SUMMARY The additive main effects and multiplicative interaction (AMMI) model first applies the additive analysis of variance (ANOVA) model to two-way data, and then applies the multiplicative principal components analysis (PCA) model to the residual from the additive model, that is, to the interaction. AMMI analysis of yield trial data is a useful extension of the more familiar ANOVA, PCA, and linear regression procedures, particularly given a large genotype-by-environment interaction. Model selection and validation are considered from both predictive and postdictive perspectives, using data splitting and F-tests, respectively. A New York soybean yield trial serves as an example. Yield trials generate observations of yield, ordinarily replicated, for a number of genotypes grown in a number of environments (site-year combinations). Often the data are rather noisy, with a standard deviation for plot yields in excess of 25 % of the mean. An additional challenging feature of these data is the frequent presence of important and complex genotype-by-environment (GE) interactions. Plant breeders use yield trials to identify promising genotypes, and agronomists use them to make recommendations for farmers. The level of success in meeting these goals depends critically on two factors: (i) the accuracy of yield estimates, and (ii) the magnitudes of genotype-by-site, genotype-by-year, and genotype-by-site-by-year interactions (Talbot, 1984). In essence, these two factors reflect within-trial accuracy and between-trial predictability. This paper addresses only the first concern. Nothing is said regarding between-trial predictability, or agrotechnology transfer, other than to observe that success with withintrial accuracy is a necessary prelude to success with between-trial predictability. The within-trial accuracy of a statistical model may be assessed by two fundamentally different criteria: Postdictive success concerns a model's fit to its own data, whereas predictive success concerns the fit between a model constructed using part of the data and validation data not used in modelling. In either case, the statistical setting is that of an incompletely specified model, where empirical considerations enter into the decision to include a given' potential source in the model, or alternatively to relegate it to the model's residual (Bancroft, 1964). Whenever the data are noisy, postdiction and prediction are different tasks, and in general the model chosen by predictive criteria will be different and simpler than the model chosen by postdictive criteria. Because the several replicates of a yield trial constitute a noisy sample, a model chosen by predictive criteria may be expected to provide yield estimates that are closer to the true means (and to validation observations) than will a model chosen by postdictive criteria. This claim is readily subjected to experimental test. In what follows, the relative performances of statistical models chosen

Model selection and validation for yield trials with interaction

Publisher Summary This chapter presents the statistical analysis of multilocation trials. Multilocation trials play an important role in plant breeding and agronomic research. Data from such trials have three main agricultural objectives—to accurately estimate and predict yield based on limited experimental data; to determine yield stability and the pattern of response of genotypes or agronomic treatments across environments; and to provide reliable guidance for selecting the best genotypes or agronomic treatments for planting in future years and at new sites. Agronomists use multilocation trials to compare combinations of agronomic factors, such as fertilizer levels and plant density, and on this basis make recommendations for farmers. Breeders compare different improved genotypes to identify the superior ones. Data collected in multilocation trials are intrinsically complex, having three fundamental aspects—namely, structural patterns; nonstructural noise; and relationships among genotypes, environments, and genotypes and environments considered jointly. Pattern implies that a number of genotypes respond to certain environments in a systematic, significant, and interpretable manner, whereas noise suggests that the responses are unpredictable and uninterpretable.

Statistical analyses of multilocation trials

Publisher Summary The chapter discusses the use of genotype-by-environment interaction for crop cultivar development. The chapter begins with definitions of genotype, environment, and phenotype, and discusses the influence of environment on heredity that may result in modification of a phenotype and lead to genotype-environment (GE) interaction. Some terms from ecological genetics are used and explained. The chapter discusses the causes of genotype-environment interaction and ways to deal with it, stability statistics, and ways to exploit or minimize interaction. A crop cultivar development program has two major components—crop breeding methodology and performance evaluation of improved cultivars in target areas. Implications of GE interaction in breeding are discussed. The concepts of stability are presented. Methodology for identifying stable genotypes and environmental factors that may be responsible for stable or unstable performance is also presented. .

Using genotype-by-environment interaction for crop cultivar development

https://ecommons.cornell.edu/bitstream/1813/32839/1/BU-738-M.pdf

Discussion of : Statutory and Recommended List Trials of Crop Varieties in the United Kingdom

SUMMARY The United Kingdom has recently set up a new system of crop variety performance trials to meet European Economic Community directives concerning the marketing of seeds. This has led to a reappraisal of statistical practices in statutory variety testing including trial design, methods of data analysis and allocation of resources. The paper describes some of the problems encountered and reports work done so far in resolving them. This work includes the construction of a catalogue of generalized lattice designs. A computerbased system is used for routine data processing; it incorporates least squares procedures appropriate to incomplete varieties x trials tables. Much remains to be done in designing series of trials and interpreting their results.

Statutory and Recommended List Trials of Crop Varieties in the United Kingdom

SUMMARY In incomplete two-way tables, analysis of variance can be used only to find adjusted means and sums of squares. It is proposed that, even in very incomplete tables, missing plot values can sometimes be fitted and the interaction sum of squares partitioned into principal components in the same way as with complete data. An example is given in detail in which this method of analysis gives a useful guide to the combination of results from many different trials.

G. H. Freeman

Papers

Analysis of Interactions in Incomplete Two‐Way Tables