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Crop Science 41:302-308 (2001)
© 2001 Crop Science Society of America

CROP BREEDING, GENETICS & CYTOLOGY

Evaluation of U.S. and Yugoslavian Maize Populations as Sources of Favorable Alleles

Slobodan Trifunovica, Ivan Husica, Milorad Rosulja and Radomir Stojsinb

a Maize Research Institute, Zemun Polje, S. Bajica 1, 11080 Belgrade-Zemun, Yugoslavia
b Monsanto, Agricultural sector, Mailzone GG6A, 700 Chesterfield Parkway North, St. Louis, MO 63198

Corresponding author (sltrifun{at}yahoo.com)


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Choice of an appropriate donor of alleles for use in reselection programs of existing inbred lines of maize (Zea mays L.) is crucial to the success of such programs. Well-adapted local populations or exotic improved populations might be used as donors to improve a target genotype. The objectives of this study were to: (i) evaluate U.S. and Yugoslav maize populations as donors of favorable alleles for improvement of two single cross hybrids, (ii) estimate Dudley's relationship values to determine which inbred parent should be improved, and (iii) compare four estimators of the value of populations: Dudley's minimally biased estimators (Lplµ*), minimum upper bound (UBND), predicted three-way cross (PTC), and net improvement (NI). Lplµ*, UBND, PTC, and NI showed significant differences among donors for grain yield. The highest values of favorable alleles were detected in populations, which had already undergone some type of family-based recurrent selection for grain yield. The evaluation of Dudley's relationships between donors and parents of elite hybrids generally agreed with pedigree information. The improvement of both hybrids should be done with populations EP1, BS12C8, BS26, and ZPSyn1. The population EP1 can be used for comparative improvement of all three traits in the hybrid B73 x Mo17. Simultaneous improvement of grain yield and ear length in the hybrid A82/9 x L155 can be achieved with several donor populations. Rank correlations among applied estimators were positive and generally highly significant. The largest correlation values for grain yield were detected between Lplµ* and PTC.

Abbreviations: Lplµ*, Dudley's minimally biased estimators • NI, net improvement • PTC, predicted three-way cross • UBND, minimum upper bound • BSSS, Iowa Stiff Stalk Synthetic • FAO, Food and Agriculture Organization • RCBD, randomized complete block design


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
THE UTILIZATION PERIOD OF MAIZE HYBRIDS is limited and they are usually replaced with newer hybrids with better agronomic traits and properties required on the market. Reselection of inbred parents of existing hybrids, by the pedigree method of selection (Bernardo, 1990a), is the common method used in commercial maize breeding programs. In this breeding system, an appropriate donor of desirable traits should be identified. Selection of donors is crucial to the success of such breeding programs (Hallauer and Miranda, 1988).

The largest number of favorable alleles is accumulated in the best hybrid, grown in a certain area (Dudley, 1984a,b). The identification of additional favorable alleles for quantitative traits not present in that hybrid is one of the most important tasks facing a breeder. Dudley (1984a)(b) developed procedures for identifying donors containing alleles not present in parental inbreds. At a later time, Dudley (1987a)(b) modified the theory to remove the assumption that the average frequency of favorable alleles (Pj) at the Class j loci was equal to the average frequency of favorable alleles (Pk) at the class k loci. This assumption could lead to erroneous estimates of Lplµ* (Gerloff, 1985). Pfarr and Lamkey (1992), as well as Zanoni and Dudley (1989) compared the original and the modified method and found the modified procedure to be superior.

Fabrizius and Openshaw (1994) studied 20 donor maize populations. They contained 0, 25, 50, 75, and 100% of new germplasm in relation to the target elite hybrid under improvement. Five population estimators were applied: relative number of favorable alleles (Lplµ*) lacking in inbreds of the elite hybrid (Dudley, 1987b), minimum upper bound (UBND) (Gerloff and Smith, 1988), net improvement (NI) (Bernardo, 1990a,b), predicted three way cross (PTC) (Hallauer and Miranda, 1988), and testcross of the population to the single cross hybrids (TCSC) (Kramer and Ullstrup, 1959; Stuber, 1978). Populations with high percentages of new germplasm were better donors of favorable alleles. On the basis of rank correlations, all statistics except NI ranked populations similarly. The NI statistic was unable to distinguish populations from one another and had a large standard error (SE).

