Optimization of unbalanced composites of base populations in breeding programs
DOI:
https://doi.org/10.33158/ASB.r277.v12.2026Keywords:
Maize breeding, varietal composites, performance prediction, heterosis, genetic optimization, cultivar composites, hybrid combinationsAbstract
The extremely large number of possible composites complicates the use of composites to form base populations for recurrent selection schemes, even when the number of parents is relatively small. Given the practical infeasibility of synthesizing and evaluating all possible composites, prediction formulas are used for different types of base populations. For composites, in 1970, Vencovsky) proposed the following formula: which allows the expected value of a quantitative trait to be predicted as a function of the parental contribution weights (here denoted as fi). This study presents a mathematical procedure for deriving formulas to calculate the parental contribution weights that maximize the predicted performance of an unbalanced composite. The derivations were developed for composites involving three parents, although the procedure can be extended to a larger number of parents. Mathematical optimization techniques were used to identify the point of maximum predicted performance. Two situations may arise: the optimum may involve contributions from all three parents, or it may exclude one of them, potentially reducing the genetic variability of the composite. In the latter case, a procedure is adopted to impose a minimum contribution from the excluded parent while minimizing the reduction in the predicted performance of the resulting composite. Another objective was to determine the factors that influence the increase in predicted performance of the maximized unbalanced composite relative to the balanced composite. Two practical examples using maize diallel-cross data illustrate the application of the maximization procedure under the two situations described above. Overall, the maximization procedure for unbalanced composites substantially enhances the utility of composite prediction methods.
Downloads
References
Bernardo, R. (2003). Parental selection, number of breeding populations, and size of each population in inbred development. Theoretical and Applied Genetics, 107, 1252–1256. https://doi.org/10.1007/s00122-003-1375-0
Eberhart, S. A., Harrison, M. N., & Ogada, F. (1967). A comprehensive breeding system. Der Züchter, 37, 169–174. https://doi.org/10.1007/BF00329524
Falconer, D. S. (1989). Introduction to quantitative genetics. (3rd ed.). London, England: Longman.
Hallauer, A. R., & Miranda Filho, J. B. (1988). Quantitative genetics in maize breeding. (2nd ed.). Iowa, USA: Iowa State University Press.
Hoffman, K. M., & Kunze, R. (1973). Linear algebra. (2nd ed.). Hoboken, Nova Jersey , EUA: Prentice-Hall.
Kraja, A., & Dudley, J. W. (2000). Identification of tropical and temperate maize populations having favorable alleles for yield and other phenotypic traits. Crop Science, 40(4), 941–947. https://doi.org/10.2135/cropsci2000.404941x
Lou, X. Y., Zhu, J. (2002). Analysis of genetic effects of major genes and polygenes on quantitative traits. Theoretical and Applied Genetics, 104, 414–421. https://doi.org/10.1007/s001220100692
Márquez-Sánchez, F. (1992), Inbreeding and Yield Prediction in Synthetic Maize Cultivars Made with Parental Lines: I. Basic Methods. Crop Science, 32(2): 345-349. https://doi.org/10.2135/cropsci1992.0011183X003200020013x
Melchinger, A. E., Geiger, H. H., Utz, H. F., & Schnell, F. W. (2003). Effect of recombination in the parent populations on the means and combining ability variances in hybrid populations of maize (Zea mays L.). Theoretical and Applied Genetics, 106(2), 332–340. https://doi.org/10.1007/s00122-002-1000-7
Mickelson, H. R., Cordova, H., Pixley, K. V., & Bjarnason, M. S. (2001). Heterotic relationships among nine temperate and subtropical maize populations. Crop Science, 41(4), 1012–1020. https://doi.org/10.2135/cropsci2001.4141012x
Miranda Filho, J. B. (1974). Predição de médias de compostos em função das médias das variedades parentais e das heteroses dos cruzamentos. Relatório Científico do Instituto de Genética (ESALQ/USP), 8, 134–138.
Miranda Filho, J. B., & Chaves, L. J. (1991). Procedures for selecting composites based on prediction methods. Theoretical and Applied Genetics, 81, 265–271. https://doi.org/10.1007/BF00215732
Miranda Filho, J. B., & Vencovsky, R. (1984). Analysis of diallel crosses among open pollinated varieties of mayze (Zea mays L.). Maydica, 29, 217–234.
Mochizuki, N. (1970). Theoretical approach for the choice of parents and their number to develop a highly productive synthetic variety in maize. Japanese Journal of Breeding, 20(2), 105–109. https://doi.org/10.1270/jsbbs1951.20.105
Paliwal, R. L. (2001). Mejoramiento del maíz por selección recurrente. In: Paliwal, R., Granados, G., Lafitte, H., & Violic, A. (Eds.). El maíz en los trópicos: Mejoramiento y producción. p. 123–144. Rome, Italy: FAO.
Paterniani, E., & Miranda Filho, J. B. (1978). Melhoramento de populações. In: Paterniani, E. (Ed.). Melhoramento e produção de milho no Brasil. p. 202–246. Piracicaba, SP: ESALQ.
Reif, J. C., Hamrit, S., Heckenberger, M., Schipprack, W., Maurer, H. P., Bohn, M., & Melchinger, A. E. (2005). Trends in genetic diversity among European maize cultivars and their parental components during the past 50 years. Theoretical and Applied Genetics, 111(5), 838–845. https://doi.org/10.1007/s00122-005-0004-6
Sahagún-Castellanos, J., & Villanueva-Verduzco, C. (2003). Coeficiente de endogamia de las variedades sintéticas de cruzas dobles. Agrociencia, 37, 641–655.
Soengas, P., Ordás, B., Malvar, R. A., Revilla, P., & Ordás, A. (2003). Heterotic patterns among flint maize populations. Crop Science, 43(3), 844–849. https://doi.org/10.2135/cropsci2003.8440
Trifunovic, S., Husic, I., Roulj, M., & Stojsin, R. (2001). Evaluation of U.S. and Yugoslavian maize populations as sources of favorable alleles. Crop Science, 41(2), 302–308. https://doi.org/10.2135/cropsci2001.412302x
Vencovsky, R. (1970). Alguns aspectos teóricos e aplicados relativos a cruzamentos dialélicos de variedades. Tese de livre-docência. Piracicaba, SP: ESALQ/USP.
Vencovsky, R., & Miranda Filho, J. B. (1972). Determinação do número possíveis compostos e pares de compostos. Relatório Científico do Instituto de Genética (ESALQ/USP), 6, 120–123.
Vencovsky, R., Zinsly, J. R., & Vello, N. A. (1971). Comparação de médias estimadas e observadas na síntese de um composto de variedades de milho (Zea mays L.). Ciência e Cultura (Suplemento), 23, 127–128.
Vencovsky, R., & Barriga, P. (1992). Genética biométrica no fitomelhoramento. Ribeirão Preto, SP: Sociedade Brasileira de Genética.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Del Águila, R. M., Souza Junior, H.
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
