Analysis of T-RFLP data using analysis of variance and ordination methods: a comparative study.

The analysis of T-RFLP data has developed considerably over the last decade, but there remains a lack of consensus about which statistical analyses offer the best means for finding trends in these data. In this study, we empirically tested and theoretically compared ten diverse T-RFLP datasets derived from soil microbial communities using the more common ordination methods in the literature: principal component analysis (PCA), nonmetric multidimensional scaling (NMS) with Sørensen, Jaccard and Euclidean distance measures, correspondence analysis (CA), detrended correspondence analysis (DCA) and a technique new to T-RFLP data analysis, the Additive Main Effects and Multiplicative Interaction (AMMI) model. Our objectives were i) to determine the distribution of variation in T-RFLP datasets using analysis of variance (ANOVA), ii) to determine the more robust and informative multivariate ordination methods for analyzing T-RFLP data, and iii) to compare the methods based on theoretical considerations. For the 10 datasets examined in this study, ANOVA revealed that the variation from Environment main effects was always small, variation from T-RFs main effects was large, and variation from T-RFxEnvironment (TxE) interactions was intermediate. Larger variation due to TxE indicated larger differences in microbial communities between environments/treatments and thus demonstrated the utility of ANOVA to provide an objective assessment of community dissimilarity. The comparison of statistical methods typically yielded similar empirical results. AMMI, T-RF-centered PCA, and DCA were the most robust methods in terms of producing ordinations that consistently reached a consensus with other methods. In datasets with high sample heterogeneity, NMS analyses with Sørensen and Jaccard distance were the most sensitive for recovery of complex gradients. The theoretical comparison showed that some methods hold distinct advantages for T-RFLP analysis, such as estimations of variation captured, realistic or minimal assumptions about the data, reduced weight placed on rare T-RFs, and uniqueness of solutions. Our results lead us to recommend that method selection be guided by T-RFLP dataset complexity and the outlined theoretical criteria. Finally, we recommend using binary or relativized peak height data with soil-based T-RFLP data for ordination-based exploratory microbial analyses.

Marker pair selection for mapping quantitative trait loci.

Mapping of quantitative trait loci (QTL) for backcross and F(2) populations may be set up as a multiple linear regression problem, where marker types are the regressor variables. It has been shown previously that flanking markers absorb all information on isolated QTL. Therefore, selection of pairs of markers flanking QTL is useful as a direct approach to QTL detection. Alternatively, selected pairs of flanking markers can be used as cofactors in composite interval mapping (CIM). Overfitting is a serious problem, especially if the number of regressor variables is large. We suggest a procedure denoted as marker pair selection (MPS) that uses model selection criteria for multiple linear regression. Markers enter the model in pairs, which reduces the number of models to be considered, thus alleviating the problem of overfitting and increasing the chances of detecting QTL. MPS entails an exhaustive search per chromosome to maximize the chance of finding the best-fitting models. A simulation study is conducted to study the merits of different model selection criteria for MPS. On the basis of our results, we recommend the Schwarz Bayesian criterion (SBC) for use in practice.

Use of AMMI and linear regression models to analyze genotype-environment interaction in durum wheat.

The joint durum wheat (Triticum turgidum L var 'durum') breeding program of the International Maize and Wheat Improvement Center (CIMMYT) and the International Center for Agricultural Research in the Dry Areas (ICARDA) for the Mediterranean region employs extensive multilocation testing. Multilocation testing produces significant genotype-environment (GE) interaction that reduces the accuracy for estimating yield and selecting appropriate germ plasm. The sum of squares (SS) of GE interaction was partitioned by linear regression techniques into joint, genotypic, and environmental regressions, and by Additive Main effects and the Multiplicative Interactions (AMMI) model into five significant Interaction Principal Component Axes (IPCA). The AMMI model was more effective in partitioning the interaction SS than the linear regression technique. The SS contained in the AMMI model was 6 times higher than the SS for all three regressions. Postdictive assessment recommended the use of the first five IPCA axes, while predictive assessment AMMI1 (main effects plus IPCA1). After elimination of random variation, AMMI1 estimates for genotypic yields within sites were more precise than unadjusted means. This increased precision was equivalent to increasing the number of replications by a factor of 3.7.

AMMI adjustment for statistical analysis of an international wheat yield trial.

Multilocation trials are important for the CIMMYT Bread Wheat Program in producing high-yielding, adapted lines for a wide range of environments. This study investigated procedures for improving predictive success of a yield trial, grouping environments and genotypes into homogeneous subsets, and determining the yield stability of 18 CIMMYT bread wheats evaluated at 25 locations. Additive Main effects and Multiplicative Interaction (AMMI) analysis gave more precise estimates of genotypic yields within locations than means across replicates. This precision facilitated formation by cluster analysis of more cohesive groups of genotypes and locations for biological interpretation of interactions than occurred with unadjusted means. Locations were clustered into two subsets for which genotypes with positive interactions manifested in high, stable yields were identified. The analyses highlighted superior selections with both broad and specific adaptation.

Full and reduced models for yield trials.

