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Published online 1 September 2007
Published in Crop Sci 47:1905-1913 (2007)
© 2007 Crop Science Society of America
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CROP BREEDING & GENETICS-NOTES

How Many Parents Give the Highest Yield in Predicted Synthetic and Composite Populations of Maize?

F. J. Kutkaa,* and M. E. Smithb

a Dickinson Research Extension Center, North Dakota State Univ., 1041 State Ave., Dickinson, ND 58601
b Dep. of Plant Breeding and Genetics, Cornell Univ., Ithaca, NY 14853

* Corresponding author (frank.kutka{at}ndsu.edu).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
Some U.S. farmers are still interested in open-pollinated (OP) maize (Zea mays L.), but most varieties are low yielding. How would one develop high-yielding OP varieties, and what are their commercial prospects? To answer this question, we analyzed data from published diallel experiments using Wright's equation. There were seven diallels with inbreds and 14 with populations. The number of inbreds needed to form high yielding synthetics was on average from five to eight lines. The highest predicted yields for composites were on average with three to seven populations. The potential of synthetics and composites as OP varieties in the USA has not been fully examined, though these would probably not be economical for grain in the U.S. Corn Belt. However, their yields may show improvement over current OP varieties and they may be commercially viable in some limited circumstances.

Abbreviations: CIMMYT, Centro Internacional de Mejormiento de Maiz y Trigo (International Center for Improvement of Maize and Wheat) • OP, open-pollinated

How Many Parents Give the Highest Yield in Predicted Synthetic and Composite Populations of Maize?

F. J. Kutkaa,* and M. E. Smithb

a Dickinson Research Extension Center, North Dakota State Univ., 1041 State Ave., Dickinson, ND 58601
b Dep. of Plant Breeding and Genetics, Cornell Univ., Ithaca, NY 14853

* Corresponding author (frank.kutka{at}ndsu.edu).

Some U.S. farmers are still interested in open-pollinated (OP) maize (Zea mays L.), but most varieties are low yielding. How would one develop high-yielding OP varieties, and what are their commercial prospects? To answer this question, we analyzed data from published diallel experiments using Wright's equation. There were seven diallels with inbreds and 14 with populations. The number of inbreds needed to form high yielding synthetics was on average from five to eight lines. The highest predicted yields for composites were on average with three to seven populations. The potential of synthetics and composites as OP varieties in the USA has not been fully examined, though these would probably not be economical for grain in the U.S. Corn Belt. However, their yields may show improvement over current OP varieties and they may be commercially viable in some limited circumstances.

Abbreviations: CIMMYT, Centro Internacional de Mejormiento de Maiz y Trigo (International Center for Improvement of Maize and Wheat) • OP, open-pollinated


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
THERE IS SOME renewed interest in maize (Zea mays L.) seed saving among organic and other low-input farmers in the USA and Canada (Smith et al., 2003; Lamkey, 2001). When they grow open-pollinated (OP) varieties, it is most often for silage purposes (V. Kucyk, personal communication, 2003; N. Place, personal communication, 2000) and forage yields of some OP varieties have compared favorably with those of hybrid varieties (e.g., Smith et al., 2003; Bertoia, 2001; Everett and Crowder, 1965; Conlon, 1960), though not always (Lauer et al., 2001). However, OP grain yield is usually less than 70% of hybrid yields (e.g., P. Carr, personal communication, 2007; K. Lamkey, personal communication, 2003; Carena, 2005a; Kutka et al., 2004; Pratt, 2004; Smith et al., 2003; Bertoia, 2001). These relatively low grain yields of OP populations leave farmers in the USA who wish to save maize seed for grain production at a distinct economic disadvantage (Kutka, 2005). Even much improved populations available from universities, like recent cycles of the populations NDSAB (from North Dakota State University; Carena, 2005a, 2005b) and CG-SS (from the University of Guelph; Lee et al., 2003), fall short of economic break-even points (75–90% of hybrid yield) calculated with the U.S. grain prices and costs of production from 2004 and 2005 (Baltensperger et al., 2005; Kutka, 2005; Kutka et al., 2004). Recent grain prices would likely raise these break-even points much higher still.

Seed-saving farmers and public breeders in the USA can improve OP populations through selection. However, even with the most rapid results seen for gridded mass selection or modified ear-to-row selection, it is unlikely that OP populations with economically competitive grain yields would result for several decades (e.g., Weyrich et al., 1998; Gardner, 1978). It appears that if farmers were to have economically competitive OP populations they would need new populations.

