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a Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
b USDA-ARS, Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
* Corresponding author (krlamkey{at}iastate.edu)
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ABSTRACT |
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 TOPNOTES ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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INTRODUCTION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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Favorable epistatic deviations may become fixed and maintained in inbred lines (Lamkey et al., 1995). These epistatic effects could explain why certain inbreds are more successful than others in forming hybrids, and this knowledge can be beneficial when researchers set up breeding programs (Hallauer and Miranda, 1988; Lamkey et al., 1995). The detection of a high incidence of epistasis among hybrids would suggest that hybrid breeding programs select for epistatic effects.
Measures of epistasis in maize hybrids have been estimated by (i) triple-test crosses, (ii) making comparisons of single, three-way, and double cross hybrids, or (iii) measuring variance components (Hallauer and Miranda, 1988). Epistasis has been measured by generation means analysis (Hallauer and Miranda, 1988) making it possible to detect epistatic effects on the basis of means—a more powerful test than examining variance components (Fenster et al., 1997). The original generation means analysis proposed by Hayman (1958) measured the different generations derived from a cross between two pure lines. Melchinger (1987) proposed testcrossing the generations from Hayman's analysis to an inbred tester, which removes dominance effects from the model that tended to overwhelm the epistatic effects. The gene effects estimated in Melchinger's model are in reference to the F2 testcross populations versus the F2 population per se in Hayman's model.
We used the analysis developed by Melchinger (1987) for testcross means of a cross between two inbred lines, their F1, F2, and backcross generations. This is a continuation of the work of Lamkey et al. (1995) who first attempted to measure epistatic effects in North American maize germplasm using testcrosses in a generation means analysis. Our aim was to extend the research of Lamkey et al. (1995) to a greater range of U.S. maize germplasm to get a broader view of the importance of epistasis. The significance of the findings reported by Lamkey et al. (1995) suggested that epistasis might play a significant role in many other elite maize hybrids. An experiment designed to test this hypothesis was consequently initiated. An advantage of our experiment compared with previous studies of epistasis is that we have evaluated a large number of hybrid combinations in a single experiment.
The objectives of our research were (i) to estimate genetic means and effects when Melchinger's (1987) Model 1 and Model 2 are applied to testcross progeny sets from a wide selection of maize hybrids, (ii) to determine whether epistasis is present and influencing phenotypic variation, (iii) to clarify which model best explains the variation in the data collected, and (iv) to establish whether these models are useful in detecting epistasis in U.S. elite maize hybrids.
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MATERIALS AND METHODS |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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Testcrosses of each hybrid progeny set will be referred to as testcross progeny sets. The two testers for the non-BSSS hybrid progeny sets were B104 and B73. B104 was derived from BS13, a population formed from the BSSS heterotic group (Hallauer et al., 1997). Inbred B73 was derived from an advanced recurrent selection population (Cycle 5) of BSSS (Russell, 1972). The two testers for the BSSS hybrid progeny sets were B97 and B112. B97 was selected from Cycle 9 of a reciprocal recurrent selection program in Iowa Corn Borer Synthetic No. 1 (BSCB1) (Hallauer et al., 1994). B112 was selected from Cycle 11 of the BSCB1 population (A.R. Hallauer, personal communication, 2001). The 10 hybrid progeny sets from each heterotic group were crossed to two testers from the opposite heterotic group producing 40 unique testcross progeny sets. Inbred lines were labeled arbitrarily as P1 or P2 in a cross generally with the earliest released line within the hybrid pair designated as P1. An inbred line will always be P1 or P2 within hybrids but may be labeled P1 in one hybrid and P2 in another hybrid. The label for a testcross progeny set followed the form: (P1 x P2) * tester.
Adequate seed was not available for testcrossing after producing the backcross generation of (B37 x B84). These two entries were replaced with filler plots in the field evaluation, and their phenotypic data were removed from the analysis.
Field Evaluation
The 240 entries were evaluated in a 12 x 20 row-column lattice [
(0,1)] experimental design with two replications at five locations for two years. Testcrosses were evaluated at Ames, Carroll, Crawfordsville, Fairfield, and Rippey, IA, in 1999 and 2000. Experimental plots consisted of two rows, 5.49 m long with 0.76 m between rows. Data collected on plots included silking date (days after planting when 50% of the plants in a plot showed visible silks), ear height (cm), plant height (cm), root lodging (percentage of plants leaning greater than 30° from vertical), stalk lodging (percentage of plants with stalks broken at or below the highest ear), machine harvestable grain yield adjusted to 155 g kg-1 grain moisture (Mg ha-1), and grain moisture concentration at harvest (g kg-1). The results presented here focus primarily on the effects of epistasis on grain yield across the 40 testcross progeny sets.
Statistical Analysis
Individual environments were analyzed by a mixed-model lattice analysis where rows and columns were fit as random effects and entries were fit as fixed effects. Residuals from these analyses were used to test for normality and outliers. The raw data, corrected for outliers, was used to compute the combined analysis, where the entry x environment interaction along with rows and columns were fit as random effects. Entries and environments were fit as fixed effects. The variance of the combined entry means was calculated by dividing the average of the variance of the difference between all possible treatment pairs by two.
