A model for the study of quantitative inheritance

HE actions of genes controlling quantitative characters may be described the use of gene models. FISHER (1918) constructed a gene model which included dominance at a single locus. He stated that there may be a deviation from the simple additive effects between loci, similar to dominance at one locus, if more than one locus affected a given character. He called the deviation epistacy and introduced the term dual epistacy to indicate the interaction of all possible pairs of loci affecting the given character. Later, FISHER, IMMER and TEDIN (1932) used this gene model to describe the actions of any number of genes on a given character assuming there was no epistacy. GRIFFING (1950) introduced an epistatic parameter into a model, but the model is not easily extended to an arbitrary number of loci. The present paper contains a model based on the factorial model used in the design of experiments and some applications of this model to some data. THE FACTORIAL GENE MODEL The factorial model may be exemplified by the case of a dihybrid. The relative frequencies of the nine genotypes obtained from selfing the complete heterozygote may be represented in the following manner :