Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations

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.

Predicting evolutionary rescue via evolving plasticity in stochastic environments

Phenotypic plasticity and its evolution may help evolutionary rescue in a novel and stressful environment, especially if environmental novelty reveals cryptic genetic variation that enables the evolution of increased plasticity. However, the environmental stochasticity ubiquitous in natural systems may alter these predictions, because high plasticity may amplify phenotype–environment mismatches. Although previous studies have highlighted this potential detrimental effect of plasticity in stochastic environments, they have not investigated how it affects extinction risk in the context of evolutionary rescue and with evolving plasticity. We investigate this question here by integrating stochastic demography with quantitative genetic theory in a model with simultaneous change in the mean and predictability (temporal autocorrelation) of the environment. We develop an approximate prediction of long-term persistence under the new pattern of environmental fluctuations, and compare it with numerical simulations for short- and long-term extinction risk. We find that reduced predictability increases extinction risk and reduces persistence because it increases stochastic load during rescue. This understanding of how stochastic demography, phenotypic plasticity, and evolution interact when evolution acts on cryptic genetic variation revealed in a novel environment can inform expectations for invasions, extinctions, or the emergence of chemical resistance in pests.