Advancing population ecology with integral projection models: a practical guide

Abstract

Summary1. Integral projection models (IPMs) use information on how an individual's state influences its vital rates -survival, growth and reproduction -to make population projections. IPMs are constructed from regression models predicting vital rates from state variables (e.g. size or age) and covariates (e.g. environment). By combining regressions of vital rates, an IPM provides mechanistic insight into emergent ecological patterns such as population dynamics, species geographic distributions or life-history strategies. 2. Here, we review important resources for building IPMs and provide a comprehensive guide, with extensive R code, for their construction. IPMs can be applied to any stage-structured population; here, we illustrate IPMs for a series of plant life histories of increasing complexity and biological realism, highlighting the utility of various regression methods for capturing biological patterns. We also present case studies illustrating how IPMs can be used to predict species' geographic distributions and life-history strategies. 3. IPMs can represent a wide range of life histories at any desired level of biological detail. Much of the strength of IPMs lies in the strength of regression models. Many subtleties arise when scaling from vital rate regressions to population-level patterns, so we provide a set of diagnostics and guidelines to ensure that models are biologically plausible. Moreover, IPMs can exploit a large existing suite of analytical tools developed for matrix projection models.

Modeling Adaptive and Nonadaptive Responses of Populations to Environmental Change

“…Age is included only in models for species with overlapping generations. Following standard convention for IPMs (Coulson 2012;Merow et al 2014;Rees et al 2014;Ellner et al 2016), we use primes to indicate the character value of an individual at the end of a time step. For example, this allows us to show how an individual with phenotype Z can develop over a time step to a potentially different phenotype Z 0 or how a parent with genotype G can produce an offspring with genotype G 0 .…”

“…The definitions of all variables and functions are summarized in table 1. Our starting point is a widely used phenotypic modeling approach that many readers will be familiar with (Coulson 2012;Merow et al 2014;Rees et al 2014). We then extend this approach by developing dynamic models of the phenotype decomposed into its genetic and environmental components.…”

“…IPMs are now a widely used tool in ecology and evolution because of their versatility and the ease with which they can be parameterized (Merow et al 2014). All key statistics routinely estimated in population ecology, quantitative genetics, population genetics, and life history describe some aspect of a character distribution or its dynamics .…”

“…Processes 1-6 (and consequently also 8) can be influenced by the biotic or abiotic environment. Integral projection models (IPMs) provide a very flexible structured modeling framework that allow each of these processes to be simultaneously modeled (Easterling et al 2000;Coulson 2012;Merow et al 2014).…”

“…They consequently offer great potential to study ecological and evolutionary responses to environmental change (Coulson et al 2011). However, most IPMs to date have been restricted to phenotypic variation in that they do not include genotypephenotype maps (Merow et al 2014). A small number of evolutionarily explicit IPMs that do include these maps have been developed.…”