On the interpretation and relevance of the Fundamental Theorem of Natural Selection.

The attempt to understand the statement, and then to find the interpretation, of Fisher's "Fundamental Theorem of Natural Selection" caused problems for generations of population geneticists. Price's (1972) paper was the first to lead to an understanding of the statement of the theorem. The theorem shows (in the discrete-time case) that the so-called "partial change" in mean fitness of a population between a parental generation and an offspring generation is the parental generation additive genetic variance in fitness divided by the parental generation mean fitness. In the continuous-time case the partial rate of change in mean fitness is equal to the parental generation additive genetic variance in fitness with no division by the mean fitness. This "partial change" has been interpreted by some as the change in mean fitness due to changes in gene frequency, and by others as the change in mean fitness due to natural selection. (Fisher variously used both interpretations.) In this paper we discuss these interpretations of the theorem. We indicate why we are unhappy with both. We also discuss the long-term relevance of the Fundamental Theorem of Natural Selection, again reaching a negative assessment. We introduce and discuss the concept of genic evolutionary potential. We finally review an optimizing theorem that involves changes in gene frequency, the additive genetic variance in fitness and the mean fitness itself, all of which are involved in the Fundamental Theorem of Natural Selection, and which is free of the difficulties in interpretation of the Fundamental Theorem of Natural Selection.