Dudley et al. (1996) studied 20 improved populations as sources of favorable alleles for three elite single cross hybrids. For grain yield, 15 of these 20 populations had significantly high relative estimates of favorable alleles, while none of the populations showed potential for reducing ear height. Lplµ* values for grain yield increased as the yield of the target hybrids decreased. This was expected because the lower the yield of the target hybrid, the larger the number of loci lacking favorable alleles.

Lplµ*, UBND, PTC, and NI are all biased estimates of the relative number of favorable alleles at the class l loci. A bias exists because there is a difference between the expectations of these statistics and the true parameter value. Empirical results fail to confirm the expectation due to sampling error, epistasis, or unequal genetic effects among loci. This bias will change with the choice of estimator and the genetic populations being evaluated (Fabrizius and Openshaw, 1994). While Lplµ*, UBND, and PTC estimate potential improvement likely to be achieved, the net improvement statistic (NI) was proposed to identify populations that could provide an immediate contribution to a reference hybrid. Hogan and Dudley (1991) and Fabrizius and Openshaw (1994) have shown the effectiveness of Dudley's method, compared to UBND, PTC, and NI estimators. Dudley's method has a smaller SE than the other estimators (Fabrizius and Openshaw, 1994; Bernardo, 1990b). Dudley's theory also provides more useful information than the other three methods.

It is assumed that the well adapted local populations or populations resulting from some type of family-based recurrent selection have a satisfactory level of favorable alleles and can be used as donors for improving target genotypes. Heterotic patterns among U.S. Corn Belt and Yugoslavian maize populations studied by Misevic (1989) suggested the possibility of using Yugoslav local varieties as an alternative heterotic pattern to BSSS (Iowa Stiff Stalk Synthetic) or ‘Lancaster Sure-Crop’.

The objectives of this study were to: (i) evaluate U.S. and Yugoslav populations as donors of favorable alleles for improvement of two single cross hybrids, (ii) determine which inbred parent should be improved, and (iii) compare the efficiency of applied estimators to rank populations according to their values as donors of favorable alleles.


    MATERIAL AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Twelve populations (Table 1) were chosen as potential donors of favorable alleles for improving two target hybrids, B73 x Mo17 and A82/9 x L155. Eight populations were of Yugoslav origin and four populations (BS12C8, BS26, AS5 and AS6) originated in the USA. Five out of eight Yugoslav populations (DZ1215, DB1924, BZ1165, DB1208 and BB1257) are open-pollinated varieties from different parts of the former Yugoslavia. The other three Yugoslav populations (ZPSyn1, 1/9B and EP1), and each of the four U.S. populations have undergone some type of family-based recurrent selection. B73 (BSSSC5) and Mo17 (C103 x 187-2) are U.S. public inbreds, while A82/9 (A662 x B73) and L155 (C 123 Ht) are proprietary inbred lines from the Maize Research Institute, Zemun Polje. Both hybrids represent the same heterotic pattern (BSSS x Lancaster Sure Crop), but belong to different Food and Agriculture Organization (FAO) corn maturity groups. The hybrid B73 x Mo17 is of FAO 700, while the hybrid A82/9 x L155 belongs to FAO 450.


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Table 1. Maize populations evaluated as potential donors of favorable alleles to two single cross hybrids and their parentage in Yugoslavian environments

 
Twelve populations were crossed to inbred lines B73, Mo17, A82/9, and L155. Each population x inbred line cross was represented by approximately 100 ears and a bulk sample was formed.

Three independent experiments were conducted. In Exp. 1, the cross between inbreds B73 and Mo17 was used as the target hybrid to be improved, and was planted with the 24 crosses (populations by inbred parents of the target hybrid). A randomized complete block design (RCBD) with three replications was used. All entries were evaluated in two-row plots (7.28 m2) with 54 900 plants ha-1 as the population density.

