Practical Test and Inference on the Inheritance of Dual Multi-Factors and Tri-Normal Distributions of Quantitative Characters

The multi-factorial hypothesis of quantitative trait inheritance originated from Nilson’s wheat hybridization experiments. It takes unit traits as the object and is based on the binomial distribution mathematically. Due to the requirement of the same distribution, it cannot include genes of other distributions. This is its limitation. Moreover, it does not incorporate the environmental effects that constitute the phenotype, so it is not comprehensive enough. This article started from the overallness of quantitative traits, was based on the central limit theorem, and was analyzed from both the genotype and the environment and proposed the assumption on the inheritance of dual multi-factors and tri-normal distributions of quantitative traits. This genetic model was tested with practical examples, and three inferences were made. Method and Results: Firstly, the overallness of quantitative traits was discussed, thus the above assumption was proposed. Next, using many examples of normal distribution of quantitative characters in the homogeneous populations, the research on the identification of the environments without GEI was carried out. Then, the examples of normal distribution of the same quantitative characters in the homogeneous populations and in the segregated populations of the same family were used. By means of normal distribution of quantitative characters in the homogeneous populations, it was indicated that the test locations were the environments without GEI. By utilizing the properties of normal distribution and variance, it was proven that normal distribution of phenotypic value for quantitative traits in a segregated population was formed by adding normal distribution of genotypic value and environmental effect, which enables the genetic model to be tested in practice. Three types of normal distribution of quantitative traits were inferred, indicating that the quantitative characters of a considerable number of organisms in nature obey a normal distribution, expressing continuous variation.