Synthetics are random-mating populations formed by intermating a group of inbred lines (Bernardo, 2002). This approach to higher yields in maize was proposed by Jones (1918) and later confirmed in the literature review of Hayes (1963). Sprague and Jenkins (1943) found that their synthetics yielded no better than OP varieties, but did suggest it was feasible to find combinations that would outyield OP populations. Combining ability was ignored in this study (Hayes et al., 1955), and Hayes et al. (1944) reported the formation of an eight-line synthetic that was competitive with Minhybrid 403 for grain yield. Yields of advanced generation synthetics formed by Lonnquist and McGill (1956) were higher than parent OP populations by 9 to 22% and reached 88 to 102% of the yield of US 13, the double cross hybrid check. Cordova and Marquez-Sanchez (1976) developed a five-line synthetic that yielded as well as two single cross hybrids and better than two double cross hybrid checks. These support the approach promoted by CIMMYT (1999) in forming high-yielding synthetics based on 8 to 10 maize families, including inbreds.

Composites are random-mating populations formed by intermating a group of populations. This can quickly increase yield and useful genetic diversity in OP populations (e.g., Rincon-Sanchez and Ruiz-Torres, 2005; Miranda Filho and Vencovsky, 1984; Castro et al., 1968; Gardner and Paterniani, 1967), though attention must be paid to how composites are formed to achieve the highest yields (Marquez-Sanchez, 1992b). In some cases, composite populations have yielded as well as the best varietal hybrids and nearly as well as commercial double cross hybrids (Silva and Miranda Filho, 2003; dos Santos et al., 1994; Naspolini Filho et al., 1981). A composite of Mexican OP populations and a few early generation inbred lines, formed in the 1940s, outyielded the best local OP populations by 15% and more (Matchett, 2006).

While many studies in the last 40 years have examined the issues surrounding the formation of these populations (Sahagun-Castellanos, 2001), few maize breeders or farmers in the USA or Canada today have experience with the formation of synthetics or composites for release as high-yielding OP varieties. An aid for this purpose is the formula based on work by Wright (1922) with inbred lines of cavies (guinea pigs [Cavia porcellus L.]) and first published by Kinman and Sprague (1945). "Wright's equation" is F2 = F1 – (F1 – P)/n, where F2 represents the expected performance of the F2 generation of the synthetic or composite, F1 represents the average performance of all possible single crosses among the parents being considered, P represents the average performance of those parents, and n represents the number of parents. The F2 generation is considered because for diploid synthetics, Hardy–Weinberg equilibrium is reached in one generation (Busbice, 1970).

Wright's equation largely ignores epistatic effects and relates F2 yields in a linear fashion with heterozygosity. Use of this equation requires the per se yield of the inbreds and complete diallel crossing data for the set. Then performance of possible synthetics is calculated and the best parents intermated. Use of this equation has been proposed for composites as well (e.g., Miranda Filho and Vencovsky, 1984; Eberhart et al.,1967), though a simpler experimental alternative for composites using a half sib procedure has been developed for very large sets of parents (Chaves and Miranda Filho, 1997).

With Wright's equation, one predicts that more of the average heterosis in crosses among the parents will be retained as more parents are included in the population (Fig. 1 ). However, there are diminishing returns with additional parents (Fig. 1). With 10 parents, 90% of the heterosis is retained in the F2, whereas with 20 parents about 95% of the heterosis is retained. With few parents, the specific combining ability (high F1 yields) may be the most important consideration, while the importance of the average performance of all single crosses for each parent (general combining ability) increases with additional numbers of parents (Marquez-Sanchez, 1979). The choice and number of the parents in the diallel is critical (Kinman and Sprague, 1945) since this determines the potential for finding high F1 yields, high general combining ability, and high yielding parents per se.


Figure 1
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  		Figure 1. The amount of heterosis retained in the F2 generations of synthetic varieties with various numbers of inbred parents based on Wright's (1922) equation.

 
Generally speaking, how many parents in synthetics and composites should be used to give the highest yields? More would appear to be better for capturing the most heterosis that is expressed and increasing the likelihood of later success with recurrent selection. Kinman and Sprague (1945) added maize lines sequentially to hypothetical synthetics based on high average yield for all crosses involving each line (basically general combining ability) and concluded that four to six lines would give the highest yields because average F1 yield dropped when more lines were added above this optimum. Retaining a higher proportion of heterosis in the F2 with additional parents did not outweigh the effect of reduced average F1 yields, a result later confirmed by a modeling study (Gallais, 1990).

