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Dimensional Balance Among Yield Components and Maximum Yield in an 8 x 8 Diallel of Barley¹

Dimensional balance between yield components played a key role in determining yield of barley (Hordeum vulgare L. Emend., Lam.). The ratios of Y/X, Z/X, and Y/Z, where X = heads/plant, Y = seeds/head and Z = mg/ kernel, were found to account for 72% of the variation in yield of 28 Ft crosses from an 8 x 8 diallel of barley. Such a high correlation between the shape of the yield parallelepiped as measured by these ratios and yield meant an almost 1:1 correspondence between shape and yield.

As yield increased the relative rate of expenditure of available resources for each component measured by component ratios increased for Z/X, decreased for Y/Z, and remained constant for Y/X.

The highest-yielding crosses were found to have a high value of X and Y and a low value of Z when compared to the low-yielding group and to the estimated mathematical optimum. The difference between the calculated optimum shape of the yield parallelepiped and the observed shape at the high yield levels was ascribed to component compensation. Negative correlations between Y and Z and between yield and Z indicated that as yield increased, increased values of Y would be attained at the expense of Z.

Key Words: Hordeum vulgare L. Emend. Lam. • Yield parallelepiped • Components of yield

² Professor of Crop Science and former graduate student, respectively, M.S.U., East Lansing, MI 48824.

Received for publication March 1, 1973.