The Variance and Response of Biological Systems to Variability in Births and Survivals

Abstract

This study presents an age-structured population model with a density-dependent birth rate. The dynamics are driven by a constant harvesting rate but fluctuating perturbations in births and age-specific survival rates. From this are obtained expressions for the variance and frequency response of the mature stock. Similar expressions for other components, such as yield, can be derived. The frequency spectra of the noise are left in a general form but the significance of assuming perfect correlation, within one time unit, or zero correlation among variations in age-specific survival rates, is illustrated. It is shown that increased correlation increases total variance and will also alter the frequency-response spectrum. In addition it is shown that the phase shift of the component of the population under study, relative to the noise source, is directly obtainable.