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Characteristics of Elite Population Selected on Ratio Criterion: I. Traits with Equal Genetic Variances

USDA-ARS, Mississippi State, MS 39762

^* Corresponding author.

In breeding, multiple trait selection is often a complex problem. One straightforward possibility when selecting for two traits is to base selection on the ratio of two trait values, particularly if the ratio has a biological or economic interpretation. In this study, selection was simulated on the ratio of two polygenically inherited Traits X and Y which were normally distributed and had genetic variances of one. The criterion for selection was the ratio (X/Y). The research objectives were to determine in the selected elite population (i) the responses of the numerator and denominator traits and the ratio, per se, to increasing selection pressure, (ii) the effect of genetic correlation between two traits on ratio selection, and (iii) the selection differentials of ratio trait for estimation of realized heritability. When the two traits had equal variances and means, selection to increase the ratio caused a greater decrease in the mean value of the denominator trait than an increase in the numerator trait. Conversely, selection to decrease the ratio always decreased the mean of the numerator trait more than it increased the denominator trait. For a highly negative genetic correlation (–0.75) between traits, the selection response of the ratio was maximized. When genetic correlation was 0.50 or 0.75, the response of one component trait was near zero. The standardized selection differential for the ratio trait, in comparison with the normally distributed trait, was biased upwards with selection for increased ratio and biased downwards with selection for decreased ratio.

Received for publication January 28, 1994.