The sensitivity of age-structured populations to environmental variability

Abstract The sensitivity of a periodically reproducing population with overlapping generations to fluctuations in its environment is examined with a model that preserves the essential features of the age structure of the population. The effect of fluctuations is introduced by perturbing the recruitment of young individuals. This is appropriate for many populations of interest. It is found that the return time is in very poor correspondence with the population's sensitivity to noise and, except for determining whether a system is either stable or unstable, is of little use. The results are affected very little by the preservation or not of age structure within the adult population, and only in detail by the use of discrete rather than continuous-time models. The determining factors are the form of the stock-recruitment relationship (particularly the degree of density dependence) and the way in which noise is introduced. For a specific example based on the North Sea herring, we find that sensitivity to noise increases monotonically as exploitation increases, and this is primarily determined by the behavior of the dominant eigenvalue rather than the subdominant modes of the response. Such an increase in sensitivity is undesirable in managed populations. The variance of the population and yield depend upon the density-dependent nature of the noise, and the form of this is particularly important for overexploited stocks. In general there can be a tradeoff between yield and stability of yield.