Abstract
Around 1923 the soon-to-be famous Soviet mathematician and probabilist Sergei N. Bernstein started to construct an axiomatic foundation of a theory of heredity. He began from the premise of stationarity (constancy of type proportions) from the first generation of offspring. This led him to derive the Mendelian coefficients of heredity. It appears that he had no direct influence on the subsequent development of population genetics. A basic assumption of Bernstein was that parents coupled randomly to produce offspring. This paper shows that a simple model of non-random mating, which nevertheless embodies a feature of the Hardy-Weinberg Law, can produce Mendelian coefficients of heredity while maintaining the population distribution. How W. Johannsen’s monograph influenced Bernstein is discussed.
Highlights
The model used here is of a population consisting of three types of female and male individuals denoted by T0, T1 and T2
Bernstein hoped that mathematics could help to unify the various theories of evolution
We demonstrate that stasis is possible under non-random mating
Summary
The model used here is of a population consisting of three types of female and male individuals denoted by T0, T1 and T2. Bernstein (1924) repeated the steps above leading to the derivation of the Hardy-Weinberg proportions He turned the problem around by asking, if the population maintains constant proportions of types, namely {a, g, b}, after an initial round of mating, and assuming mating is random, whether this implies t)hat the heredity coefficients are necessarily those given by M. He began with a general form denoted by M where M is given by ép êê1- p - p ëê p q 1- q - q q r 1- r - r r s 1- s - s s t 1- t - t t u 1- u - u u v 1- v - v v w 1- w - w w xù 1- x - xúú x ûú this form is too general to work towards constancy of type proportions from the first generation and Bernstein modified it to
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