r- and K-selection in fluctuating populations is determined by the evolutionary trade-off between two fitness measures: Growth rate and lifetime reproductive success.

In a stable environment, evolution maximizes growth rates in populations that are not density regulated and the carrying capacity in the case of density regulation. In a fluctuating environment, evolution maximizes a function of growth rate, carrying capacity and environmental variance, tending to r-selection and K-selection under large and small environmental noise, respectively. Here we analyze a model in which birth and death rates depend on density through the same function but with independent strength of density dependence. As a special case, both functions may be linear, corresponding to logistic dynamics. It is shown that evolution maximizes a function of the deterministic growth rate r0 and the lifetime reproductive success (LRS) R0 , both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r0 and average lifetimes are small, whereas R0 dominates and lifetimes are larger under small noise. Thus, K-selection is closely linked to selection for large R0 so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r0 and R0 ) tend to be maximized at low and high densities, respectively, favoring density-dependent changes in the optimal life history.