An interpretation and proof of the fundamental theorem of natural selection

Fisher's “Fundamental Theorem of Natural Selection” has long caused controversy in population genetics theory. Viewed as a statement about the increase, or rate of increase, of mean fitness over time, it encounters difficulties with cases arising in a multi-locus system for which mean fitness can decrease. An interpretation of the theorem is put forward here which implies that it is correct as a mathematical statement, but of less biological value than was claimed by Fisher.