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CROP BREEDING, GENETICS & CYTOLOGY

Predicting Progeny Means and Variances of Winter Wheat Crosses from Phenotypic Values of Their Parents

Institute of Plant Breeding, Seed Science, and Population Genetics, Univ. of Hohenheim, D-70593 Stuttgart, Germany

* Corresponding author (melchinger{at}uni-hohenheim.de)

	ABSTRACT

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
The efficiency of breeding programs could be increased by predicting the prospects of crosses for line development before producing and testing lines derived from them. In this study, we examined the performance of F_4:n (n = 7 or 8) lines randomly derived from 30 winter wheat (Triticum aestivum L.) crosses produced by a factorial mating of five high yielding with six high baking quality cultivars. Our objectives were to (i) contrast the midparent value _ij with _ij for each cross and apply tests for the presence of epistasis, (ii) compare the estimates of the variance between means of crosses (²_c) with the average segregation variance within crosses (), (iii) determine the variation in ²_gij among crosses, (iv) evaluate the use of various parameters for predicting c_ij, ²_gij, and U_ij, and (v) briefly describe quantitative-genetic theory for interpretation of our experimental findings. Twenty-two lines per cross and the respective parents were evaluated in four environments for seven agronomic and quality traits. Additionally, 44 F_2:4 lines per cross were tested in hills in two environments. On the basis of first-degree statistics, parental means were good predictors of cross means, yet significant epistatic effects were observed for most traits. In agreement with quantitative-genetic expectations, the genetic variance between ²_c was of the same size as the variance between parental means and the average of F_4:n lines within crosses for all traits but sedimentation. Here, the two parental groups differed significantly in their mean, and was significantly larger than ²_c. Estimation of the segregation variance (²_gij) for individual crosses is not recommended because they (i) have a large standard error, (ii) can be assessed reliably only in advanced selfing generations, and (iii) are expected to have a minor influence on differences in the usefulness among crosses. Among all predictors investigated, only the parental means can be recommended for predicting the usefulness of crosses.

Abbreviations: ²_g, genetic variance • AFLP, amplified fragment length polymorphism • PD, squared phenotypic difference between two parents • PE, phenotypic Euclidean distance • QTL, quantitative trait loci • R, expected selection gain • SSR, simple sequence repeat • SSD, single seed descent • U, usefulness

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
IN BREEDING OF PURE-LINE CULTIVARS, new genetic variation is usually generated by crossing elite lines or cultivars followed by selfing or production of doubled haploids. Given a high number of parent lines, the number of possible crosses that could be exploited as base populations is excessively large. If the potential of crosses could be predicted without producing and testing the crosses or their progenies, this would greatly improve the efficiency of breeding programs by concentrating the resources for line development and testing on the most promising base populations.

In a biometric approach to this problem, Schnell and Utz (1975) introduced the concept of "usefulness" of crosses for line development. For a cross i x j between parents i and j, usefulness is defined as U_ij = c_ij + R_ij, where c_ij denotes the population mean of all possible homozygous lines that can be derived from i x j without selection and R_ij is the expected selection gain, when a fraction of these lines is selected with regard to a given selection criterion. Under a constant selection intensity for all crosses, R_ij depends on the genetic variance (²_gij) of the homozygous lines and the heritability (h²_ij) of the trait under study in the specific cross i x j. Other criteria closely related to usefulness are the "varietal ability" (Gallais, 1979) and the "probability of obtaining transgressive segregants" (Jinks and Pooni, 1976). Precise estimates of U_ij and its components c_ij and ²_gij are difficult to obtain especially for small grains because seed shortage prohibits intensive testing in plots and across multiple environments in early breeding generations. Therefore, reliable information can be obtained only in the parental and late generations.

Under a model with purely additive gene effects, the midparent value m_ij is a perfect predictor of c_ij. The value of parents may be impaired only in the presence of epistasis and linkage disequilibrium (Kearsey and Pooni, 1996). Phenotypic correlations between _ij and _ij for grain yield in wheat were usually moderate for data from a single environment (Bhatt, 1973; Fowler and Heyne, 1955) but fairly high (0.7 < r_p < 0.8) for data from multiple environments (Busch et al., 1974; Lupton, 1961). Results from a recent study with barley (Hordeum vulgare L.) confirmed these findings (Schut et al., 1998).

