Elasticity analysis of population growth: Implications of matrix model construction

Abstract

Elasticity analysis can help ecologists and population managers to rank demographic processes based on their relative contributions to population growth. Here, numerous studies are reviewed where results of elasticity analysis that appear to be specific to the analyzed data can, to some extent, be anticipated on the basis of how the population projection matrix (PPM) was constructed in these studies, independently, or largely so, of the parametrization of this matrix with data. Focus is on the elasticities of population growth at demographic equilibrium to the entries of a time-independent population projection matrix. An essential component in the construction of a PPM is establishing its pattern, here defined as the location of nonnegative entries of the matrix and their demographic meaning. Studies using age-classified models are reviewed separately from studies using stage-classified models. While reviewing both types of studies, several interrelated rules are recalled that can help derive a ranking of elasticities, either from the pattern of the PPM alone or in combination with very little demographic data. It is suggested that greater awareness of the existence of these rules can be beneficial for practitioners of elasticity analysis: some desired results of this analysis can at times be predicted a priori or without full parametrization of the PPM; moreover, the rules can contribute to informing decisions based on the results of elasticity analysis.