Simple Methods for Calculating Age‐Based Life History Parameters for Stage‐Structured Populations: Ecological Archives M062-002

Abstract

Stage—classified matrix models are important analytical and theoretical tools for the study of population dynamics; in particular, these models may be appropriate for populations in which survivorship and fecundity are dependent on size or developmental stage, populations in which the age of individuals is difficult to determine, and populations in which there are multiple types of newborns. Nevertheless, methods for analyzing the implications of a population's stage—transition matrix have been limited in comparison to methods available for age—structured models (life tables or Leslie matrices). In this paper we show that all of the standard age—based measures of life history traits can be derived from a stage—transition model. By decomposing the transition matrix into separate birth, survival, and fission matrices we derive simple, direct formulas for age—based life history traits such as the discrete survivorship function, l x, maternity function, f x, mean age at maturity, and net reproductive rate, R o, and also population parameters, including the stable age distribution, age—specific reproductive value, and generation time. These provide a common set of parameters for comparing age—structured and stage—structured populations or comparing populations with differently structured life cycles. In addition, we define four measures of age and life—span that summarize the relationship between stage and age in a stage—structured population: age distribution and mean age of residence for each stage class, expected remaining life—span for individuals in each stage class, and total life—span conditional on reaching a given stage class. We illustrate the use of our methods to address specific ecological questions by applying them to several previously published demographic data sets. These questions include: (1) what are the demographic effects of crowding on the tropical palm Astrocaryum mexicanum?; (2) how important is the initial rosette size in determining life history of teasel, Dipsacus sylvestris?; and (3) how old are reproducing adults in a stage—classified population of pink lady's—slipper, Cypripedium acaule? Our results may also be useful for evaluating the adequacy of a given stage—transition model.