Prediction of ²_gij on the basis of parental information remains still an unsolved problem (Bohn et al., 1999). Important questions in this context are how large is the variation in ²_gij between different crosses of unrelated lines and how precisely can it be estimated so that the error could safely be ignored in prediction of U_ij. Another important comparison relates to the genetic variance between the means of crosses (²_c) versus the average segregation variance within crosses (). Wright and Cockerham (1986) provided quantitative-genetic expectations for the case that both parents originate from the same germplasm pool (i.e., for intrapool crosses). However, no such theory is available when the parents are chosen from different germplasm pools (i.e., for interpool crosses) to increase the segregation variance in crosses.

In this study, we present results of a mating experiment with five adapted high yielding cultivars and six high baking quality cultivars in winter wheat representing an adapted x unadapted crossing array. The genetic similarities of these cultivars were reported previously in a companion study (Bohn et al., 1999). From each of the 5 by 6 interpool crosses a random sample of 22 F_4:n (n = 7 or 8) lines was tested. Objectives of our research were to (i) contrast the midparent value _ij with _ij for each cross and apply tests for the presence of epistasis, (ii) compare the estimates of the variance between means of crosses (²_c) with the average segregation variance within crosses (), (iii) determine the variation in ²_gij among crosses, (iv) evaluate the use of various parameters for predicting c_ij, ²_gij, and U_ij, and (v) briefly describe quantitative-genetic theory for interpretation of our experimental findings.

	THEORY

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Assumptions
We consider populations of lines derived without selection by single seed descent (SSD) from crosses between pure-bred parents i and j. Parents i and j originated from populations ^I and ^II, respectively. Although the lines may have common ancestors, they are by definition assumed to be unrelated. In the absence of epistasis, Wright and Cockerham (1986) derived expectations for the genetic variances between and within crosses of parents from a single population on the basis of a one-locus model, allowing for an arbitrary number of alleles. This model was extended for epistatic effects and linkage disequilibrium between two loci k and l to derive quantitative-genetic interpretations for the estimated epistatic effects and genetic variances of crosses between parents from two different populations (Melchinger, 2000, unpublished data). While the formulas are given for two loci, the generalization is straightforward by summing over all possible pairs of loci influencing the trait expression.

Genetic Model
The genotypic value of a homozygous individual with haplotype k_rl_s (, {I,II}) was partitioned according to the following model:

(1)

Here, µ_e = population mean of homozygous lines from _e; a_kr = additive effect of allele r at locus k in _e; a_ls = additive effect of allele s at locus l in _e; aa_krls = additive x additive effect between allele r at locus k and allele s at locus l, defined with respect to population _e if = , or _e x _e if ; _e = population with identical gene frequencies as , but in linkage equilibrium.

Means
Suppose parent i from ^I with haplotype k^I_rl^I_s is crossed with parent j from ^II with haplotype k^II_ul^II_v. The frequency of haplotypes in the resulting population of homozygous lines developed by SSD without selection is ¹/₄(1 + _kl) for the parental haplotypes k^I_rl^I_s and k^II_ul^II_v and ¹/₄(1 - _kl) for the recombinant haplotypes k^I_rl^II_v and k^II_ul^I_s, where _kl is the linkage disequilibrium between loci k and l. The parameter _kl can be expressed as a function of the linkage value _kl (Schnell, 1961) or recombination frequency r_kl between loci k and l:

Hence, the phenotypic mean (c_ij) of lines derived from the cross between parents i and j can be expressed in terms of the above genetic model as:

(2)

The difference d_ij between c_ij and corresponding midparent value m_ij is purely a function of epistatic effects

(3)

When crosses between parents i (i = 1, ... n^I) from ^I and j (j = 1, ... n^II) from ^II are produced according to a factorial mating design, the values d_ij can be subdivided like the observations in a two-way table

(4)

with quantitative-genetic interpretation of the overall mean e_.., general epistatic effects e_i. and e_.j from parents i and j, respectively, and specific epistatic effects e_ij as shown in Eq. [5] to [8] (Table 1). All these effects depend on _kl and become zero for absolutely linked loci _kl (= 1, _kl = 1) even in the presence of epistasis.

