Abstract. Both means and year-to-year variances of climate variables such as temperature and precipitation are predicted to change. However, the potential impact of changing climatic variability on the fate of populations has been largely unexamined. We analyzed multiyear demographic data for 36 plant and animal species with a broad range of life histories and types of environment to ask how sensitive their long-term stochastic population growth rates are likely to be to changes in the means and standard deviations of vital rates (survival, reproduction, growth) in response to changing climate. We quantified responsiveness using elasticities of the long-term population growth rate predicted by stochastic projection matrix models. Short-lived species (insects and annual plants and algae) are predicted to be more strongly (and negatively) affected by increasing vital rate variability relative to longer-lived species (perennial plants, birds, ungulates). Taxonomic affiliation has little power to explain sensitivity to increasing variability once longevity has been taken into account. Our results highlight the potential vulnerability of short-lived species to an increasingly variable climate, but also suggest that problems associated with short-lived undesirable species (agricultural pests, disease vectors, invasive weedy plants) may be exacerbated in regions where climate variability decreases.

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How much does environmental autocorrelation matter to the growth of structured populations in real life contexts? Interannual variances in vital rates certainly do, but it has been suggested that between-year correlations may not. We present an analytical approximation to stochastic growth rate for multistate Markovian environments and show that it is accurate by testing it in two empirically based examples. We find that temporal autocorrelation has sizeable effect on growth rates of structured populations, larger in many cases than the effect of interannual variability. Our approximation defines a sensitivity to autocorrelated variability, showing how demographic damping and environmental pattern interact to determine a population's stochastic growth rate.

Elasticities in stochastic matrix models are used to understand both population and evolutionary dynamics. We examine three such elasticities: stochastic elasticity E(ij)(S) with respect to the (i, j) matrix element, the elasticity E(ij)(S mu) with respect to the mean mu(ij) of the matrix element, and the elasticity E(ij)(S sigma) with respect to the variability sigma(ij) of the matrix element. We show that the stochastic elasticity E(S) does not accurately describe the effect of variability; one should use E(S sigma) and E(S mu). We establish two general properties of these elasticities: a sum rule that connects them and a limit on the sum of the E(S sigma). We discuss the implications of these properties for the analysis of buffering and selection on the average rates versus the variability of rates.

How does life history affects the short-term elasticities of population growth rate? We decompose short-term elasticity as a sum of (i) the effect of the perturbation in rates on the unperturbed population structure and (ii) the effect of the original vital rates on the difference in structure between the original and the perturbed population. We provide exact analytical formulas for these components. In a population at its stable stage distribution (SSD), short-term elasticity is determined mainly by the SSD and reproductive value. In a non-stable population, short-term elasticity depends also on the projection of initial structure on the SSD, equal to population momentum. Non-stable stage structures matter most to elasticity if stages are missing that take time to fill in. We show how the demographic damping rate of the original population determines the rate at which short-term elasticity converges to its limiting values.