Twenty-five entries (24 crosses of populations to inbred parents of the target hybrid, as well as the hybrid A82/9 x L155) were evaluated in Exp. 2. This experiment was also arranged in a RCBD with three replications. Population density was 62 100 plants ha-1 and two-row plots (6.44 m2) were the experimental units.

The third trial was composed of the four inbreds (parents of the two target hybrids) and eight additional inbreds (B84, CM105, N152, L70/9, L105, Td81, ZPL 39, and ZPL 373/9) arranged in a four-replicate RCBD with 40 plants per plot (62 100 plants ha-1). Two-row plots (6.44 m2) were used.

The three experiments were grown together at three locations in Yugoslavia (Zemun Polje, Indjija, and Beèej) in two years (1996 and 1997). The soil type at all three locations is calcareous chernozem (fine-loamy, mixed, active, mesic, Typic Calcixeroll). Fertilizer was applied at a rate of 400 kg ha-1 of 10:30:20 (N:P:K) preplowing, and 200 kg ha-1 of urea (46% of N) at seed bed preparation. Planting and harvesting were done by hand. Plots were over-planted and then thinned to desired density. Grain yield measured for each plot was converted to Mg ha-1 and adjusted to 140 g kg-1 moisture. Ear length (cm) was measured on 10 plants per entry from each replication after harvest, while grain moisture (g kg-1) was recorded at harvest. Common cropping practices for maize production were applied.

Each location x year combination was considered a random environment in the analysis of variance. For each environment, all three experiments were analyzed as a RCB design using the MSTAT-C program (MSTAT-C, 1988). The genotype x environment interaction mean square was used to calculate standard errors of all statistics reported. Mean grain yield over six environments was used to estimate the relative number of favorable alleles present in the donor populations and not present in the hybrid being improved (Lplµ*). Modified procedures were used to evaluate new favorable alleles (Dudley, 1987b). The UBND estimates were calculated as the minimum of {[(I1 x Py) - I1], [(I2 x Py) - I2]} according to Gerloff and Smith (1988). The PTC was computed as [(I1 x Py) + (I2 x Py)]/2 (Hallauer and Miranda, 1988). The NI was calculated according to Bernardo (1990b). All four estimators were compared by Spearman's rank correlation coefficient (Steel and Torrie, 1960).

Positive and high estimates of the relative number of favorable alleles (Lplµ*) are desirable for traits inherited dominantly. Jqjµ* and Kqkµ* indicate the relative frequency of recessive alleles. The Lplµ* - (Jqjµ* or Kqkµ*) relation is used as an indicator of whether to self from the F1 generation (inbred x population) or to backcross to the inbred line prior to selfing. If the relative number of favorable alleles (Lplµ*) is equal to the relative number of unfavorable alleles (Jqjµ* or Kqkµ*), selfing is recommended, but if the relative number of unfavorable alleles (Jqjµ* or Kqkµ*) is significantly higher than the relative number of favorable alleles (Lplµ*), backcrossing to the inbred parent is performed. The decision whether to consider Jqjµ* or Kqkµ* depends on the relationship of Py to I1 and I2. If the population is more related to I1, Jqjµ* is taken into consideration. On the other hand, if it is more related to I2 then Kqkµ* is a measure of the relative number of recessive alleles.

The relationship values are estimated according to the following formula of Dudley (1988):

where (I1 x Py) and (I2 x Py) are phenotypic values of crosses among inbred lines and populations. If the relationship values are positive, the population is more related to I1, and conversely, if they are negative, the population is more related to I2. If recessive alleles are favorable in some traits, the values of populations can be measured by the expression (Jqjµ* or Kqkµ*) - Lplµ*. Significant and positive estimates suggest that the population can contribute to improvement of the observed trait in the elite hybrid.

Populations can be used as direct sources for development of inbred lines. The relative values of the populations as direct sources of inbred lines can be estimated by the expression Lplµ* + Jpjµ* or (I2 x Py) - I2, if I2 is selected to be the inbred parent together with the inbred that may be eventually derived from the donor population. Likewise, the expression Lplµ* + Kpkµ* or (I1 x Py) - I1, is used for estimation if I1 is selected to be the inbred parent together with the inbred derived from donor population.


