A comparison of planned unbalanced designs for estimating heritability in perennial tree crops

One hundred families of average size 10 are allocated in single-tree plots to 20 blocks in several planned unbalanced designs. Based on the variance of the estimate of heritability from the Minimum Variance Quadratic Unbiased Estimates and 100% survival, the three partially balanced designs are equally efficient. A design with variable family size is more efficient for heritabilities (h(2)) generally less than 0.25; an equal family size design is more efficient for h(2) generally greater than 0.25. A design with a large number of small families is more efficient at high h(2) than that with a small number of large families; a design with fewer families of larger size is more efficient at low h(2). Two-tree plot designs are never more efficient than single-tree plot designs and are also shown to be sensitive to the magnitude of the variance components that generate a given h(2), whereas the single-tree plot designs are not.