	MATERIALS AND METHODS

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Plant Materials
A sample of five winter wheat cultivars representing a high yielding population of breeding lines were mated in a factorial design with a sample of six lines representing a population with high baking quality to establish 30 crosses for development of new lines. Cultivars Florian, Jubilar, Pfeuffers Schernauer Winterweizen (Schernauer), Condor, and Breustedts Werla (Werla) were used as the high yielding females and cultivars Brucker Harrachweizen (Harrach), Admonter, Anda, Berthold, Rabe, and Gudin as the males with high baking quality (Table 2). Except for cultivars Admonter and Harrach, which originated from Austria, all cultivars were of German origin and widely grown in Austria and Germany. The parental material has been described in detail by Bohn et al. (1999). For each cross, 44 random F₂-derived lines in F₄ (F_2:4 lines) were developed in the field without artificial selection and tested in hills (Exp. 1). One ear was chosen from each F_2:4 line and multiplied in the field. In generation F₇ and F₈ a sample of 22 unselected lines (F_4:n lines with n = 7,8) were tested in plots (Exp. 2).

Data Analyses
Phenotypic Data
The mean and phenotypic standard deviation of the F_2:4 lines in hills (Exp. 1) were estimated for each cross separately with the entries of each main plot to obtain predictors for usefulness from early generations. Analyses of variance were performed for the split-plot experiments (Exp. 2) for each cross separately with the entries of each main plot to estimate genetic variance components. A random model was used for the phenotypic value x_klm of line m in set l and environment k of a given cross:

with µ for the mean of the cross and with effects e_k for environments (year x location combination), s_l for sets, g_lm for lines within sets, and (se)_kl, (ge)_klm for the corresponding interactions. Here, (ge)_klm is confounded with the plot error. Furthermore, different genotypic and genotype x environment interaction variances are assumed for each cross. The average genetic variance within crosses was estimated by the average of ²_gi, the variance component of g_lm. For the parents, replication effects within environments instead of set effects and homogeneous plot errors for both parental groups was assumed. Genetic component ²_p = /2 was estimated as the average of the two parental components of variance. The variance among crosses ²_c was estimated as the variance component in a combined model of the F_4:n lines with environments, crosses, sets within crosses, and lines within crosses and sets, assuming crosses as random.

The genetic variance ²_gij for each cross together with its standard error (SE) were estimated as described by Searle (1971). From the 30 SE the average SE () was calculated. Homogeneity of ²_gij across all crosses was tested by the Bartlett test (Snedecor and Cochran, 1980) using Satterthwaite's approximation for the degrees of freedom of a linear function of mean squares (Searle, 1971). Differences between means of the parental groups (females vs. males) were tested by appropriate t-tests with the mean square of parents within groups as error term and the epistatic differences with the cross x environment and midparent x environment variance as the error term (see Snedecor and Cochran, 1980). Variance ratios (Table 3) were tested by an approximative two-sided F-test using Satterthwaite's approximation for the degrees of freedom.

(13)

where X_is and X_js are the phenotypic mean values of parents i or j for trait s across environments. The second measure was the multivariate phenotypic distance or Euclidean distance (PE_ij) between two parents i and j determined after Sokal (1961):

(14)

where _is and _js are the standardized phenotypic mean values of parents i or j for trait s, and t is the total number of traits (t = 7).

Estimation of Correlation Coefficients
For each trait, correlation coefficients were calculated for (i)_ij with _ij or ^*_ij, the mean of the F_2:4 lines, and (ii) ²_gij with P_ij, PÊ_ij, and the logarithm of the phenotypic variance of F_2:4 lines, respectively.

	RESULTS

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Means of Parents and Lines Derived from Crosses
The means of the female and male parent groups differed significantly (P < 0.01) only for sedimentation (Table 2). A comparison of the variation within groups with the LSD for the parent means revealed significant genetic variation between parents within groups for all traits except sedimentation and grain protein concentration (see also Table 3 with the F-tests for ²_p).

The contrast between the mean of the midparent values (_..) and the overall mean of all 660 F_4:n lines (_..), which corresponds to the overall mean of epistatic effects ê_.. (see Eq. [5]), was significant (P < 0.05) only for plant height and kernel weight (Table 4). However, for both traits ê_.. was smaller than 3.1% of _... General epistatic effects ê_i. (or ê_.j) were significant in a few cases for heading date, plant height, and kernel weight, but showed no uniform sign. No significant specific epistatic effects (ê_ij) were detected for any of the traits (data not shown).

View this table: [in this window] [in a new window]   Table 5. Mean, minimum, and maximum genetic variance (2gij) estimated from 22 F4:n lines (n = 7, 8) per cross based on 30 winter wheat crosses for heading date, plant height, lodging, kernel weight, and grain yield evaluated in four environments and for sedimentation and grain protein concentration evaluated in three environments. Mean, minimum, and maximum of parental phenotypic Euclidean distance (PÊ) between parents of the 30 crosses.

