Transient population dynamics and short-term sensitivity analysis of matrix population models

Abstract

Demographic analysis methodologies which consider the transient dynamics of a population promise to be highly relevant for population conservation and management, but the present methods of analysis are still in the early stages of being developed. The methods require a knowledge of a population’s initial stage-structure, and produce output which is complicated, and difficult to describe succinctly. This paper investigates whether the initial stage-structure is always required in order to obtain reliable information on the transient population dynamics. The paper also presents new methods for succinctly presenting the data from these near-term demographic analyses. The work of Fox and Gurevitch [Am. Naturalist 156 (2000) 242] is extended by deriving an analytical formula which decomposes their near-term sensitivity into two components: one which does not require the populations initial stage-structure to be measured, and one which does. This decomposition is used to estimate the sensitivity of the analysis to the initial population stage structure, without a knowledge of the population structure. The near-term sensitivity analysis is extended to look at several measures for the near-term sensitivity of population growth rate. These new measures allow the information contained in the analysis to be condensed, and for a comparison to be made between near-term and asymptotic sensitivity analyses. The methods are demonstrated by analysing empirical data on the cactus Coryphantha robbinsorum.