Effect of Control Plot Density, Control Plot Arrangement, and Assumption of Random or Fixed Effects on Nonreplicated Experiments for Germplasm Screening Using Spatial Models

Consequently, unreplicated experiments are commonplace in early generation trials (Kempton and Gleeson, Early generation selection experiments typically involve several 1997; Martin, 2002). Because of the number of genohundred to thousands of lines. Various systematic and statistical techniques have been developed to increase effectiveness and efficiencies types included and large land area requirements, repliin such experiments, including the development and application of cated check variety plots are usually distributed over spatial statistical models. In this study, mixed model equations were the trial area as a method of local control, and the yields used to provide least squares means (LSMEANs) and best linear unof the check variety are used as a yard-stick against biased predictors (BLUPs) and compare selection effectiveness and which to assess the yield of each test plot (Kempton, efficiencies to observed (Y) and true values in simulated experiments 1984). Different systematic arrangements of check plots varying in size (10 10, 20 20 and 30 30 grids), control plots have been used (Kempton, 1984; Besag and Kempton, densities (0, 5, 10, 20, and 50%), control plot arrangements (high, 1986; Cullis et al., 1989; Martin, 2002) to reduce the cost medium, and low A-optimality), and spatial range of influence (short of including too many checks in the experiment. Baker and long). Results were similar for all grid sizes. In experiments in which the simulated land areas were highly variable (short range), and McKenzie (1967), however, questioned the value none of the predictors, Y, LSMEAN, or BLUP, were very effective of systematically arranging control plots and concluded in identifying the true superior genotypes. When the simulated land that the distribution of checks in the experiment should areas were less variable (long range), use of BLUPs consistently rereflect the spatial variability pattern in the field to make sulted in the highest proportion of true top ranking genotypes identiadjustments on the genotype estimates. fied across all control plot densities, while using the observed values Federer (1956, 1961, 1963), Steel (1958), and Searle consistently resulted in identification of the lowest proportion of the (1965) introduced augmented designs to handle lack of true top ranking genotypes. Effectiveness of LSMEANs was depenreplication of treatments. These designs were found to dent on control plot density and arrangements. Use of BLUPs for early be of little practical value since up to 50% of the total generation germplasm screening experiments should result in a high effectiveness in selecting truly superior germplasm and high efficiency plots were used by the check variety, and the designs because of the ability to account for spatial variability with the use emphasized testing line differences rather than estimaof few or no control plots. tion of gross genotypic values (Lin and Poushinsky, 1983). Various methods of adjusting the yield of each new line to the yields of nearby check plots have also I early generation selection experiments, lines numbeen used, including nearest neighbor analysis (Papabering from several hundreds to thousands are typidakis, 1937; Bartlett, 1937) as well as different fertility cally evaluated. In these trials, the breeder is primarily indexes (Lin and Poushinsky, 1985; Besag and Kempton, interested in the selection and identification of superior 1986). However, these methods, though useful, do not lines for further improvement as opposed to precise esspecify the nature of the relationship between the neightimation or prediction of their means and accurate estiboring plots. mation of error for comparing lines (Patterson and SilOne of the assumptions in analysis of data from devey, 1980). In addition to the large numbers of lines that signed experiments is that experimental errors are indeneed to be evaluated, early generation trials often have pendent. In agricultural field experiments, however, ada limitation in that little seed is available for each line. jacent plots are often correlated (Hayes, 1925; Griffee, Thus, replication may not be always possible (Federer 1928; Briggs and Shebeski, 1967; Hadjichristodoulou and Raghavarao, 1975), especially if plots are to be large and Della, 1975). The presence of the correlation, if unenough for proper yield assessment (Kempton, 1984). controlled, may bias treatment comparisons and inflate residual variation (Grondona et al., 1996). However, Boi Sebolai, Botswana College of Agriculture, Private Bag 0027, Gabest linear unbiased estimates may still be obtained if borone Botswana; J.F. Pedersen, USDA-ARS, NPA Wheat, Sorghum one accounts for the lack of independence (Aitken, 1934). and Forage Research, 344 Keim Hall, Univ. of Nebraska-Lincoln, The application of geostatistical models to account for Lincoln, NE 68583-0937; D.B. Marx, Dep. of Biometry, Univ. of the correlation in analysis of data from agricultural exNebraska-Lincoln, Lincoln, NE 69583; D.L. Boykin, USDA, ARS, MSA, 141 Experiment Stn. Rd., Stoneville, MS 38776. Joint conperiments is increasingly becoming important. These tribution of the USDA-ARS and the Univ. of Nebraska Agric. Exp. models use various correlation structures to model the Stn. as Paper no. 14799, Journal Series, Nebraska Agric. Exp. Stn. variation related to the location of the experimental units Received 4 Nov. 2004. *Corresponding author ([email protected]). in the field and result in an increase in the accuracy and Published in Crop Sci. 45:1978–1984 (2005). precision of estimates of variety effects (Cullis and GleeCrop Breeding, Genetics & Cytology son 1989, 1991; Zimmerman and Harville 1991; Brownie doi:10.2135/cropsci2004.0643 et al., 1993; Qiao et al., 2000). Martin (1986) assumed that © Crop Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA in spatial designs, there are positive correlations which