for going from raw mass spectrometry data to metaXCMS results, visualized as Venn diagrams and exported Microsoft Excel spreadsheets. There is no upper limit to the number of sample groups or individual samples that can be compared with the software, and data from most commercial mass spectrometers are supported. The speed of the analysis depends on computational resources and data volume, but will generally be less than 1 d for most users. metaXCMS is freely available at http://metlin.scripps.edu/metaxcms/.     

中国17个优良玉米自交系的分子标记杂合性及其与杂交种性状的关系研究

在玉米单交种育种中 ,鉴定高产杂交种和具有优良特性的自交系是一个重要的问题。研究以 1 7个优良玉米自交系为亲本 ,按照双列杂交配组合 ,利用 RAPD技术分析了 1 7个自交系的多态性以及 RAPD标记与 9个重要农艺性状 (包括产量 )的关系。基于 RAPD标记计算的相似系数聚类将 1 7个自交系分为 5个类群 ,经分析与系谱亲缘关系基本一致。杂交种性状及其特殊配合力与亲本间的遗传距离是高度相关的 ,与聚类前比较 ,聚类后平均遗传距离与平均产量、平均特殊配合力的相关系数显著提高 ,类间平均产量高于类内平均产量。RAPD技术可揭示优良玉米自交系的系谱亲缘关系 ,将自交系划分成不同的类群 ,从而为选择类间自交系杂交 ,进行亲本选配和分子标记辅助育种提供一种方法。     

Prediction of single-cross hybrid performance in maize using haplotype blocks associated with QTL for grain yield

Marker-based prediction of hybrid performance facilitates the identification of untested single-cross hybrids with superior yield performance. Our objectives were to (1) determine the haplotype block structure of experimental germplasm from a hybrid maize breeding program, (2) develop models for hybrid performance prediction based on haplotype blocks, and (3) compare hybrid performance prediction based on haplotype blocks with other approaches, based on single AFLP markers or general combining ability (GCA), under a validation scenario relevant for practical breeding. In total, 270 hybrids were evaluated for grain yield in four Dent × Flint factorial mating experiments. Their parental inbred lines were genotyped with 20 AFLP primer–enzyme combinations. Adjacent marker loci were combined into haplotype blocks. Hybrid performance was predicted on basis of single marker loci and haplotype blocks. Prediction based on variable haplotype block length resulted in an improved prediction of hybrid performance compared with the use of single AFLP markers. Estimates of prediction efficiency (R ² ) ranged from 0.305 to 0.889 for marker-based prediction and from 0.465 to 0.898 for GCA-based prediction. For inter-group hybrids with predominance of general over specific combining ability, the hybrid prediction from GCA effects was efficient in identifying promising hybrids. Considering the advantage of haplotype block approaches over single marker approaches for the prediction of inter-group hybrids, we see a high potential to substantially improve the efficiency of hybrid breeding programs. Tobias A. Schrag and Hans Peter Maurer contributed equally to this work.     

Comparison of parameters from rhythmometric models with multiple components on hybrid data

Population multiple components is a statistical tool useful for the analysis of time-dependent hybrid data. With a small number of parameters, it is possible to model and to predict the periodic behavior of a population. In this article, we propose two methods to compare among populations rhythmometric parameters obtained by multiple component analysis. The first is a parametric method based in the usual statistical techniques for comparison of mean vectors in multivariate normal populations. The method, through MANOVA analysis, allows comparison of the MESOR and amplitude-acrophase pair of each component among two or more populations. The second is a nonparametric method, based in bootstrap techniques, to compare parameters from two populations. This test allows one to compare the MESOR, the amplitude, and the acrophase of each fitted component, as well as the global amplitude, orthophase, and bathyphase estimated when all fitted components are harmonics of a fundamental period. The idea is to calculate a confidence interval for the difference of the parameters of interest. If this interval does not contain zero, it can be concluded that the parameters from the two models are different with high probability. An estimation of p-value for the corresponding test can also be calculated. Both methods are illustrated with an example, based on clinical data. The nonparametric test can also be applied to paired data, a special situation of great interest in practice. By the use of similar bootstrap techniques, we illustrate how to construct confidence intervals for any rhythmometric parameter estimated from population multiple components models, including the orthophase, bathyphase, and global amplitude. These tests for comparison of parameters among populations are a needed tool when modeling the nonsinusoidal rhythmic behavior of hybrid data by population multiple component analysis.     

