Incomplete block designs for genetic testing: Statistical efficiencies with missing observations

Abstract

Missing observations are common in forest genetic field trials and are expected to reduce statistical efficiencies of any applied field designs. Such reductions could lower the presumed efficiency and other benefits of implementing any incomplete block designs (ICBs). In this study, we addressed this by computer simulation of a full-sib progeny trial with up to 20% of the observations missing. Four scenarios of missing observations (random, row, column, and genetic mortality) and tests of both clones and seedling families were examined. Two types of ICBs (alpha and no constraint) with single-tree plots, and their corresponding randomized complete block design (RCB), were considered on test sites with gradient and patchy environmental variation. Our simulations show that: (1) the statistical efficiencies of estimating family (or clone) means with both ICB and RCB were very sensitive to the percentage, not the scenarios, of missing observations examined; (2) the statistical efficiencies for both ICB and RCB were reduced as the number of missing observations increased, except in the cases of clonal genetic mortality; (3) the relative efficiency of ICB over RCB (at equal levels of missing observations) was reduced slightly as the level of missing observations increased; (4) the relative efficiencies for the seedling family tests were a little more sensitive to the levels of missing observations than those for the clonal tests, and; (5) the two ICBs showed little variation in the relative efficiencies across the missing observation scenarios and test conditions examined. Implications of these results for forest genetic field trials are discussed.