Yield trials frequently have both significant main effects and a significant genotype x environment (GE) interaction. Traditional statistical analyses are not always effective with this data structure: the usual analysis of variance (ANOV A), having a merely additive model, identifies the GE interaction as a source but does not analyze it; principal components analysis (PCA), on the other hand is a multiplicative model and hence contains no sources for additive genotype or environment main effects; and linear regression (LR) analysis is able to effectively analyze interaction terms only where the pattern fits a specific regression model. The consequence of fitting inappropriate statistical models to yield trial data is that the interaction may be declared nonsignificant, although a more appropriate analysis would find agronomically important and statistically significant patterns in the interaction. Therefore, agronomists and plant breeders may fail to perceive important interaction effects. This paper compares the above three traditional models with the additive main effects and multiplicative interaction (AMMI) Model, in an analysis of a soybean (Glycine max (L.) Merr.] yield trial. ANOV A fails to detect a significant interaction component, PCA fails to identify and separate the significant genotype and environment main effects, and LR accounts for only a small portion of the interaction sum of squares. On the other hand, AMMI analysis reveals a highly significant interaction component that has clear agronomic meaning. Since ANOV A, PCA, and LR are sub-cases of the more complete AMMI model, AMMI offers a more appropriate first statistical analysis of yield trials that may have a genotype x environment interaction. AMMI analysis can then be used to diagnose whether or not a specific sub-case provides a more appropriate analysis. AMMI has no specific experimental design requirements, except for a two-way data structure.Additional Index Words: Additive main effects and multiplicative interaction model, Analysis of variance, Biplot, Linear regression, Glycine max (L.) Merr., Principal components analysis.

To maximize yield throughout a crop's heterogeneous growing region, despite differences in cultivar rankings from place to place due to genotype‐environment interactions, frequently it is necessary to subdivide a growing region into several relatively homogeneous mega‐environments and to breed and target adapted genotypes for each mega‐environment. The objectives of this study are to identify relevant criteria for evaluating mega‐environment analyses and to apply the Additive Main Effects and Multiplicative Interaction (AMMI) model to mega‐environment analysis. The proposed analysis is illustrated using a Louisiana corn (Zea mays L.) trial. Statistical strategies for identifying mega‐environments should meet four criteria: flexibility in handling yield trials with various designs, focus on that fraction of the total variation that is relevant for identifying mega‐environments, duality in giving integrated information on both genotypes and environments, and relevance for the primary objective of showing which genotypes win where. The AMMI model meets these criteria effectively when the usual biplots are supplemented with several new types of graphs designed to address questions about mega‐environments. Preliminary results indicate that a small and workable number of mega‐environments often suffices to exploit interactions and increase yields.

The methodology used by the International Maize and Wheat Improvement Center (CIMMYT) to develop and improve its maize (Zea mays L.) germplasm involves evaluation of families or experimental varieties in extensive international testing trials. The genotype‐environmental interaction is produced by differential genotypic responses to varied environmental conditions. Its effect is to limit the accuracy of yield estimates and complicate the identification of specific genotypes for specific environments. The objective of this study was to use the Additive Main effects and Multiplicative Interaction (AMMI) method, with additive effects for genotypes and environments and multiplicative terms for genotype‐environment interaction, for analyzing data from two international maize cultivar trials. Results from the first trial were: (i) predictive assessment selected AMMI with one principal component axis, (ii) AMMI increased the precision of yield estimates equivalent to increasing the number of replications by a factor of 4.30, (iii) AMMI provided much insight into genotype‐environment interactions, and (iv) AMMI selected a different highest‐yielding genotype than did treatment means in 72% of the environments. Results for the second trial were that predictive assessment selects the AMMI with none of the principal component axes, which increased precision equivalent to increase the number of replications by a factor of 2.59.

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.

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The objective of this work was to describe the relationship between elongation rate and diameter of maize roots and to estimate the length and growth duration of lateral roots of maize. Diameters and elongation rates of roots were measured in situ on plants grown 5 weeks in small rhizotrons under greenhouse conditions. At the end of the experimental period the roots were harvested and diameters of axile and lateral roots were measured. The frequency distribution of diameters of harvested roots was bimodal with a minimum at 0.6 mm; 97% ofaxile roots were larger than this value and 98% of the lateral roots were smaller. Root elongation per day increased as diameter increased but the slope of the relationship with lateral roots was about 2.5 times that with axile roots when separate linear regressions were fitted to the two populations. The length of lateral roots found on axillary roots between the base and about 30 cm from the apex was approximately 2.2 cm. All of the data was consistent with the hypothesis that the lateral roots grew for about 2.5 days and then ceased growing. The axillary roots continued to grow throughout the experimental period at a rate of about 3 cm day -~.

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The diageotropica mutant of tomato (Lycopersicon esculentum Mill.) Ethylene Treatments. Fixed concentrations of ethylene were supplied to whole plants by means of a gas flow system similar to the one described by Goeschl (2). With this system, it was possible to provide accurate continuous flow ethylene atmospheres down to 0.005 ,ul/l depending upon the ethylene concentration in the air.Whole plants were placed in 30-liter containers with an ethylene-air flow rate of 7.5 liters/hr through the container.Concentrations of 10, 1, 0.1, 0.05, 0.005 and 0.0 ,l/ 1 ethylene were applied to plants over a 12-hr period. Lower concentrations could not be accurately measured with available equipment. Treatments, at each concentration, except 10 and 1 tul/l, were repeated three times with two mutant plants at each concentration. Fresh, untreated plants were used in each replicate. No light was provided during treatment. For controls, untreated mutant and normal plants were placed in sealed containers and left on the bench top with the treated material during the 12-hr experiment.Chemical Treatment of Stem Sections and Leaf Segments. Whole plants were brought into the laboratory from the greenhouse. Leaves were immediately cut off the main stem and side branches at the base of the petiole, and leaf segments in turn were cut off the petiole. These were weighed and 1 to 2 g of the leaf material placed in a 50-ml Erlenmeyer flask. The remaining stem internode regions were cut into pieces 20 to 30 mm long, weighed, and placed in 50-ml Erlenmeyer flasks at 10 g/flask.In an initial experiment, 13-ml vials were used with 0.5 to 1 g of stem or leaf tissue in each. One milliliter of water was added to each vial, and one-fifth of the vials were immediately sealed with serum caps. These first vials were sampled for ethylene content after 2 hr, air was blown into each vial to flush out ethylene, and they were then recapped along with 385 www.plantphysiol.org on May 10, 2018 -Published by Downloaded from