The entries and entries x environment sum of squares were further partitioned into effects due to heterotic groups, generations, testers within heterotic groups, and hybrid progeny sets within heterotic groups. The effects of tester, generation, and the tester x generation interaction were fit for the 10 hybrid progeny sets from both BSSS and non-BSSS heterotic groups.
The generation means for each testcross progeny set combined over environments were used to fit Melchinger's (1987) Model 1 and Model 2. Each parent inbred line crossed with a tester was included four times in the experiment because each inbred was involved in four F1 hybrids in the 5 x 5 diallel. To get a better estimate of these points, each of the four parental testcrosses were averaged together.
Under the null hypothesis of no epistasis, we expect a linear relationship due solely to additive effects [dT] to explain the differences among testcross generation means. A significant additive effect indicates that genetic differences are present among generations within a testcross progeny set. The alternative hypothesis suggests this relationship deviates from linearity because of combined epistatic (nonadditive) effects [iT] to give a quadratic function. A significant epistatic effect means that additive effects alone cannot explain the variation present among generations. The superscript T in the following formulas indicates that these values pertain to testcross effects. Therefore, any observable effects within generations of a testcross progeny set are due solely to the original parents. Testcross effects are evident when comparing means of hybrid progeny sets crossed to different testers. Model 1 does not account for epistasis:
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j = allelic state at locus j (e.g., +1 if P1 contains the favorable allele at locus j and -1 if P1 contains the unfavorable allele at locus j); and dTj = one-half the average effect of a gene substitution at locus j based on the F2 testcross population.
Model 2 allows for digenic epistasis:
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defined as above; 
= 
j<kjkiTjk; and iTjk = additive-by-additive epistatic effect between loci j and k.
The genetic expectations for each generation under Model 1 and 2 were given by Lamkey et al. (1995). The genetic parameters for both models were estimated using weighted least squares:
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= column vector of estimated genetic parameters; X = a matrix with elements that are a function of the generation; W = a matrix with the inverse of the variances of the generation means on the diagonal and zero on the off-diagonal; and y = column vector of testcross means.
Weighted estimates were calculated because the parental generations are known with more precision than the remaining generations (Mather and Jinks, 1971). Standard errors for the genetic parameters were calculated as the square root of the diagonal of the (X'WX)-1 matrix. A coefficient of multiple determination (R2) was obtained to explain the amount of variation accounted for by each model. The goodness-of-fit of each model was tested with a weighted Chi-square test as described by Mather and Jinks (1971):
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RESULTS AND DISCUSSION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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Testcrosses with non-BSSS parents (B73 and B104 testers) averaged over all environments tended to have the highest grain yield (7.70 Mg ha-1). B73 testcrosses generally yielded more than all other testcrosses except in 2000 at the Crawfordsville (5.95 Mg ha-1) and Rippey (6.37 Mg ha-1) locations. B112 testcrosses had the lowest yields at all locations except Crawfordsville (8.72 Mg ha-1) and Fairfield (6.95 Mg ha-1) in 1999 and Crawfordsville (6.12 Mg ha-1) and Rippey (6.13 Mg ha-1) in 2000.
Six of the 10 testcross progeny sets from B73 had significant parental differences while only one testcross progeny set from B104 showed a difference between P1 and P2 (Fig. 1–Fig. 2). In contrast, these differences were more frequent among BSSS lines crossed to B97 and B112 (Fig. 3–Fig. 4). P1 differed from P2 in eight testcross progeny sets of both the B97 and B112 testcrosses. When the hybrid progeny sets are averaged over testers, six sets of BSSS parents had significant tester effects, generation effects, or a combination of both. A tester effect was significant in one out of the 10 sets of non-BSSS parents. The tester x generation effect was nonsignificant in all cases.
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Melchinger's (1987) Model 1 provides the expectations for a trait not affected by epistasis. Variation for significant additive effects [dT] was observed among testers. B97 and B112 testcrosses had eight and nine testcross progeny sets, respectively, with significant additive effects indicating differences among generation means (Table 1). B73 and B104 testcrosses had fewer testcross progeny sets with significant additive effects (Table 2). Six B73 testcross progeny sets had significant additive effects. The B104 testcrosses were unique because nine out of 10 additive effects were not significant, thus indicating that B104 may be masking differences among inbreds.
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0.05) epistatic component (0.37 ± 0.18) (Table 2). This set was unusual because its additive effect was not significant. There was, however, a significant difference between 
and the F2 for this set. This was depicted as a parabolic relationship (Fig. 2b). The analysis of hybrid progeny sets averaged across both testers for a given heterotic group brought out another instance for unlinked epistasis in (B37 x B73) (Table 1). An average across B73 and B104 testers did not reveal new cases for epistasis (Table 2).