    RESULTS AND DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Grain Yield
The mean comparison of population x inbred line (I1 x Py, I2 x Py) crosses indicates significant differences in grain yield (Table 2). Mean grain yield varied from 8.07 to 13.72 Mg ha-1. These differences were expected, because certain populations were assumed to be more related to one parental inbred than another on the basis of pedigree. On the average, yields of population x B73 crosses were significantly higher yielding than population x Mo17 crosses. Likewise, yields of population x A82/9 crosses were significantly higher than populations x L155 crosses (Table 2). None of the B73 and Mo17 population crosses yielded more than B73 x Mo17. Some populations crosses, however, outyielded the A82/9 x L155 target hybrid. Significant differences in average grain yield were detected among the inbred lines per se (Table 2).


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Table 2. Mean grain yield, ear length, and grain moisture of populations x inbred line crosses, inbreds per se, and target hybrids combined over six environments

 
As grain yield is mainly controlled by dominant gene effects in pure line hybrid combinations (Gamble, 1962; Moreno-Gonzáles and Dudley, 1981; Trifunovic et al., 1998), dominant alleles were considered favorable for improvement of this trait in observed hybrids. Populations that have positive and large estimates of Lplµ* represent good sources for hybrid improvement (Table 3).


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Table 3. Dudley's minimally biased estimators of 12 maize populations for grain yield Lplµ*, relationship values [(I2 x Py) - (I1 x Py) + (I2 - I1)/2], differences [Lplµ* - (Jqjµ* or Kqkµ*)] and values as direct sources for improvement of target hybrids B73 x Mo17 and A82/9 x L155 for grain yield

 
Ten of 12 populations had significant and positive estimates of the relative number of favorable dominant alleles Lplµ* for improvement of both elite hybrids (Table 3). Stojsin and Kannenberg (1995) explained that getting similar values of Lplµ* for a donor population for improvement of both target hybrids resulted from the fact that both target hybrids had one common inbred parent. In our study, the target hybrids were the representatives of the same heterotic pattern BSSS x Lancaster Sure Crop, so similar trends of estimated parameters for donor populations are expected. All populations that have undergone some type of family-based recurrent selection for grain yield showed significant values of Lplµ*. The highest Lplµ* values were detected in two U.S. populations (BS12C8 and BS26) and two Yugoslav populations (EP1 and ZPSyn1). Populations DB1208 and BB1257 (Table 3) expressed the lowest relative values of favorable alleles. These populations were collected from different geographic regions of the former Yugoslavia with no previous selection for grain yield. It seems that good adaptation alone of local maize populations does not justify their use as donors of favorable alleles. Hence, the choice of such populations should be based on testing. Dudley (1988) reported that seven out of eight populations with significant estimates of the relative number of favorable alleles for grain yield had a history of selection for grain yield, while Stojsin and Kannenberg (1995) indicated generally lower levels of favorable alleles in Cycle 0 when compared with populations that had undergone several cycles of selection.

Dudley's relationship value parameter indicates the relationship between the donor and the inbred line I1 or I2. This relationship is one of the most important factors in applied breeding programs because it influences the improvement procedure of a target hybrid. The inbred to be improved should be the one most closely related to the donor of favorable alleles. Grain yield is the trait for which evaluation of relationship is the most important because the calculation of relationship values is based on estimates of heterosis (Stojsin and Kannenberg, 1995). If the value [(I2 x Py) - (I1 x Py) + (I1 - I2)]/2 is positive, the population is more related to I1 and if it is negative, the population is more related to I2.

Populations BS12C8, BS26, AS6, and ZPSyn1 were closely related to Lancaster inbreds Mo17 and L155 (Table 3), which was in accordance with the pedigree information. Population EP1 was closely related to BSSS parents (Table 3), which is not in agreement with pedigree information. We assume that heterotic performance was not as expected due to adaptation problems encountered by exotic germplasm incorporated in the population (Table 1). Populations AS5 and 1/9B, although related to BSSS inbreds, showed no significant relationship to any of the inbred parents (Table 3), most likely due to the hybrid (population x inbred) x environment interaction. Three (DZ1215, DB1924, and BZ1165) of five open pollinated populations, having significant values of favorable alleles for grain yield, showed significant relationship to Lancaster inbreds, while the populations DB1208 and BB1257 were unrelated to inbred parents of elite hybrids (Fig. 1) . Zanoni and Dudley (1989), Hogan and Dudley (1991), and Pfarr and Lamkey (1992) also confirmed the general agreement of relationship values with pedigree information.



