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Sampling Variation and Resource Allocation in Soybean Canopy Photosynthesis Experiments¹

Canopy apparent photosynthesis (CAP) during the seed-fill period has been shown to be related to seed yield in soybean [Glycine max (L.) Merr.]. The current techniques for measuring CAP are labor intensive and time consuming. However, estimates of error variances, coefficients of variation, and genotype x environment (G x E) interaction variances have not been reported. This report describes these statistics from three field experiments conducted over 5 years. These statistics were used to calculate the number of CAP measurements (replications x measurement dates) per genotype per environment and the number of environments required to detect various levels of differences between two genotypes. There were no differences in the error variances or CVs in F_3– and F_6–derived lines. The average error variance was 7.14 (µmol CO₂ m^–2 s^–1) and the average CV was 0.179 for our 16 measurement dates. Assuming no G x E interaction and ß = 0.5 (probability of Type II error), it would require 2, 4, 7, and 28 replications with one measurement date to detect 40, 30, 20, and 10% differences, respectively, between genotypes. In two of our three experiments there were significant ( < 0.05) G x E interactions. The G x E variance components were 0.1 and 0.2 of the error variance based on a single measurement date in these two experiments. Even with the largest amount of G x E interaction present in our experiments, a 20% difference between two genotypes can be detected with four environments and a 30% difference with two environments if four CAP measurements (two measurements x two replications) per genotype per environment are made. These results are discussed in regard to efficient design of experiments to determine CAP.

Key Words: Glycine max (L.) Merr. • Error variances • Coefficient of variation • Statistics • Genotypic differences

² Professors of agronomy, Univ. of Georgia, Athens, GA 30602 and assistant professor of agronomy, Louisiana State Univ. Agric. Ctr., Baton Rouge, LA 70893, respectively.

Received for publication November 21, 1984.