The cost of natural selection revisited

In a constantly changing environment, organisms must continuously adapt or face extinction. J. B. S. Haldane argued that the “cost of natural selection” (also called the cost of substitution) puts an upper limit on the rate of adaptation, and showed that the cost (C) was a decreasing function of the initial frequency of the benefi cial alleles. Based on mutation-selection balance and 10% selective mortality, he suggested that the limit to adaptive evolution was about one allelic substitution per 300 generations. I have tested Haldane s̓ results using simulations of a population limited by density-dependent regulation and subject to a constantly changing environment that affects n (= 1–7) independent survival traits, each controlled by a single locus. I investigated the infl uence of carrying capacity (K), mutation rate (u), number of benefi cial mutations per generation (approximated by M = 2Ku) and net reproductive rate (R). Of these, M has the predominant infl uence. The effect of large changes in R was relatively small. The cost of selection (C) was measured as the shortest number of generations between an allelic substitution at all loci under selection that was consistent with population persistence. The results differed from Haldane s̓ solution. Across a range of conditions, the cost of simultaneous selection at n loci was determined by the linear relationship C = C 0 (M) + nC 1 (M), where C 0 (M) is the intercept and C 1 (M) is the slope of the linear regression of C on n, for a given M. The intercept defi ned a positive fi xed cost of substitution, that appears to refl ect genetic deaths occurring during the stochastic phase when the benefi cial alleles are rare. For M > 1/2, the cost of natural selection is substantially less than Haldane s̓ estimate; however, when M < 1/2, the cost (and particularly the fi xed cost) increases in an accelerating fashion as M is lowered. This result has important implications for conserved populations, since for u ≈ 5 ¥ 10 the carrying capacity of the population must be 50 000 for M = 1/2. To avoid low M, smaller populations should be linked together into a large metapopulation whenever possible. This large unit would be capable of adapting when the isolated parts could not. It also suggests that if M << 1, small gains in K through increases in habitat can have a very large positive infl uence on the future survival of the population in a changing environment.