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Fig. 1. Estimates of Dudley's relationship determined on the basis of yield data between populations and parent inbred lines. Positive values indicate the population is more related to Iowa Stiff Stalk Synthetic related lines B73, A82/9 and negative values indicate more relationship to Lancaster Sure-Crop related lines Mo17 and L155

 
Significant negative differences between Lplµ* and Jqjµ* or Kqkµ* (a higher number of recessive unfavorable alleles than favorable ones), indicate that backcrossing prior to selfing and development of new inbred lines would be preferred. Populations BS26 and BS12C8 had an equal number of dominant favorable and recessive unfavorable alleles (Table 3), indicating that the selection process can start from the F2 generation (population x inbred). For other populations (as donors to the hybrid B73 x Mo17), a need for backcrossing to a more closely related parent was indicated. This was expected in populations with less selection pressure. In the hybrid A82/9 x L155, backcrossing to the donor population is recommended in the populations EP1, BS12C8, and BS26 while backcrossing to the inbred parent is recommended for the rest of populations (with the exception of ZPSyn1) prior to selection [Table 3, Lplµ* - (Jqjµ* or Kqkµ*)]. Results of this experiment, are in accordance with conclusions that Lplµ* values for donors increased and needs for backcrossing decreased for the lower yielding target hybrids (Dudley et al., 1996). This was expected, as lower yields of the observed hybrid mean that a greater number of loci lack favorable dominant alleles.

Populations were also ranked for their value as direct sources of inbred lines crossed to one of the parents. The populations BS26 and BS12C8 were the best direct sources of inbred lines in combination with B73 and A82/9 (Table 3). If inbred Mo17 or L155 was one of the parents, then EP1 was the best population. The potential utility of a population as a source of new inbreds was not necessarily the same as its value as a source of favorable alleles for improvement of the elite single cross hybrid (Table 3), which is in agreement with results obtained by Dudley (1988). In this experiment, populations DZ1215, DB1924, and BS26 were closely related to inbred Mo17 according to relationship value (Table 3). They were estimated as better direct sources of new inbred lines than as donors of alleles to the hybrid B73 x Mo17. This is in agreement with Misevic (1990) for target hybrids with one parent genetically similar to the donor. The use a donor as a direct source for inbred line development would likely be more promising than use of the donor as a source of new favorable alleles.

Ranking of populations as donors of favorable alleles by the estimators Lplµ*, UBND, PTC and NI were similar (Table 4). All estimators, except UBND in the target hybrid B73 x Mo17, ranked the same populations (BS12C8, BS26, EP1, and ZPSyn1) in the first four places. Ranking of the three least useful populations as donors of favorable alleles was identical (Table 4).


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Table 4. Estimates of Lplµ*, UBND, PTC, NI and their rank in 12 populations for the target hybrids B73 x Mo17 and A82/9 x L155

 
Rank correlation among applied estimators showed positive, high and significant values for both hybrids (Table 5). In the target hybrid B73 x Mo17, populations were identically ranked by estimators Lplµ* and PTC, while the highest estimate of rank correlation (0.986**) was determined between estimators Lplµ* and NI in the target hybrid A82/9 x L155 (Table 5). Similar results were obtained by Bernardo (1990b), who found positive and significant rank correlations for grain yield among estimators Lplµ*, UBND, PTC, and NI in the two studied hybrids.


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Table 5. Correlation coefficients among studied parameters for grain yield in the hybrids B73 x Mo17 (above diagonal) and A82/9 x L155 (under diagonal), respectively

 
Fabrizius and Openshaw (1994) found statistically significant rank correlations (from 0.84** to 0.95**) for grain yield among Lplµ*, UBND, and PTC. Estimator NI was less able to detect differences among populations because of larger standard errors. In our study, significant correlations of NI with the other three estimators were probably due to large differences (as a donor of favorable alleles) between populations. Such populations can be properly ranked with less sensitive estimators.