Estimates of the genetic variance among parents (²_p), among means of crosses (_c), and among F_4:n lines within crosses () were significantly (P < 0.01) greater than zero in most cases except for sedimentation and grain protein concentration (Table 3). On the basis of an approximate two-tailed F-test, the variance ²_c was not significantly different (P < 0.05) from ²_p/2 for all traits. Likewise, the ratio ²_c : ²_g differed significantly (P < 0.05) from 1.0 only for sedimentation.

Prediction of Means and Variances
The cross means _ij were highly correlated (r_p 0.71**) with the midparent values _ij for all traits except grain protein concentration (Table 6). Correlations of _ij with cross means ^*_ij of F_2:4 lines were similarly high (r_p 0.93**) for heading date and plant height but considerably smaller for grain yield. No significant association was found between ²_gij and any distance measure (P_ij, PÊ_ij) on the basis of the parental data. Moderate correlations were obtained between ²_gij and the phenotypic variance of F_2:4 lines for heading date, plant height, and kernel weight but not for grain yield.

View this table: [in this window] [in a new window]   Table 6. Correlations of various predictors based on measures of the parents, F2:4 and F4:n lines (n = 7, 8) with population mean (ij and genetic variance (2gij) among F4:n lines of 30 winter wheat crosses for heading date, plant height, lodging, kernel weight, and grain yield evaluated in four environments and for sedimentation and grain protein concentration evaluated in three environments.

	DISCUSSION

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Comparison of Generation Means
The significant differences between the midparent value _ij and mean _ij of F_4:n lines for some crosses and traits (Table 4) could be attributable to dominance and epistasis as well as maternal effects, natural selection or heterogeneity within lines. By testing F_4:7 or F_4:8 lines, dominance and heterogeneity within lines should be negligible in view of (i) the small amount of heterosis generally observed in wheat (Jordaan et al., 1999), (ii) the small coefficients of dominance effects (1/32 or 1/64) in generations F₇ or F₈, and (iii) the small genetic variance within such lines (²_g = 7/64 ²_A + 455/4096 ²_D, ²_g = 15/128 ²_A + 911/16384 ²_D; see Wricke and Weber, 1986, p. 73). Maternal effects investigated by reciprocal crosses seem to be negligible in wheat (McNeal et al., 1968). Natural selection was also highly unlikely given the high germination rate and absence of winter killing of plants. Hence, we conclude that epistasis was the major cause for the observed differences and used the term "epistatic effects" for the contrast between _ij and _ij.

In general, the epistatic effects rarely exceeded 3% of the corresponding trait mean (Table 4). The significantly negative estimates of e_.. and e_.j detected for plant height and kernel weight might reflect an accumulation of gene combinations in some elite parents with favorable interactions for shortness and reduced grain size, associated with higher grain protein concentration. According to quantitative-genetic expectations (Eq. [5]–[9]), epistasis of type additive x additive between unlinked loci (_kl = 0, _kl = 0) has the strongest effect on the contrasts e_.., e_i., e_.j, and e_ij and might not be uncommon in an allopolyploid species such as T. aestivum. However, when positive and negative epistatic effects are present in the parents, their contribution would cancel each other in the sum.

For grain yield, the overall mean _.. of F_4:n lines was 1.2% higher than _.., the midparent mean (Table 4). This is in close agreement with other results reported in the literature. Busch et al. (1974) detected a 1.6% yield superiority of F_2:5 and F_2:6 lines across 24 wheat crosses over the midparent mean, but individual crosses showed large positive or large negative epistatic effects. Bhatt (1973) reported a 0.5% increase for 11 crosses and Lupton (1961) found a 2.2% increase across 15 crosses. In contrast, Busch et al. (1971) and Dyck and Baker (1975) reported means below the midparent values for a small number of crosses. Summarizing, generation means of unselected inbred lines from crosses may occasionally deviate from their midparent values, but in general the differences are small and can safely be ignored in the choice of parents for cultivar development.

Balance Sheet of Genetic Variation
As a result of segregation and recombination in crosses, the genetic variability can be redistributed among the various states in which it exists in the parents and progenies, but in the absence of selection, mutation, and drift, its total quantity will remain unchanged (Mather and Jinks, 1982). Under these conditions and in the absence of epistasis, Eq. [9] to [12] provide a balance sheet of genetic variation for two parental germplasm pools (Table 1). Accordingly, the genetic variance between the means of crosses (²_c) is equal to half the average variance among parents

where ²_m and ²_f refer to the genetic variance among male and female parents, respectively. By expectation, the average segregation variance among lines within crosses () is equal to ²_c only if (i) the male and female parents both originate from the same population (i.e., ^I = ^II) and (ii) covariances between additive effects of different loci can be ignored or occur only between absolutely linked loci (_kl = 1). However, when the parent populations differ in their allele frequencies and means, this variation (µ^I - µ^II)² = (_k)² will at least partly contribute to an increased variance compared to ²_c (Eq. [9], Table 1).

