A quantitative trait is assumed to be genetically affected by a polygenic e
ffect and a major effect of a single dialellic locus. Such a model is calle
d mixed model of inheritance and the identified gene is denoted as quantita
tive trait locus (QTL). By choosing the part of the QTL-variance, the degre
e of dominance and the Frequency of the favourable allele it is possible to
generate distributions with given level of asymmetry characterised by skew
ness and kurtosis. If the ratio of QTL- and phenotypic variance is small (l
ess than 8%), then genotype-environment interaction can be used in the mixe
d inheritance model to explain values of skewness and kurtosis estimated wi
th poultry data. The situation is considered where the environmental varian
ces given for the three QTL-genotypes show a wide range. In most of these c
ases the short- and long-term selection does not effects the high values fo
r skewness and kurtosis over multiple generations. Further the ratio of res
ponse to selection and the difference of selection depends on the selection
intensity.