Incomplete block designs for genetic testing: statistical efficiencies of estimating family means

Abstract

A half-sib progeny trial with single-tree plots on one test site of various environmental variations is simulated to examine the relative statistical efficiencies of randomized incomplete block designs (ICBs) over their corresponding randomized complete block design (RCB) in estimating family means. The ICBs with full constraint (FC), half constraint (HC), and no constraint (NC) over replicates and an alpha design (Alpha) are considered. A geostatistical spatial model is employed, which allows specifications of patchy and systematic environmental variations across the test site and estimations of block and error components with SAS PROC MIXED. The simulation shows that Alpha is the most efficient ICB in the 21 scenarios of patchy and systematic site variations, followed by NC and HC, and these ICBs (except FC) are generally more efficient than RCB in terms of the average variance of a family mean contrast. The gains in statistical efficiencies with implementations of Alpha and NC (rather than RCB) in forest genetic testing can be high, depending largely on the nature (and level) of spatial environmental variation. Practical implications of these simulated results for forest genetic trials are discussed.