Analyses of Skewness and Kurtosis for Detecting Gene Interaction in a Doubled Haploid Population¹

Abstract

It was shown that the third cumulant (K 3 ) of a biparental doubled haploid population is equal to zero in the absence of gene interaction, it is greater and smaller than zero in the presence of complementary and duplicate interactions, respectively; and that the fourth cumulant (K 4 ) is negative or near zero in the absence of gene interaction, it is always positive in the presence of gene interaction. Therefore, K 3 and K 4 can be used for detecting gene interaction and identifying the nature of gene interaction in a doubled haploid population. The third and fourth cumulants for grain yield, heading date, and plant height were studied in four biparental doubled haploid populations of barley ( Hordeum vulgare L.). In one population, complementary interaction was detected for heading date and in another population, duplicate interaction was observed for plant height. It was proved that gene interaction was absent for grain yield and plant height in one population.