In accordance with these quantitative-genetic expectations, no significant difference was found between ²_c and ²_p/2 for all traits in our study (Table 3). While ²_c was mostly smaller than , a significant difference between these variances could be confirmed only for sedimentation because of the large standard errors associated with the variance component estimates. The larger estimate of ²_g compared with for sedimentation is consistent with the significant difference in the means of male and female parents for this trait (Table 4), because the latter reflects differences in allele frequencies between both parent populations, which enhance according to theory (Eq. [12], Table 1). Another explanation might be negative covariances between additive effects at unlinked (_kl = 0) or loosely linked loci, which may arise from preponderance of repulsion phase of favorable alleles at different loci in the parents. However, these explanations are rather speculative unless detailed QTL (quantitative trait loci) analyses enable us to monitor allele frequencies and linkage disequilibria for loci affecting the genetic variation of agronomically important quantitative traits.

Prediction of Means and Selection Gain among Crosses
Application of the usefulness criterion and calculation of the selection response R_c requires prediction of the cross means c_ij. Our results confirmed that midparent values _ij are fairly good predictors of _ij (Table 6, 0.71 r_p 0.90 except grain protein concentration). Similar correlations (0.73 r_p 0.78) between both measures were found in earlier studies for grain yield in wheat (Busch et al., 1974; Lupton, 1961). Because _ij and _ij were highly correlated, the selection response R_c based on indirect selection for _ij is expected to be high (based on Eq. [19.5], Falconer and Mackay, 1996), given a high heritability for the parental phenotypic means. The correlations of cross means of F_2:4 lines, ^*_ij, with _ij were similarly high as the correlations of _ij with _ij for the highly heritable traits heading date and plant height, but considerably lower for traits grain yield and kernel weight (Table 6). This could be attributable to the following reasons: (i) F_2:4 lines were tested in hills in two environments, whereas parents were evaluated in plot trials across four environments and (ii) hill plots in early generations are less reliable than plot experiments with pure-breeding lines because of competition effects and larger experimental errors (Schut et al., 1998). In conclusion, prediction of c_ij by the midparent value _ij is clearly the method of choice because for promising potential parents, reliable phenotypic data are generally available to breeders from previous tests or can readily be obtained before producing or even testing progeny from selfing generations.

Variation and Prediction of the Segregation Variance within Crosses
Heterogeneity of ²_gij among crosses was found only for a few traits (Table 5). Possible explanations for this result are (i) the variation among the true values of ²_gij was small and/or (ii) the precision of estimates of ²_gij was poor and not sufficient to detect existing differences among crosses. For unrelated parents from populations in linkage equilibrium, quantitative-genetic expectations show that the variance of ²_gij among crosses converges towards zero at the order O(1/L) as the number L of independently segregating QTL with equal contributions to the trait variation increases (Melchinger, 2000, unpublished results). Thus, for truly polygenic traits such as grain yield, one can expect only a small variation in ²_gij among crosses from unrelated lines. However, the second reason cannot be ruled out because in our study the standard deviation of ²_gij among crosses exceeded the average standard error of ²_gij by more than 30% only for heading date, lodging, and kernel weight (Table 5). Hence, the use of 22 F_4:n lines per cross was presumably not adequate to estimate ²_gij for individual crosses with sufficient precision. However, reducing the standard error of ²_gij by one half would require testing about 100 lines per cross, which is not feasible for a larger number of crosses.

In contrast to the prediction of c_ij, correlations of ²_gij with distance measures P_ij and PÊ_ij were small and varied in sign (Table 6). Consistent with our findings, Busch et al. (1971) reported that crosses between high and low yielding lines, corresponding to a large P_ij value, released no significantly larger segregation variance than crosses within the high or low parent group. Likewise, PÊ_ij was also an unreliable predictor of ²_gij in oat, Avena sativa L. (Moser and Lee, 1994). Three reasons may explain the poor association between ²_gij and its predictors.

1. The parents, and consequently P_ij and PÊ_ij, are measured with low precision. This is rather unlikely in our study given the high heritabilities of the parental means for most traits (Table 2).
   
