The mutational load with epistatic gene interactions in fitness.

HE mutational load is defined as the proportion by which the population (CROW 1958). In a very large population, where the mutant genes are kept in low frequencies by the balance between mutation and selection, it represents the intensity of natural selection at the genotypic level. The mutational load in a large population was first calculated by HALDANE (1937) without assuming an epistatic component in fitness. Later, a similar but more detailed calculation was carried out by KIMURA (1961). Also, the mutational load in a small population was studied by KIMURA, MARUYAMA and CROW (1963). The purpose of the present paper is to investigate the effect of epistasis on the mutational load, using a model which assumes that the fitness is a function of the number of mutant genes in an individual. In particular, we will elaborate the case of quadratic interaction in fitness, namely, the deleterious effect of mutant genes to an individual is given by the quadratic expression of the number of mutant genes. This includes a case where the deleterious effect is proportional to the square of the number of mutant genes. Such a model may be realistic if the phenotypic suppression of mutational damage by developmental homeostasis breaks down rapidly as the number of mutant genes increases. In follows, we assume very population and investigate first the free among mutant genes. Then, investigate population of a hypothetical organism having only one pair of chromosomes within which no crossing takes place. also study the mutational load under asexual repro-duction. Finally, these results will be compared with other types of epistasis such as threshold character and “diminishing type” epistasis.