Analysis of data from experiments using double labeling

Frequently as a result of experiments in which two isotopes are used one is left with a sequence of samples, the ratio of labeling in each sample, and the problem of analyzing the ratios. Suppose that the experiments are designed so that one expects uniform labeling except for one or two special groups of samples. The problem, then, is to find these groups. Because of the variability in the count rate from sample to sample, the variance of the ratios differs from sample to sample making statistical analysis difficult. Furthermore, there is significant serial correlation in the sample disintegrations per minute for each of the isotopes. We have found that the serial correlation in the labeling ratio is small and of questionable significance in controls but becomes significant when there is a subsequence of samples in which the labeling ratio differs from that in the remainder of the gel. We examine the analysis of variance as a test for significant deviations in the labeling ratio and suggest a method for plotting deviations of labeling ratio from the average background labeling ratio. Finally, we develop a method of estimating the mean labeling ratio from the regression of disintegrations per minute of one isotope on those of the other isotope. This provides another way of plotting deviations in labeling ratio in terms of the residuals around the line of regression.     

Prediction of maize single-cross hybrid performance: support vector machine regression versus best linear prediction

Accurate prediction of the phenotypic performance of a hybrid plant based on the molecular fingerprints of its parents should lead to a more cost-effective breeding programme as it allows to reduce the number of expensive field evaluations. The construction of a reliable prediction model requires a representative sample of hybrids for which both molecular and phenotypic information are accessible. This phenotypic information is usually readily available as typical breeding programmes test numerous new hybrids in multi-location field trials on a yearly basis. Earlier studies indicated that a linear mixed model analysis of this typically unbalanced phenotypic data allows to construct ɛ-insensitive support vector machine regression and best linear prediction models for predicting the performance of single-cross maize hybrids. We compare these prediction methods using different subsets of the phenotypic and marker data of a commercial maize breeding programme and evaluate the resulting prediction accuracies by means of a specifically designed field experiment. This balanced field trial allows to assess the reliability of the cross-validation prediction accuracies reported here and in earlier studies. The limits of the predictive capabilities of both prediction methods are further examined by reducing the number of training hybrids and the size of the molecular fingerprints. The results indicate a considerable discrepancy between prediction accuracies obtained by cross-validation procedures and those obtained by correlating the predictions with the results of a validation field trial. The prediction accuracy of best linear prediction was less sensitive to a reduction of the number of training examples compared with that of support vector machine regression. The latter was, however, better at predicting hybrid performance when the size of the molecular fingerprints was reduced, especially if the initial set of markers had a low information content.     

Prediction of maize hybrid performance using similarity in state and similarity by descent information

We evaluated the efficiency of the best linear unbiased predictor (BLUP) and the influence of the use of similarity in state (SIS) and similarity by descent (SBD) in the prediction of untested maize hybrids. Nine inbred lines of maize were crossed using a randomized complete diallel method. These materials were genotyped with 48 microsatellite markers (SSR) associated with the QTL regions for grain yield. Estimates of four coefficients of SIS and four coefficients of SBD were used to construct the additive genetic and dominance matrices, which were later used in combination with the BLUP for predicting genotypic values and specific combining ability (SCA) in unanalyzed hybrids under simulated unbalance. The values of correlations between the genotypic values predicted and the means observed, depending on the degree of unbalance, ranged from 0.48 to 0.99 for SIS and 0.40 to 0.99 using information from SBD. The results obtained for the SCA ranged from 0.26 to 0.98 using the SIS and 0.001 to 0.990 using the SBD information. It was also observed that the predictions using SBD showed less biased than SIS predictions demonstrating that the predictions obtained by these coefficients (SBD) were closer to the observed value, but were less efficient in the ranking of genotypes. Although the SIS showed a bias due to overestimation of relatedness, this type of coefficient may be used where low values are detected in the SBD in the group of parents because of its greater efficiency in ranking the candidates hybrids.     

Transformations of count data for tests of interaction in factorial and split-plot experiments

In applied entomological experiments, when the response is a count-type variable, certain transformation remedies such as the square root, logarithm (log), or rank transformation are often used to normalize data before analysis of variance. In this study, we examine the usefulness of these transformations by reanalyzing field-collected data from a split-plot experiment and by performing a more comprehensive simulation study of factorial and split-plot experiments. For field-collected data, significant interactions were dependent upon the type of transformation. For the simulation study, Poisson distributed errors were used for a 2 by 2 factorial arrangement, in both randomized complete block and split-plot settings. Various sizes of main effects were induced, and type I error rates and powers of the tests for interaction were examined for the raw response values, log-, square root-, and rank-transformed responses. The aligned rank transformation also was investigated because it has been shown to perform well in testing interactions in factorial arrangements. We found that for testing interactions, the untransformed response and the aligned rank response performed best (preserved nominal type I error rates), whereas the other transformations had inflated error rates when main effects were present. No evaluations of the tests for main effects or simple effects have been conducted. Potentially these transformations will still be necessary when performing these tests.     

