Constructing stage-structured matrix population models from life tables: comparison of methods.

Abstract

A matrix population model is a convenient tool for summarizing per capita survival and reproduction rates (collectively vital rates) of a population and can be used for calculating an asymptotic finite population growth rate (λ) and generation time. These two pieces of information can be used for determining the status of a threatened species. The use of stage-structured population models has increased in recent years, and the vital rates in such models are often estimated using a life table analysis. However, potential bias introduced when converting age-structured vital rates estimated from a life table into parameters for a stage-structured population model has not been assessed comprehensively. The objective of this study was to investigate the performance of methods for such conversions using simulated life histories of organisms. The underlying models incorporate various types of life history and true population growth rates of varying levels. The performance was measured by comparing differences in λ and the generation time calculated using the Euler-Lotka equation, age-structured population matrices, and several stage-structured population matrices that were obtained by applying different conversion methods. The results show that the discretization of age introduces only small bias in λ or generation time. Similarly, assuming a fixed age of maturation at the mean age of maturation does not introduce much bias. However, aggregating age-specific survival rates into a stage-specific survival rate and estimating a stage-transition rate can introduce substantial bias depending on the organism’s life history type and the true values of λ. In order to aggregate survival rates, the use of the weighted arithmetic mean was the most robust method for estimating λ. Here, the weights are given by survivorship curve after discounting with λ. To estimate a stage-transition rate, matching the proportion of individuals transitioning, with λ used for discounting the rate, was the best approach. However, stage-structured models performed poorly in estimating generation time, regardless of the methods used for constructing the models. Based on the results, we recommend using an age-structured matrix population model or the Euler-Lotka equation for calculating λ and generation time when life table data are available. Then, these age-structured vital rates can be converted into a stage-structured model for further analyses.