Before making further comparisons, we will consider the relationship between the F1 and the F2. The F1 and F2 have the same gametic array when considering the population as a whole. Therefore, these generations are expected to have the same mean values with epistasis and no linkage (Melchinger, 1987). When the F1 and F2 testcross means did differ and there was a nonsignificant epistatic effect, the observed differences in means are due to linked epistatic effects (Melchinger, 1987). There were four instances where the F1 and F2 testcross means differed [(B91 x B99)*B104; (B97 x B99)*B104; (B14A x B84)*B97; and (B14A x B73)*B112], and these sets did not have significant epistatic effects (Tables 1–2). Therefore, there were four cases for linked epistatic effects.
Given the original experimental test of the epistatic model (Melchinger et al., 1988) and a subsequent study (Lamkey et al., 1995) were evaluated without the F1, we removed it from our data set to determine whether inclusion of this generation may have affected our ability to detect significant genetic parameters. Removing the F1 did not alter our findings for genetic effects on grain yield. Those effects that were significant remained so and those that were not likewise remained nonsignificant.
How well do the additive effect and additive-by-additive epistatic effect explain the variation in a testcross progeny set? Although epistatic effects per se were rarely significant for grain yield, in certain crosses, including epistasis explained a substantial amount of the variation among generation means. For Model 1 of B104 testcrosses, sums of squares accounted for up to 67% of the variation. In Model 2, a maximum of 85% of the variation was explained. This was in contrast to Model 1 for other testers that accounted for up to 96% of the variation (B73 testcrosses; Table 2) and Model 2 up to 99% of the variation (B112 testcrosses; Table 1). The group of crosses of BSSS lines to non-BSSS testers (B97 and B112) provided the best fit to the epistatic model as they explained a higher amount of variation (R2) than did B73 and B104 testcrosses.
One prominent exception in the group of B97 and B112 testcrosses involved (B73 x B84), the parental lines studied by Lamkey et al. (1995). Model 2 accounted for the least amount of the variation among the generation means for both the B97 and the B112 testers (42 and 54%, respectively). When studied by Lamkey et al. (1995), this cross was evaluated with the Mo17 tester, and Model 2 explained 69% of the variation among generation means. The Mo17 testcross gave evidence for a classic case of epistasis. The additive effect indicated a distinction among generation means, and unlinked epistasis was detected. In addition, the parents significantly outyielded the backcross and F2 generations. For the B97 and B112 testcrosses, the values for generation means did not differ, there was no significant epistatic effect, and the parent means overlapped those of the backcross and F2 generations. This is strong evidence that detection of epistasis appears to be tester dependent (Eta-Ndu and Openshaw, 1999). The parental lines chosen by Lamkey et al. (1995) were crossed to a tester that allowed maximum expression of the genetic differences between progeny generations to obtain a detectable level of epistatic effect.
Implications for Statistical Modeling of Epistasis
The reported experimental design allows for performance comparisons among several lines and their progeny in relation to each other, in combination with different testers, and across heterotic groups. Because of these factors, we have been able to make broader statements regarding epistasis than earlier studies.
Analysis of 40 testcross progeny sets indicated that epistatic effects especially for grain yield were not as prevalent as expected on the basis of previous reports using Melchinger's (1987) testcross generation means models. These results were contrary to our initial expectations. Earlier research suggested that epistasis would be common in testcrosses involving a cross between two related parents (Lamkey et al., 1995). However, in our study, the epistatic effect was rarely significant (Tables 1– 2). The large R2 values for Model 1 combined with the infrequent detection of epistasis suggested a minor role for epistasis.
A better fit to a linear model may suggest no net epistatic effects because presence of both positive and negative epistatic effects could cancel out and produce a linear response (Hallauer and Miranda, 1988). Failure of our epistatic model can also indicate higher order linked or unlinked epistatic interactions (e.g., trigenic epistasis) (Mather and Jinks, 1971) or confounding of some epistatic effects within the measurement for additive effects (Cheverud and Routman, 1995). Averaging testcross means over environments has been observed to have a role in detection of epistasis. For example, when means were pooled over environments, Martin and Hallauer (1976) observed a decrease in frequency of significant epistatic effects compared to the individual environment analyses.
Choice of parents (Sprague et al., 1962) and testers (Melchinger, 1987) is important for measuring epistasis as well as the genotype x environment combinations studied (Martin and Hallauer, 1976). An enhancement to our study would be to incorporate lines selected expressly for specific combining ability and determine whether we can detect epistasis using that material. Such lines for evaluation could be the parent lines used in commercial maize hybrids. The parents, however, have to be more than just the best lines available; they have to be measurably different when crossed to the same testers. Testing these lines would allow for a direct measure of epistasis and its effect on commercial hybrids.
We know epistasis has a role in phenotype expression (Coe et al., 1988; Avery and Wasserman, 1992), but an appropriate test to estimate it accurately is elusive. Thus, recognizing the inadequacy of current statistical models for estimating epistasis, some suggest, "it is time to move on" to approaches where genotypes are known (Templeton, 2000). Results of marker-assisted studies of quantitative traits clearly show that epistasis plays a role in their inheritance (Yu et al., 1997), as well as in plant growth and development (Li et al., 1997). Approaches like these involve actively searching for epistasis, rather than it being what is left over after all other factors (e.g., additive and dominance effects) have been accounted for (Templeton, 2000).
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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Received for publication October 26, 2001.
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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