2. Estimates of ²_gij have a high standard error and, consequently, a low repeatability. This could be a major cause for most traits as discussed above.
   
3. No correlation exists between the "true" values of ²_gij and PE_ij or PD_ij. The latter reason most likely applies to PE_ij, which is not trait specific but rather measures the overall diversity of parents and, therefore, does not reflect the true genetic diversity at QTL contributing to ²_gij for a given trait.
   

The phenotypic variance of F_2:4 lines showed significant but low correlations with ²_gij of F_4:n lines from the same crosses. The correlations were consistently higher for traits with smaller standard errors of ²_gij. However, determining the genetic variance in generation F₄ to predict the usefulness of a cross is too late for practical breeding purposes because parents have been chosen already and selection within crosses has already started.

In general, plant breeders use pedigree information to guess roughly the magnitude of the segregation variance. Application of molecular markers for estimating the relationship between parents may improve the situation, if molecular markers are closely linked with QTL involved in the trait expression. However, strong linkage disequilibrium between molecular markers and QTL is expected to exist only between parents originating from different germplasm pools. In our companion study (Bohn et al., 1999), the parental lines were genotyped with 21 SSR (simple sequence repeat) and 16 AFLP (amplified fragment length polymorphism) primer–enzyme combinations but no significant association was found between genetic distances on the basis of these markers and ²_gij for all seven traits. In summary, we conclude that prediction of ²_gij remains yet an unsolved problem.

Prediction of Usefulness
The usefulness of a cross, U_ij = c_ij + i h_{ij gij}, is a function of the parameters c_ij and ²_gij assuming i h_ij to be a constant with a value close to 1.0. The variation of U_ij depends on ²_c and var. In this study, ²_c (Table 3) was at least five times larger than var (calculated from Table 5 after Kendall and Stuart, 1963, Chap. 10.6) for all traits except grain protein concentration and lodging. The true variation in genetic variances among crosses is expected to be smaller taking into account the large error of variance components. Consequently, estimates of U_ij (here estimated by the mean of the four best lines, data not shown) were only loosely associated with the phenotypic or genetic standard deviations of the F_2:4 and F_4:n generations. Hence, the additional contribution of _gij for predicting U_ij was negligible for most traits. This is consistent with reports in maize (Melchinger et al., 1998) and faba beans, Vicia faba L. (Gumber et al., 1999). The low contribution of differences in _gij to the variation of U_ij may be surprising and has apparently been overlooked in the literature.

A key question of the breeder is, which proportion of the resources should be allocated to the selection among vs. within crosses. The answer is mainly determined by the fact that information on _ij is available from former breeding cycles without additional costs. The greater the correlation coefficients r(_ij, _ij) the more powerful is the selection between parents and the greater should be the selection intensity between crosses (Utz and Schnell, 1979). If no information about the parents exists, several authors (Yonezawa and Yamagata, 1978; Weber, 1979) recommended producing a maximum of crosses with a minimum of lines within a cross. However, even in this unfavorable situation, Schnell (1982) pointed out that it should be more economical to test n parents instead of progenies of the n(n - 1)/2 possible crosses.

	CONCLUSIONS

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On the basis of our results with winter wheat, parental means can be successfully applied for predicting the usefulness of their crosses. In the case of two different parental germplasm pools, the differences in gene frequencies will increase the genetic variance within crosses as compared with the variance between crosses. As a consequence, this will increase the chance of selecting superior transgressive lines. Estimating the genetic variance and epistatic effect of a cross is not recommended because of their large standard errors, the too late assessment during the breeding process, and the expected low influence on the variation in the usefulness criterion between crosses. Early evaluations of bulks or lines in autogamous crops most likely produce inaccurate information because of the masking effects of dominance and/or competition and the limited seed supply in the early generations. Two additional reasons make the use of midparent values attractive for the selection between crosses.

1. Agronomic information of potential parents is usually available without additional tests before crosses are produced.
   
2. Given a fixed budget or test capacity, indirect selection for means of crosses based on the parental performance will result in a much higher selection intensity than direct selection based on progeny performance of crosses.
   

	ACKNOWLEDGMENTS

 
The authors thank the late Dr. M.-L. Snoy and W. Daum (State Breeding Institute, University of Hohenheim) for the highly skilled conduct of the long-term experiment. This paper is dedicated to Prof. Dr. Dr. h.c. F.W. Schnell on the occasion of his 88th anniversary, whose ideas were instrumental in the design and analysis of this study.

Received for publication October 13, 2000.

	REFERENCES

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 

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