Age × stage‐classified demographic analysis: a comprehensive approach

Abstract

This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age‐classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage‐classified populations, in both ecology and human demography. Here, we use the vec‐permutation formulation of multistate matrix population models to incorporate age‐ and stage‐specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra‐cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age‐classified point of view, stage structure is a form of unobserved heterogeneity. From a stage‐classified point of view, age structure is unobserved heterogeneity. In an age × stage‐classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage‐classified demography will become more common and more important.

Skewed distributions of lifetime reproductive success: beyond mean and variance

“…Derivatives of this probability with respect to these parameters should be computable using known approaches, e.g. Caswell et al () or Steiner et al ().…”

Climate change and functional traits affect population dynamics of a long‐lived seabird

“…In such an analysis, traits might be fixed over the lifetime of the individual, as wing length at fledging clearly is. Or, they might be dynamic, changing over the individuals lifetime according to a set of age‐ or stage‐dependent transition matrices (e.g., Caswell, ; Caswell & Salguero‐Gómez, ; for a general methodology see Caswell, de Vries, Hartemink, Roth, & van Daalen, ). Foraging behaviours, for example, are not necessary static traits and may change over the lifetime of an individual.…”

Savanna canopy trees under fire: long‐term persistence and transient dynamics from a stage‐based matrix population model

“…Here, we present the general form of matrix population models as well as the specific form of our model including the life-history stages and the parameterization of transition matrices. For a thorough introduction to the mathematical properties of matrix models, see Caswell (2001Caswell ( , 2014 and Caswell et al (2018).…”