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 r and the lifetime reproductive success (LRS) R , both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r and average lifetimes are small, whereas R dominates and lifetimes are larger under small noise. Thus, K-selection is closely linked to selection for large R so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r and R ) tend to be maximized at low and high densities, respectively, favoring density-dependent changes in the optimal life history.