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Sample Size and Experimental Design for Detecting Differential Anatomical Composition of Smooth Bromegrass Stems and Leaves¹

Precise quantitative assessment of anatomical composition in smooth bromegrass (Bromus inermis Leyss.) is difficult due to (i) small differences among many genotypes or types of treatments, (ii) an extreme amount of random variation, and (ill) an associated requirement for large sample sizes. The objectives of this study were to determine the importance of sources of error and to develop a strategy for more precise estimation of genetic differences in anatomical composition of smooth bromegrass stems and leaf blades. Eighteen clones were grown at Arlington, WI in 1982 in two randomized complete blocks of spaced plants. Two leaf blades of each of two tillers were sampled from each plant at early heading for estimation of percentage cross-sectional area of stem and leaf blade anatomical components. for stem characters, the variance component due to tillers within plants was always the largest. Repeatability of clone means was generally low and resulted in poor power (<45%) for pairwise tests of clone means with true differences of 20 or 40% of the range among clone means (R^–_c). Power was adequate for vascular bundle number (VBN), diameter, and percentage phloem at 60% of R^–_c but never exceeded 55% for percentage chlorenchyma, vascular bundle schlerenchyma, and vascular bundle tissue. Sample sizes required for 80% power varied considerably among characters but should be larger than the four total tillers per clone sampled in this study. Replication should be kept to a minimum (two) for all characters except VBN and xylem. The optimum number of tillers per plant was one for VBN and two for xylem. For all leaf blade characters, except VBN, the leaf age x tiller variance component was the largest. Repeatability was slightly higher than for most stem characters, but power for small differences (20 or 40% of R^–_c) was similarly low, except for VBN. Power was nearly 60% or greater for all characters at 80% of R^–_c and nearly 80% or greater for all characters at 100% of R^–_c. Small total sample sizes (e.g., eight total leaf blades per clone) would be adequate for VBN and percentage vascular bundle tissue, but not other characters. Future studies of these leaf blade characters should emphasize (i) a minimum number leaf blades per plant, (ii) sampling leaves of equal ages, (iii) tiller per plant, and (iv) adequate experimental replication.

Key Words: Bromus inermis Leyss. • Experimental error • Grass breeding • Least significant difference • Precision • Power • Repeatability • Variance components

² Assistant professor, Univ. of Wisconsin-Madison and former graduate research assistant (currently graduate research assistant, Dep. of Agronomy. The Pennsylvania State Univ. Park, PA 16802).

Received for publication April 23, 1984.