Clarification and Reevaluation of Population‐Based Diallel Analyses

Abstract

Plant breeders and geneticists often use diallel mating designs to obtain genetic information about a trait of interest from a fixed or randomly chosen set of parental lines. Diallel analyses of broad‐based populations have frequently been conducted by means of three analyses presented by Gardner and Eberhart in 1966. The original paper of Gardner and Eberhart used sequential model fitting to obtain estimates of effects and corresponding sums of squares. This approach, although having a long history, suffers from shortcomings which have led to confusion about what hypotheses the analyses actually test. The objectives of this paper were to delineate clearly all models implicitly required to perform Gardner and Eberhart Analyses II and III, and to present explicit formulas for effects in terms of the population means which are fundamental and unambiguous. While developing formulas of effects, we discovered a typographic error associated with variety effects in the original example of Analysis II. Our results also indicate that Analyses II and III effect formulas are rather nonintuitive both biologically and genetically, and incorporate multipliers that are functions of the number of parents. Another specific result shows that the varietal effects obtained in Gardner and Eberhart's Analysis III are “unconstrained” estimates, while those from the Analysis II are estimates constrained by the assumption of “no heterosis.” These results have implications for the use and interpretation of such effects. A SAS computer program for analyzing diallels among broad‐based populations according to Gardner and Eberhart's Analyses II and III is also reported.

Combining Ability and Heterosis for Forage Yield among Elite Alfalfa Core Collection Accessions with Different Fall Dormancy Responses

“…Entries were treated as a whole-plot factor and years as a subplot factor. The mathematical formulas and approaches used to estimate diallel component eff ects have been described elsewhere (Murray et al, 2003). Entries and years were considered fi xed eff ects, and blocks were random eff ects.…”

Partial Decomposition of the Genetic Correlation between Forage Yield and Fiber Using Semihybrids

“…The second analysis consisted of the varietycross diallel Analysis II of Gardner and Eberhart (1966). Analysis II computations were made using contrasts in the general linear hypothesis approach described by Murray et al (2003). Analysis II computations were made using contrasts in the general linear hypothesis approach described by Murray et al (2003).…”

“…This analysis partitioned the 15 df for crosses into varieties (3 df), average heterosis (1 df), variety heterosis (3 df), specific heterosis (2 df), and reciprocal heterosis (6 df). Reciprocal heterosis, not included in the model of Murray et al (2003), was computed as the pooled sum of squares for six contrasts of C ij vs. C ji (the ijth cross mean vs. its reciprocal). Reciprocal heterosis, not included in the model of Murray et al (2003), was computed as the pooled sum of squares for six contrasts of C ij vs. C ji (the ijth cross mean vs. its reciprocal).…”

Effects of open- and self-pollination treatments on genetic estimations in maize diallel experiment

“…The three most commonly-used methods in diallel analysis are those of Jinks-Hayman, GardnerEberhart and Griffing (Murray et al, 2003). Although all these methods have similar goals, they use different computation procedures.…”