Wricke and Weber (1978) made crosses among 18 selfed lines of rye and calculated synthetic yields in the manner of Kinman and Sprague (1945); the best performing synthetics were predicted to have three to eight lines. Marquez-Sanchez (1979) found that nine lines formed the highest-yielding synthetic from a diallel of 12 partially inbred, tropical maize lines. He also reported that Ortiz-Cereceres (1961) had found that the highest-yielding maize synthetics had 8 to 12 lines and that Cordova and Marquez-Sanchez (1976) had found the highest yields for maize synthetics with five lines. We wondered whether additional data would confirm these results, and what sort of results might be found when applying Wright's equation and the method of Kinman and Sprague (1945) to formulating composites of maize populations (Eberhart et al., 1967).


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 REFERENCES
 
In addition to the work of Kinman and Sprague (1945) and Molina Galan (1968, evaluated in Marquez-Sanchez, 1979), we used data published from inbred and population diallels where parent and cross yield data were all presented (Tables 1 and 2 ). A study by Brkic et al. (2003) was also used when the authors shared previously unpublished inbred yield data. Together these total seven diallel studies with inbred lines and 14 diallel studies with populations.


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  		Table 1. Summary of maize inbred diallel experiments used for analysis with Wright's equation to determine how to formulate high yielding synthetic populations.

 

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  		Table 2. Summary of maize population diallel experiments used for analysis with Wright's equation to determine how to formulate high yielding composite populations.

 
For each data set we calculated the average yield for all crosses with each parent if that had not already been presented. Parents were then ordered from highest cross average to lowest cross average and sequentially added to hypothetical synthetic or composite populations using Wright's equation just as Kinman and Sprague (1945) originally did. For diallels with inbred lines, all possible numbers of parents were evaluated for each data set. Since predicted composite yield tended to drop off for large numbers of parents, only up to eight parents from each experiment were considered in these analyses. The resulting predictions of F2 yield were then standardized as a percentage of the yield of the highest-yielding single cross in the respective data set (Tables 1 and 2). This conservative approach was taken as there were no standard external checks across experiments and the highest-yielding crosses within an experiment may represent the yields of future hybrid varieties. Means of these yield percentages across experiments were compared among numbers of parents by using t tests, with significance considered at p < 0.05.

Data from two experiments provided an opportunity to test the suitability of using Wright's equation for predicting composite population yields. F1 and F2 yields for each single cross were determined in a five population diallel in Mexico (Castro et al., 1968) and a six population diallel in Brazil (Paterniani, 1980; Gardner and Paterniani, 1967). For each data set modifications of the model suggested by Gardner and Eberhart (1966) were employed by the authors to predict F2 yield. We predicted F2 yield for each population single cross from these studies using Wright's equation. Observed and predicted F2 yields in each experiment were correlated for each prediction model and the r values reported.


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
REFERENCES
 
Synthetic Populations
While Kinman and Sprague (1945) concluded that four to six lines would make for the highest-yielding maize synthetics, results with additional inbred diallels (Table 3 ) showed five to nine lines gave the highest predicted yields (Fig. 2 ). This range in predicted optimum number of parents was the same as that found by Wricke and Weber (1978), Cordova and Marquez-Sanchez (1976), and Ortiz-Cereceres (1961). Across all the experiments the highest average yield, relative to the highest single cross within each experiment, was 78.2% for synthetics with six lines. That average was not significantly different from the average predicted F2 yields for synthetics with five, seven, or eight lines.


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  		Table 3. Maize inbred lines used in the calculation of synthetic population F2 yields.{dagger}

 

Figure 2
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  		Figure 2. Predicted yields of hypothetical F2 generations of maize synthetic populations formed with different numbers of inbred lines. All yields are standardized to percent yield of the highest-yielding single cross within each study.

 
Using only the results for the diallels with 12 or more inbred lines (Zanoni and Dudley, 1989; Misevic, 1989; Molina Galan, 1968; Hayes, 1963), the highest average yield was with nine lines at 79.7% of the highest single cross yield. That average was not significantly different for predicted yields with 5 to 12 lines (P > 0.26), and was nearly significantly different for synthetics with four lines (P = 0.051). Additional data with large diallels gave similar results to those of Marquez-Sanchez (1979) with the data from Molina Galan (1968).

It appears that the number of inbred lines to use when forming a high yielding synthetic may be from 5 to 12 lines, and possibly more, with the exact number depending on the particular inbreds (Kinman and Sprague, 1945) and number of them used in the diallel. These results further support the suggestion by CIMMYT (1999) that synthetics be based on 8 to 10 lines. However, none of these studies fully explored the major heterotic patterns from the USA and the Americas (Kutka, 2005; Taller and Bernardo, 2004; Troyer, 2000) and many major groupings determined by Liu et al. (2003) using DNA markers were not considered. Most of the diallels we examined also included two or more related lines. Often these related lines had low yield in combination and their inclusion held down average F1 yields. This is a critical point, since average F1 yield becomes more important to predicted F2 yields as the importance of extra parents wanes (Fig. 1).