Bayesian analysis of genetic architecture of quantitative trait using data of crosses of multiple inbred lines

Using the data of crosses of multiple of inbred lines for mapping QTL can increase QTL detecting power compared with only cross of two inbred lines. Although many fixed-effect model methods have been proposed to analyze such data, they are largely based on one-QTL model or main effect model, and the interaction effects between QTL are always neglected. However, effectively separating the interaction effects from the residual error can increase the statistical power. In this article, we both extended the novel Bayesian model selection method and Bayesian shrinkage estimation approaches to multiple inbred line crosses. With two extensions, interacting QTL are effectively detected with high solution; in addition, the posterior variances for both main effects and interaction effects are also subjected to full Bayesian estimate, which is more optimal than two step approach involved in maximum-likelihood. A series of simulation experiments have been conducted to demonstrate the performance of the methods. The computer program written in FORTRAN language is freely available on request.     

Genome-based prediction of maize hybrid performance across genetic groups,testers, locations,and years

Key message

The calibration data for genomic prediction should represent the full genetic spectrum of a breeding program. Data heterogeneity is minimized by connecting data sources through highly related test units.

Abstract

One of the major challenges of genome-enabled prediction in plant breeding lies in the optimum design of the population employed in model training. With highly interconnected breeding cycles staggered in time the choice of data for model training is not straightforward. We used cross-validation and independent validation to assess the performance of genome-based prediction within and across genetic groups, testers, locations, and years. The study comprised data for 1,073 and 857 doubled haploid lines evaluated as testcrosses in 2 years. Testcrosses were phenotyped for grain dry matter yield and content and genotyped with 56,110 single nucleotide polymorphism markers. Predictive abilities strongly depended on the relatedness of the doubled haploid lines from the estimation set with those on which prediction accuracy was assessed. For scenarios with strong population heterogeneity it was advantageous to perform predictions within a priori defined genetic groups until higher connectivity through related test units was achieved. Differences between group means had a strong effect on predictive abilities obtained with both cross-validation and independent validation. Predictive abilities across subsequent cycles of selection and years were only slightly reduced compared to predictive abilities obtained with cross-validation within the same year. We conclude that the optimum data set for model training in genome-enabled prediction should represent the full genetic and environmental spectrum of the respective breeding program. Data heterogeneity can be reduced by experimental designs that maximize the connectivity between data sources by common or highly related test units.     

Comparisons of DNA marker-based genetic diversity with phenotypic estimates in maize grown in Pakistan

We compared DNA-based genetic diversity estimates with conventional estimates by investigating agronomically important traits in maize grown in the northwestern region of Pakistan. RAPD markers were used to characterize 10 commonly cultivated maize genotypes. The same material was tested for phenotypic variation of quantitative traits using replicated field trials. The genetic distances between pairs of genotypes using RAPD data were used to generate a similarity matrix and to construct a phenogram. Statistical analyses were carried out on the data obtained from field trials of all maize genotypes for days to 50% tasseling, days to 50% silking, plant height, ear height, grain yield, grain weight per cob, and ear length. Analysis of variance and single degree of freedom contrasts were performed on morphological data to examine the relationship between molecular-based clusters and agronomic traits. A molecular marker-based phenogram led to the grouping of all genotypes into four major clusters, some of which were distantly related. These clusters contained one to four genotypes. Analysis of variance showed significant variations among all genotypes for agronomic traits. The single degree of freedom contrasts between groups of genotypes indicated significant differences for most traits. Pair-wise comparisons between clusters were also significant. The two types of data correlated well, providing an opportunity for better choices for selection.     

Genetic analysis of Verticillium wilt tolerance in cotton using pedigree data from three crosses

Summary Three crosses and descendant generations were used in a field study of the inheritance of tolerance to Verticillium wilt, caused by Verticillium dahliae Kleb., in upland cotton (Gossypium hirsutum L.). The tolerant cultivar Acala SJC-1 was crossed to more susceptible parents, breeding line S5971 and cultivars Acala 4-42 and Deltapine 70. Seven generations were evaluated for each cross: the two parents (P₁ and P₂), F₁; F₂, F₃, and reciprocal backcrosses (B₁ and B₂). The genetic control of tolerance in these crosses appears to involve more than one gene, based on an unsatisfactory fit to expected phenotypic distributions for the generations under a single-locus model. An analysis of generation means indicated that pooled additive and pooled dominance effects over loci were adequate to explain the variation among generations for crosses of SJC-1 X S5971 and SJC-1 X DPL70. Tolerance in these crosses appeared to be controlled by recessive factors. For the SJC-1 X 4-42 cross, an adequate fit to a digenic epistatic model was not possible, and none of the genetic parameters except the F₂ mean were significant. Heritabilities for tolerance to Verticillium wilt, determined from regressions of F₃ progeny on F₂ parents for the crosses of SJC-1 X S5971 and SJC-1 X DPL70, ranged from 0.12 to 0.28. Therefore, individual plant selection for improved tolerance is expected to be inefficient.Contribution from the Department of Botany and Plant Sciences, University of California, Riverside, CA 92521, USA, to be included in a dissertation by the senior author in partial fulfillment of the Ph. D. degree