Empirical results routinely demonstrate that the reduced Additive Main effects and Multiplicative Interaction (AMMI) model achieves better predictive accuracy for yield trials than does the full treatment means model. It may seem mysterious that treatment means are not the most accurate estimates, but rather that the AMMI model is often more accurate than its data. The statistical explanation involves the Stein effect, whereby a small sacrifice in bias can produce a large gain in accuracy. The corresponding agricultural explanation is somewhat complex, beginning with a yield trial's design and ending with its research purposes and applications. In essence, AMMI selectively recovers pattern related to the treatment design in its model, while selectively relegating noise related to the experimental design in its discarded residual. For estimating the yield of a particular genotype in a particular environment, the AMMI model uses the entire yield trial, rather than only the several replications of this particular trial, as in the treatment means model. This use of more information is the source of AMMI's gain in accuracy.

Imputing missing yield trial data.

The Additive Main effects and Multiplicative Interaction (AMMI) statistical model has been demonstrated effective for understanding genotype-environment interactions in yields, estimating yields more accurately, selecting superior genotypes more reliably, and allowing more flexible and efficient experimental designs. However, AMMI had required data for every genotype and environment combination or treatment; i.e., missing data were inadmissible. The present paper addresses the problem. The Expectation-Maximization (EM) algorithm is implemented for fitting AMMI depite missing data. This missing-data version of AMMI is here termed "EM-AMMI". EM-AMMI is used to quantify the direct and indirect information in a yield trial, providing theoretical insight into the gain in accuracy observed and into the process of imputing missing data. For a given treatment, the direct yield data are the replicates of that treatment, and the indirect data are all the other yield data in the trial. EM-AMMI is used to inpute missing data for a New York soybean yield trial. Important applications arise from both unintentional and intentional missing data. Empirical measurements demonstrate good predictive success, and statistical theory attributes this success to the Stein effect.

Accuracy and selection success in yield trial analyses.

Yield trials serve research purposes of estimation and selection. Order statistics are used here to quantify the successes or problems to be expected in selection tasks commonly encountered in breeding and agronomy. Greater accuracy of yield estimates implies greater selection success. A New York soybean yield trial serves as a specific example. The Additive Main effects and Multiplicative Interaction (AMMI) statistical model is used to increase the accuracy of these soybean yield estimates, thereby increasing the probability of successfully selecting, on the basis of the empirical yield data, that genotype which has the maximum true mean. The statistical strategy for increasing accuracy is extremely cost effective relative to the alternative strategy of increasing the number of replications. Better selections increase the speed and effectiveness of breeding programs, and increase the reliability of variety recommendations. Selection tasks are frequently more difficult than may be suspected.

Predictive and postdictive success of statistical analyses of yield trials.

The accuracy of a yield trial can be increased by improved experimental techniques, more replicates, or more efficient statistical analyses. The third option involves nominal fixed costs, and is therefore very attractive. The statistical analysis recommended here combines the Additive main effects and multiplicative interaction (AMMI) model with a predictive assessment of accuracy. AMMI begins with the usual analysis of variance (ANOVA) to compute genotype and environment additive effects. It then applies principal components analysis (PCA) to analyze non-additive interaction effects. Tests with a New York soybean yield trial show that the predictive accuracy of AMMI with only two replicates is equal to the predictive accuracy of means based on five replicates. The effectiveness of AMMI increases with the size of the yield trial and with the noisiness of the data. Statistical analysis of yield trials with the AMMI model has a number of promising implications for agronomy and plant breeding research programs.

Effect of zinc on translocation of iron in soybean plants.

Zinc interfered with translocation of iron from roots to above ground parts of Glycine max. (L.) Merrill var. Hawkeye. During periods in which zinc impeded iron translocation, it also suppressed the production of reductant by roots. Addition of iron, as a ferric metal chelate (iron ethylenediaminedihydroxyphenylacetic acid), to the growth medium overcame the interference of zinc. In the root epidermis, potassium ferricyanide formed a precipitate (Prussian blue) with ferrous iron derived from the previously supplied iron ethylenediaminedihydroxyphenylacetic acid. The reduction of ferric iron was suppressed by zinc.

Nonessentiality of boron in fungi and the nature of its toxicity.

AN INVESTIGATION WAS UNDERTAKEN TO DETERMINE WHETHER ANY OF THE FOLLOWING FUNGI HAD A REQUIREMENT FOR BORON (B): Saccharomyces cerevisiae, Aspergillus niger, Neurospora crassa, and Penicillium chrysogenum. Boron was unessential, and hence a study was made of the concentrations of B that reduced the growth of S. cerevisiae and P. chrysogenum and the mode of action of the B toxicity. Fifty and 4000 mg B/liter, respectively, significantly (5% level) reduced the growth of the latter 2 species.In both, glycolysis appeared to be inhibited by toxic levels of B, since the cells accumulated fructose-1,6-diP and ADP, but were low in glyceraldehyde-3-P and ATP. With S. cerevisiae growing on glucose, 150 mg B/liter significantly reduced CO(2) evolution. When glyceraldehyde was substituted for glucose, CO(2) evolution and O(2) consumption were unaffected by this level of B.Aldolase was suspected of being inhibited by high B, and this was confirmed using a crude aldolase extract from S. cerevisiae and purified rabbit muscle aldolase. The inhibition of aldolase by B was uncompetitive.With aldolase activity being reduced by toxic levels of B, the fungi were apparently unable to utilize carbohydrates at a rate sufficient to maintain the metabolic processes involved in growth and reproduction.