Building integral projection models with non-independent vital rates

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co-vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs, and include cases where the processes co-vary as a function of time (temporal variation), co-vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population-level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life-history evolution.

Integral projection models

Integral projection models (IPMs) allow projecting the behaviour of a population over time using information on the vital processes of individuals, their state, and that of the environment they inhabit. As with matrix population models (MPMs), time is treated as a discrete variable, but in IPMs, state and environmental variables are continuous and are related to the vital rates via generalised linear models. Vital rates in turn integrate into the population dynamics in a mechanistic way. This chapter provides a brief description of the logic behind IPMs and their construction, and, because they share many of the analyses developed for MPMs, it only emphasises how perturbation analyses can be performed with respect to different model elements. The chapter exemplifies the construction of a simple and a more complex IPM structure with an animal and a plant case study, respectively. Finally, inverse modelling in IPMs is presented, a method that allows population projection when some vital rates are not observed.

ipmr: Flexibly implement Integral Projection Models in R

Integral projection models (IPMs) are an important tool for studying the dynamics of populations structured by one or more continuous traits (e.g. size, height, color). Researchers use IPMs to investigate questions ranging from linking drivers to plant population dynamics, planning conservation and management strategies, and quantifying selective pressures in natural populations. The popularity of stage-structured population models has been supported by R scripts and packages (e.g. IPMpack, popbio, popdemo, lefko3) aimed at ecologists, which have introduced a broad repertoire of functionality and outputs. However, pressing ecological, evolutionary, and conservation biology topics require developing more complex IPMs, and considerably more expertise to implement them. Here, we introduce ipmr, a flexible R package for building, analyzing, and interpreting IPMs. The ipmr framework relies on the mathematical notation of the models to express them in code format. Additionally, this package decouples the model parameterization step from the model implementation step. The latter point substantially increases ipmr's flexibility to model complex life cycles and demographic processes. ipmr can handle a wide variety of models, including density dependence, discretely and continuously varying stochastic environments, and multiple continuous and/or discrete traits. ipmr can accommodate models with individuals cross-classified by age and size. Furthermore, the package provides methods for demographic analyses (e.g. asymptotic and stochastic growth rates) and visualization (e.g. kernel plotting). ipmr is a flexible R package for integral projection models. The package substantially reduces the amount of time required to implement general IPMs. We also provide extensive documentation with six vignettes and help files, accessible from an R session and online.