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Fischer (1930) stated his fundamental theorem of natural selection (ftns) as ‘the rate of increase in fitness of any organism at any time is equal to its genetic (additive) variance in fitness at that time’. The theorem related to an idealised population and he thought that it held ‘the supreme position among the biological sciences’. His proof of the theorem is, however, not understood. This has given rise to questions concerning not only the validity of the proof but also concerning the importance of the theorem.
Various attempts have been made to develop a theory of the genetical effects of assortative mating, using various models. The earliest and most famous is that of Fisher (1918). However, this has run into a difficulty in that his paper is far from easy to understand even despite the efforts of Kempthorne (1957) and Moran and Smith (1966) to simplify his presentation. A key paragraph is the following (which we give in abbreviated form).