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An Empirical Approach for the Prediction of Maize F₂ Synthetics with Varying Numbers of Lines¹

A method is proposed to predict the yield of an F₂ synthetic of maize (Zea mays L.) based on Wright's formula, F₂ = ₁ – ₁ – )/n. Its basic principle is the fitting of the expected yields of F₁ and P to asymptotic curves that are functions of the number of lines (n) involved the synthetics. The asymptote of the F₁ function is assumed to be the yield (V) of the open-pollinated cultivar from which the lines are derived, that is, the base population. Although it is not possible to define the limit of the P function, the average (P) of the possible lines derived from the base population may be used. Curves for F₁ and P were calculated for every n-line group by selecting the highest yielding F₁ synthetic (best F₁ synthetic) out of the C (m, n) possible combinations of m lines. The calculated data were fitted to a theoretical asymptotic curve ( a hyperbola) by non-linear least squares to estimate the corresponding points on the curves. The F₂ prediction was a curve with a minimum at n=2, maximum at n=k and a limit V as n increased. A comparison is made between this method and that used by M.L. Kinman and G. F. Sprague in 1945 with data obtained from the Mexican maize breeding program for the humid tropics.

Key Words: Optimum line number for synthetics • Wright's formula for synthetic prediction • Optimizing yields of synthetics • Zea mays L.

² Professor of plant breeding, Genetics Dep., Postgraduate College, SARH, Chapingo, Mexico.

Received for publication October 13, 1977.

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