This is not meant as a criticism of these authors, who had other goals, but it seems that studies designed to reach for higher yielding synthetics have yet to be implemented. A short and arbitrary list of germplasm representing heterotic patterns that were not examined in recent diallels includes B86, B97, B114, Cateto lines, CO255, F2, Iodents, LH123Ht, N199, NC296, Pa760, Pa875, SD46, and Tuxpeno lines (e.g., Goldstein, personal communication, 2006; Troyer, 2000; Mungoma and Pollak, 1988). It may be that studies designed to examine synthetic formation from the entire breadth of maize germplasm that can be readily used in the USA and Canada would obtain higher relative yields than those observed in this set of diallels. This remains to be determined experimentally.

Composite Populations
While Wright's equation applies to synthetic populations formed from homozygous inbred lines (Sahagun-Castellanos, 2001; Marquez-Sanchez, 1992a; Gallais, 1990; Busbice, 1970), there is some dispute as to whether it should apply to composite populations formed with less inbred populations (Chaves and Miranda Filho, 1997; Marquez-Sanchez, 1992b; Eberhart et al., 1967). However, it has been used by maize breeders to aid in forming high yielding composites with wide genetic variation (Miranda Filho and Chaves, 1991). Our assessment of the data from Castro et al. (1968) showed that for 10 F2 populations (formed by crossing two parent populations) the observed results and the results predicted using Wright's equation were correlated at r = 0.948. For the 15 F2 populations (also from two parent crosses) evaluated by Gardner and Paterniani (1967) and Paterniani (1980) the observed F2 yields and the predicted yields were correlated at r = 0.839. These correlations were somewhat lower than those for predictions using the more complex model of Gardner and Eberhart (1966) which were r = 0.967 and r = 0.939, respectively. Wright's equation may be acceptably used to predict the yields of composite populations, though more data, especially from crosses involving more than two populations, are needed for a full assessment of its utility.

Assuming that Wright's equation is broadly acceptable for composite populations, the most efficient number of parents for forming a composite of maize populations appears different from that for a synthetic (Table 4 , Fig. 3 ). In the 14 cases given, the yields of hypothetical composites peaked at two to seven parent populations, though most peaked at three or four parents with an average of about 86% of the best population single crosses in each case. The mean of predicted yields across all experiments for three or four parent populations was significantly higher (P < 0.05) than predicted composite yields with two and eight populations (82% of best single population cross), but not significantly different from predicted composite yields with five, six, or seven populations (83–85% of best single cross).


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  		Table 4. Maize populations used in the calculation of hypothetical composite population F2 yields.{dagger}

 

Figure 3
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  		Figure 3. Predicted yields of hypothetical F2 generations of maize composite populations formed with different numbers of populations. All yields are standardized to percent yield of the highest-yielding population cross within each study.

 
The predicted increases in yield over the highest-yielding parent population by forming the highest-yielding composites ranged from –6.1% (Naspolini Filho et al., 1981) to 37.1% (Troyer and Hallauer, 1968), though most had at least marginal increases in yield (Table 4). The better yield increases are similar to some increases observed by forming composites in Mexico (Rincon-Sanchez and Ruiz-Torres, 2005) and in India (Joshi et al., 2005). These results suggest that OP populations of maize, whether old U.S. landraces, exotic populations, or even recurrent breeding populations from the Corn Belt, might be readily surpassed in yield by carefully forming composites. At the very least they may have their genetic variation increased without losing yield, which may help to improve the rate of genetic gain from further recurrent selection (Hallauer and Miranda Filho, 1995).

However, the negative result for two of the Brazilian diallels deserves further scrutiny. Using the method of Kinman and Sprague (1945), the best composite formed among the populations studied by dos Santos et al. (1994) included three recurrent populations, two of which had received nine cycles of selection for yield. The highest-yielding parent per se was BR106 (7704 kg ha–1) which yielded 92% of the best F1 population cross and the best commercial hybrid check (Pioneer Brand 3072). Predicted composite yields using the Kinman and Sprague (1945) methodology were less than that observed for this elite parent. Similarly, Naspolini Filho et al. (1981) formed a diallel among several well-adapted composite populations along with some exotic, low to average yielding populations from Mexico. One of the elite composites, CMS 06, had a yield per se of 95% of the best population cross. Predictions suggest that its yield would not be increased by composite formation. In another case, Silva and Miranda Filho (2003) evaluated a diallel with four broad-based composites crossed with six different selections from a fifth broad-based population. One of their elite composites, GN-03, yielded 96.9% of the hybrid check (Novartis Seeds Brand G-85; 7602 kg ha–1) and 97.3% of the highest-yielding population cross (GO-B/GN-03; 7567 kg ha–1). No predicted composites would outyield this elite parent. These results support the prediction of Gallais (1990) that with very low inbreeding the number of parents needed to form a high yielding population drops to one.

