Biological fitness and the fundamental theorem of natural selection.

Fisher's fundamental theorem of natural selection is proved satisfactorily for the first time, resolving confusions in the literature about the nature of reproductive value and fitness. Reproductive value is defined following Fisher, without reference to genetic variation, and fitness is the proportional rate of increase in an individual's contribution to the demographic population size. The mean value of fitness is the same in each age class, and it also equals the population's Malthusian parameter. The statement and derivation are regarded as settled here, and so the general biological significance of the fundamental theorem can be debated. The main purpose of the theorem is to find a quantitative measure of the effect of natural selection in a Mendelian system, thus founding Darwinism on Mendelism and identifying the design criterion for biological adaptation, embodied in Fisher's ingenious definition of fitness. The relevance of the newly understood theorem to five current research areas is discussed.