Projecting age-structured populations in a random environment
An environmental process was characterized by a stationary first order autoregressive process with Gaussian noise. This process was then linked to survivorship and reproductive success by logistic transformations to construct a stochastic population process, related to generalized age- dependent branching processes, for projecting age-structured populations in a random environment. Unexpectedly large fluctuations among projections of conditional mean total population size, given different realizations of the environmental process, were observed, particularly when the environmental process had a strictly positive autocorrelation function. These large fluctuations led to summarizing the results of 100 replications of projecting conditional mean total population size, given the environmental process, for 100 epochs in terms of extreme value statistics rather than the more conventional means and variances. Qualitative comparisons with fluctuations in abundance of some species of birds suggested that some choices of parameter values for the environmental process led to plausible models for the evolution of selected bird populations.
stationary first order autoregressive process with Gaussian noise
scientific article; zbMATH DE number 4039698