It may be that pushing the yield of elite composites can be difficult through further composite formation via full crosses because the F1 yields are often no higher than that of the elite parent and because the average parent yield is usually lower than the elite composite per se. However, dos Santos et al. (2000) found that smaller proportions of exotic germplasm (12.5% vs. 50%) in a backcrossed population could significantly increase the yield of elite composite populations (BR105, +15%; BR106, +4.4%) when the number of favorable alleles in the exotic populations was low. Apparently there are times when the careful addition of select alleles through backcrossing will make progress for yield of an elite composite as is often practiced with elite inbred lines used to form high yielding single cross hybrids (Troyer, 2000).

Use of Synthetic and Composite Populations Commercially
The use of any of these predicted synthetics or composites for commercial grain production does not appear promising in much of the USA. Using the best single cross F1 yields as internal checks for the inbred diallels, the highest predicted synthetic yields were only 76 to 82% of those yields (Fig. 2). Of diallel studies with commercial hybrid checks, only the results predicted from diallels in the tropics, such as dos Santos et al. (1994), attained yields over 90% of the commercial hybrids (Table 5 ). Predicted composites from research in the USA generally had 81% or less of the yield of the better hybrid checks (Table 5).


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  		Table 5. Yields (reported as kg ha–1) of best predicted composite and synthetic populations compared with hybrid checks.

 
These predicted populations for temperate areas all fall short of the break-even point predicted by Kutka (2005) and Kutka et al. (2004) for average economic and yield conditions in Iowa using 2004 economic conditions (90% of hybrid yield). Some meet or exceed the yield differential observed for several Nebraska synthetics (75%) that were shown to be economically reasonable under dryland conditions on the plains (Baltensperger et al., 2005). However, higher grain prices would render OP populations even less competitive and higher seed prices the reverse, so new economic analyses are needed to identify current break-even points. Overall it appears likely that forming high yielding synthetics and composites using adequate numbers of parents could only bring the grain yields of OP populations in the USA back to the level of competitiveness that OP landraces had with double-cross hybrids in the 1930s and 1940s, though in some cases with much improved agronomic characteristics (Lamkey, personal communication, 2003; Kutka, 2005; Kutka et al., 2004; Pratt, 2004; Smith et al., 2003).

Besides validating these predictions and the use of Wright's equation for composites, there are other issues concerning maize populations and on-farm seed production that may be worthy of further research. Since there is less heterosis for stover yield than grain yield in maize (e.g., Bertoia, 2001; Moreno-Gonzalez et al., 2000) and a few OP varieties are sometimes competitive for silage production even with low grain yields, perhaps new synthetics with higher grain yields would make acceptable silage varieties. High yielding synthetics or composites could also be put through recurrent selection and further improved for grain yield (e.g., Bletsos and Goulas, 1999; Morris et al., 1999; Weyrich et al., 1998; Gardner, 1978; Lonnquist and McGill, 1956), though whether this could occur quickly enough for these populations to reach economic competitiveness is unknown. What is clear is that the highest yields of grain and the highest economic returns for grain producers in the U.S. Corn Belt are currently best accomplished with some type of F1 hybrid (W. Goldstein, personal communication, 2005; Z. Wicks, personal communication, 2005; Carena and Wicks, 2006; Carena, 2005a; Mungoma and Pollak, 1988), though it remains to be seen whether farmers would be interested in producing their own hybrid seed or if this would be economically advantageous.


   ACKNOWLEDGMENTS
 
We thank all the researchers who published complete diallel data, including both cross and parent yields. We would like to thank I. Brkic and the other researchers in Osijek, Croatia, for sharing with us the inbred yield data needed to use their published diallel results. Thanks also go to David Baltensperger, Marcelo Carena, Walter Goldstein, Kendall Lamkey, Linda Pollack, Zeno Wicks, and reviewers for data, discussions concerning these topics, and constructive editorial comments.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Received for publication December 21, 2006.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 REFERENCES
 




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