Estimating the effect of temporally autocorrelated environments on the demography of density‐independent age‐structured populations

Summary In age‐structured populations, environmental autocorrelations influence the long‐run population growth rate as well as the variance in future population size. We used the concept of individual reproductive value to examine how autocorrelated environments affect the dynamics of age‐structured populations, leading to transparent interpretations and estimation of these effects. Environmental autocorrelation is expressed by the covariances between mean individual reproductive values for each age class and size of the same age class with stochastic components depending only on noise matrices from previous years. Thus, if an age class that is large in a given year also tends to perform better than the temporal average of that class in the contribution per individual to future population sizes, then the environmental autocorrelation will be positive. We use a simple model with temporal autocorrelation in recruitment rate to illustrate the theory through analytical results as well as stochastic simulations. We show how the effect of environmental autocorrelation, the term included in the long‐run growth rate, as well as influencing the variance of future population size, can be estimated using a combination of individual‐based demographic data and time series of fluctuations in age composition without estimating autocorrelations and cross‐correlations of large numbers of age‐specific vital rates. The method was applied to data from four mammal species. These analyses revealed that the influence of autocorrelations in the environmental noise on the dynamics of these species was small and in two populations almost negligible. The theoretical explorations as well as the empirical estimates indicate that the temporal scaling of the environmental autocorrelation must be long to substantially affect the long‐term population growth rate. The white noise approximation is therefore often very accurate.