The advantage of the PTC estimator is that data may be obtained with no evaluation of target hybrids or parent lines in the experiment. However, these data are needed for the estimation of the relationship between the donor and the inbred parent.

Ear Length
Ear length was chosen because of specific demands of the Yugoslav market for hybrids with long ear. Significant differences in ear length among hybrids and among inbreds were found (Table 2). Population x Lancaster line (Mo17 or L155) crosses had significantly longer ears on the average than population x BSSS line (B73 or A82/9) crosses.

Nine populations had significant Lplµ* values in the target hybrid B73 x Mo17 (Table 6), indicating presence of favorable alleles for ear length. Three populations (BS26, BS12C8 and EP1), ranked high for grain yield also, had high values of new favorable alleles for ear length. Since positive values of the difference Lplµ* - (Jqjµ* or Kqkµ*) were detected only in the population EP1, special attention should be paid to other populations in multi-trait selection. All populations, with the exception of BZ1208, had significant values of favorable alleles for ear length in the target hybrid A82/9 x L155 (Table 6). Because all populations had a negative value of the difference Lplµ* - (Jqjµ* or Kqkµ*) it will be necessary to give serious consideration to ear length during selection.


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Table 6. Estimates of the relative number of favorable alleles for ear length and grain moisture in B73 x Mo17 and A82/9 x L155 target hybrids

 
Grain Moisture
Significant differences among hybrids and inbreds were found for grain moisture (Table 2). Mean grain moisture of hybrids was 248.6 g kg-1. The target hybrid B73 x Mo17 was higher in grain moisture than the overall mean.

Eight populations in the B73 x Mo17 group had positive values of the difference (Jqjµ* or Kqkµ*) - Lplµ,* indicating the presence of favorable alleles for lower grain moisture (Table 6). The highest values of favorable alleles for low grain moisture were detected in the populations DB1208 and BB1257 (Table 6), which had low values of Lplµ* for grain yield. Only the population EP1, which was also highly ranked for grain yield, had more favorable recessive (Jqjµ* or Kqkµ*) than unfavorable dominant (Lplµ*) alleles for low grain moisture, suggesting the possibility of its use in simultaneous improvement of these two traits. The populations BS26, BS12C8, and ZPSyn1, highly ranked for grain yield, did not have positive values of the difference (Jqjµ* or Kqkµ*) - Lplµ* for the A82/9 x L155 target hybrid. Population DB1208, which was ranked low for grain yield, was the only population with a significant positive estimate of the difference (Jqjµ* or Kqkµ*) - Lplµ,* suggesting that none of the studied populations can be used in simultaneous improvement of grain yield and grain moisture.


    SUMMARY
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
The highest values of favorable alleles for grain yield were detected in two U.S. populations (BS12C8 and BS26) and two Yugoslav populations (EP1 and ZPSyn 1), i.e., populations which had already undergone some type of family-based recurrent selection. Open-pollinated populations, which were collected from different geographic regions, expressed the lowest relative values of favorable alleles. Only the population EP1 can be used for comparative improvement of all three traits in the hybrid B73 x Mo17. Simultaneous improvement of grain yield and ear length in the hybrid A82/9 x L155 can be achieved with several donor populations, while there is not a single population highly ranked for grain yield with favorable alleles for low grain moisture. One target hybrid should be enough to evaluate populations as donors of favorable alleles for improvement of a heterotic pattern. Dudley's relationship values for grain yield generally confirm the expectations based on pedigrees. Rank correlations among applied estimators were positive and generally highly significant. The largest correlation values for grain yield were detected between Lplµ* and PTC.


    ACKNOWLEDGMENTS
 
We gratefully acknowledge the help of Dr. Mile Ivanovic for valuable discussions and suggestions.

Received for publication September 2, 1999.


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 




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V. M. Rodriguez, R. A. Malvar, A. Butron, A. Ordas, and P. Revilla
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