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Quantitative analysis of a cross between populations poulations and their derived genetions

José Branco de Miranda Filho

Departamento de Genética, ESALQ-USP, Caixa Postal 83, 13400 Piracicaba, SP, Brasil

ABSTRACT

Formulas are presented for the biometrical interpretation of means and genetic variances of generations resulting from a cross between two random mating populations. A simple model with one locus and two alleles under the additive-dominance gene action was considered; epistasis was neglected when extended for multiple loci. Besides the formulations for generation means, two other parameters were considered: b, half the contrast for the comparison of parent population means; or the effect of selection if the parents come from a divergent selection program ; and h, the mid-parent heterosis of a quantitative trait in the population cross. Formulas for estimating b and h and for the appropriate tests of hypothesis are given based on the least square procedure. The theoretical patterns of variation of b and h and the difference between them are shown graphically.
The expected genetic variances within generations (parents included) are given according to the model, by varying allele frequencies and levels of dominance. It is expected that the values and formulas will be useful for the interpretation of studies on segregating generations following a cross between two random mating populations.

Keywords: Quantitative analysis.

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