Error Variation in Multienvironment Peanut Trials: Within-Trial Spatial Correlation and Between-Trial Heterogeneity

difficult to assure within block homogeneity. Plots close together may be more similar than distant ones. Spatial Multienvironment Trials (MET) are used to make cultivar recomvariability refers to the tendency of genotype responses, mendations about genotypes in plant breeding programs. Because of the presence of genotype environment interaction, METs are ususuch as yield trends, to follow the spatial arrangement ally conducted in multiple environments using designs that involve of plots on the ground (Mercer and Hall, 1911). Variaseveral replications per environment. Blocking of plots within each tion from plot to plot within the same block may be trial enables one to account for between plot variation. To improve due to competition between genotypes (Kempton and the comparison of genotype means, taking into account within-trial Lockwood, 1984), heterogeneity in soil fertility (Pearce, spatial correlation as well as between-trial residual variance hetero1980), insect dispersion, weeds, crop disease, or cultural geneity, alternative mixed models can be used. The objective of this aspects (Smith et al., 2001). Because of the spatial varistudy was to compare several spatial models, including or excluding ability between and within blocks, the standard analysis heterogeneity of residual variances for cultivar evaluation in a set of of variance for an RCBD does not always produce the independent peanut (Arachis hypogaea L.) METs. The modeling immost efficient comparison of genotype effects. pact was evaluated by comparing genotype means from each trial. A series of 18 METs from a peanut breeding program, as according to Statistical procedures that account for spatial variaa randomized complete block design (RCBD) at each location, were tion among plots within trials have been proposed simultaneously fitted by (i) a classic analysis of variance model for an (Papadakis, 1937; Mead, 1971; Besag, 1974, 1977; RipRCBD with blocks random and (ii) mixed models incorporating spaley, 1981; Wilkinson et al., 1983; Besag and Kempton, tial correlation through isotropic and anisotropic covariance structures 1986). Brownie et al. (1993) addressed the topic of modfor the error terms (power correlation function) and including homogeling spatial variation in crop evaluation trials by using enous and heterogeneous residual variances to take into account the polynomial trend analysis, nearest neighbor analysis, different environments having different precision. Results suggest that and a model with correlated errors. They compared the model with stationary anisotropic error structure AR1 AR1 within these methods in a set of independent maize (Zea mays each environment and heterogeneous residual variances constitutes L.) yield trials and in a soybean [Glycine max (L.) Merr.] a good alternative analysis for METs, but it was not always better than the RCBD models for peanut. Differences were found between yield trial, with a single trial in each set. Stroup et al. longand short-cycle peanut cultivars with respect to the best model. (1994) also compared methods using one-location trials and made conclusions about the benefits associated with the spatial variation modeling in a wheat (Triticum aestivum L.) MET conducted in the central region of the T comparison of genotype performance in METs USA. For yield trials at a single location, Gleeson and requires the ability to make reliable mean yield comCullis (1987), Cullis and Gleeson (1991), and Cullis et al. parisons. Commonly METs are conducted with multiple (1996) obtained more precise estimates of the cultivar replications at each location. The stratification or blockmeans by modeling spatial variation with a correlated ing of plots is a technique used to reduce the effect of error structure compared with estimates obtained under variation among plots. The blocks are groups of experithe classical analysis for an RCBD. Gilmour et al. (1997) mental units aligned in such a way that the plots within partitioned the spatial variability between plots at a sinthe blocks are as homogeneous as possible. The RCBD gle-location trial into local, global, and extraneous spais commonly used. This design is more efficient than the tial variability. The local spatial variability refers to the completely randomized design when differences between differences between plots on a small scale, and the global plots in the same block are minimal and differences among spatial variation represents nonstationary tendencies blocks are substantial (Gusmao, 1986). Heterogeneity within blocks may result in imprecise estimation of the genotype effects because of a large error variance (Stroup Abbreviations: AIC, Akaike Information Criterion; AR1, first order autoregressive; BIC, Schwarz Bayesian Information Criterion; BLUE, et al., 1994). Since METs often include a large number best linear unbiased estimator; BLUP, best linear unbiased predictor; of genotypes, the block sizes are usually large, and it is EEA, Estación Experimental Agropecuaria; G, genotype main effect; GL, genotype by location interaction effect; INTA, Instituto Nacional de Tecnologı́a Agropecuaria; L, location main effect; MET, multiF. Casanoves, Centro Agronómico Tropical de Investigación y Enseñenvironment trials; PBP, Peanut breeding program; Pow, isotropic anza, 7170 Turrialba, Costa Rica; R. Macchiavelli, Dep. of Agronomy power spatial correlation; Powa, anisotropic power spatial correlaand Soils, Univ. of Puerto Rico Mayaguez, P.O. Box 9030, Mayaguez, tion; PowaH, anisotropic power spatial correlation and heterogeneous PR 00681-9030; M. Balzarini, Facultad de Ciencias Agropecuarias, residual variances; PowH, isotropic power spatial correlation and hetUniversidad Nacional de Córdoba, cc 509, (5000) Córdoba, Argentina. erogeneous residual variances; PowRB, isotropic power spatial correReceived 15 Sept. 2004. *Corresponding author ([email protected]). lation and heterogeneous random block; RB, random block; RBH, random block with heterogeneous residual variances; RBHBH, ranPublished in Crop Sci. 45:1927–1933 (2005). Crop Breeding, Genetics & Cytology dom block with heterogeneous block variances and heterogeneous residual variances; RCBD, randomized complete block design; REML, doi:10.2135/cropsci2004.0547 © Crop Science Society of America restricted maximum likelihood; SAV, square root of average variances of mean differences. 677 S. Segoe Rd., Madison, WI 53711 USA 1927 Published online August 26, 2005