We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, N, exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, r0 and K, and the environmental variance in population growth rate, σe2. Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, θ, measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes E[Nθ]=[1−σe2/(2r0)]Kθ. This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher r0 versus higher K. However, selection also acts to decrease σe2, so the simple life-history trade-off between r- and K-selection may be obscured by additional trade-offs between them and σe2. Under the classical logistic model of population growth with linear density dependence (θ=1), life-history evolution in a fluctuating environment tends to maximize the average population size.
Elucidating fitness components of the invasive dermestid beetle Trogoderma granarium combining deterministic and stochastic demography
