On Some Mathematical Problems Arising in the Development of Mendelian Genetics

In this paper some basic problems of theoretical Mendelian genetics are presented. The general situation of an arbitrary number of linked loci for “diploids” (normal organisms) as well as for “autopolyploids” is considered, under random mating. Particular stress is laid upon formulating the problems and results within the framework of probability theory, expressing them in terms of three basic distributions, the distributions of genotypes and of gametes, and the segregation distribution. The task of the mathematical theory consists in establishing recurrence relations for the distributions of gametes and of genotypes, in integrating them and in investigating the limit behaviour of those distribution as n, the number of discrete non overlapping generations tends toward infinity.