Full text in pdf format
Predicting variety composite means without diallel crossing
Lázaro J. ChavesI; José B. de Miranda FilhoII
IEscola de Agronomia, Universidade Federal de Goiás, Caixa Postal 131, 74001-970 Goiânia, GO, Brasil.
IIDepartamento de Genética, ESALQ/Universidade de São Paulo, Caixa Postal 83, 13400-970 Piracicaba, SP, Brasil. Send correspondence to J.B.M.F.
ABSTRACT
Prediction of variety composite means was shown to be feasible without diallel crossing the parental varieties. Thus, the predicted mean for a quantitative trait of a composite is given by: Yk = a1 SVj + a2STj + a3V - a4T, with coefficients a1 = (n - 2k)/k2(n - 2); a2 = 2n(k - 1)/k2(n - 2); a3 = n(k - 1)/k(n - 1)(n - 2); and a4 = n2(k - 1) /k(n - 1)(n - 2); summation is for j =1 to k, where k is the size of the composite (number of parental varieties of a particular composite) and n is the total number of parent varieties. Vj is the mean of varieties and Tj is the mean of toperosses (pool of varieties as tester), and V and T are the respective average values in the whole set. Yield data from a 7 x 7 variety diallel cross were used for the variety means and for the "simulated" topeross means to illustrate the proposed procedure. The proposed prediction procedure was as effective as the prediction based on Yk = H - (H - V)/k, where H and V refer to the mean of hybrids (F1) and parental varieties, respectively, in a variety diallel cross. It was also shown in the analysis of variance that the total sum of squares due to treatments (varieties and toperosses) can be orthogonally partitioned following reduced model Yjj' = µ + 1/2(vj + vi') + h + hj + hj', thus making possible an F test for varieties, average heterosis and variety heterosis. Least square estimates of these effects are also given.
Keywords: variety; diallel crossing.
REFERENCES
Carvalho, H.W.L. (1980). Predição de médias de compostos de milho (Zea mays L.) para a microregião homogênea 131 do Estado da Bahia. Master's thesis, Escola Superior de Agricultura "Luiz de Queiroz", Universidade de São Paulo, Piracicaba, SP.
Eberhart, S.A. and Gardner, C.O. (1966). A general model for genetic effects. Biometrics 22: 864-881.
Eberhart, S.A., Harrison, M.N. and Ogada, F. (1967). A comprehensive breeding system. Der Zuchter 37: 169-174.
Gardner, C.O. (1967). Simplified methods for estimating constants and computing sums of squares for a diallel cross analysis. Fitot. Latinoam. 4: 1-12.
Gardner, C.O. and Eberhart, S.A. (1966). Analysis and interpretation of the variety cross diallel and related populations. Biometrics 22: 439-452.
Hallauer, A.R. and Miranda Filho, J.B. (1988). Quantitative Genetics in Maize Breeding. 2nd edn. Iowa State University Press, Ames, Iowa, pp. 468.
Jenkins, M.T. (1934). Methods of estimating the performance of double crosses in corn. J. Am. Soc. Agron. 26: 199-204.
Mather, K. (1949). Biometrical Genetics. Methuen and Co., London, pp. 162.
Mather, K. and Jinks, J.L. (1971). Biometrical Genetics. Chapman & Hall, London, pp. 382.
Miranda Filho, J.B. (1974). Cruzamentos dialélicos e síntese de compostos de milho (Zea mays L.) com ênfase na produtividade e no porte da planta. Doctoral thesis, Escola Superior de Agricultura "Luiz de Queiroz", Universidade de São Paulo, Piracicaba, SP.
Miranda Filho, J.B. and Chaves, L.J. (1991). Procedures for selecting composites based on prediction methods. Theor. Appl. Genet. 81: 265-271.
Miranda Filho, J.B. and Vencovsky, R. (1984). Analysis of diallel crosses among open-pollinated varieties of maize (Zea mays L.). Maydica 29: 217-234.
Vencovsky, R. (1970). Alguns aspectos teóricos e aplicados relativos a cruzamentos dialélicos de variedades. "Livre-Docência" thesis, Escola Superior de Agricultura "Luiz de Queiroz", Universidade de São Paulo, Piracicaba, SP.
Vencovsky, R. (1987). Herança quantitativa. In: Melhoramento e Produção de Milho (Patemiani, E. and Viegas, G.P., eds.). Ed. Fundação Cargill, Campinas (SP), pp. 735.
Vencovsky, R. and Miranda Filho, J.B. (1972). Determinação do número de possíveis compostos e pares de compostos. Rel. Cient. Inst. Genét. (Escola Superior de Agricultura "Luiz de Queiroz", Universidade de São Paulo) 6: 120-123.
Wright, S. (1922). The effects of inbreeding and crossbreeding on guinea pigs. III. Crosses between highly inbred families. USDA Bull. 1121.