Life tables: Past, present and future

Owen Jones, Interdisciplinary Center on Population Dynamics, University of Southern Denmark, Odense, Denmark; Department of Biology, University of Southern Denmark, Odense, Denmark and Fernando Colchero, Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

Background/Question/Methods
Life tables, describing how risk of death (and sometimes fertility) change with age, are a fundamental tool for describing and exploring the diversity of life histories. Their use originates in Graunt’s 1662 “bills of mortality” and they have been extensively used in human demography since then. Serious use in studies of non-humans began only in the 20th Century with the earliest being published in articles by Raymond Pearl. These articles were most notable for introducing the three types of survivorship curve. Life tables form the basis for age-structured population modelling, including the Euler-Lotka equation.

We outline the two major approaches to life table construction and use: cohort-based, where data are obtained from individuals born at (approximately) the same time and followed until death, and period-based where the data are obtained from a mixed-age population over particular time frame. In ecology, the use of life tables per se has been superseded by other methods including mark-capture-recapture methods and matrix population models (MPMs). Nevertheless, a solid understanding of life table methods and the demographic quantities they contain is crucial for a full understanding of these other methods, and of life history in general.

The widespread use of MPMs has greatly expanded the diversity of species for which we have demographic data but MPMs are mostly stage-based which makes it difficult to obtain age-trajectories of mortality and fertility, and senescence rates. Mathematical “age-from-stage” methods that estimate age-trajectories from stage-based MPMs are sometimes used to fill that gap. We explore how well this approach works by examining how well the methods recover age-trajectory parameters from simulated data.

Results/Conclusions
We illustrate the utility of life table methods and highlight that a solid understanding of these methods, and associated demographic quantities, is crucial for a full understanding of the role of life history in ecology and evolution. We then show how the usefulness of age-from-stage methods used to calculate life tables from MPM data is highly-dependent on matrix dimension and on the life history of the organism. This finding is driven by the asymptotic nature of the age-from-stage methods and the speed of convergence to the quasi-stationary stage distribution, after which estimated mortality and fertility remain constant with age. We find that low-dimension matrices underperform, as do matrices for organisms with vital rates that have only small differences among stages. Researchers using these methods should ensure that they understand the biases and uncertainties involved.