A general approach for analysis of physiologically structured population models: the R package ‘PSPManalysis’

Abstract

SummaryHow environmental conditions affect the life history of individual organisms and how these effects translate into dynamics of population and communities on ecological and evolutionary time scales is a central question in many eco-evolutionary studies.Physiologically structured population models (PSPMs) offer a theoretical approach to address such questions as they are built upon a function-based model of the life history, which explicitly describes how life history depends on individual traits as well as on environmental factors. PSPMs furthermore explicitly account for population feedback on these environmental factors, which translates into density-dependent effects on the life history. PSPMs can thus capture life histories in quite some detail but lead to population-level formulations in terms of partial differential equations that are generally hard to analyse.Here I present a general methodology and aRsoftware package for computing how the ecological steady states of PSPMs depend on model parameters and to detect bifurcation points in the computed curves where dynamics change drastically. The package makes specifying the population model unnecessary and only requires a relatively straightforward implementation of the life history functions as input. It furthermore allows for analysing the evolutionary dynamics and evolutionary singular states of the PSPMs based on Adaptive Dynamics theory.Given the central role of the individual life history in many studies, there is substantial scope for using the presented methodology in fields as diverse as ecology, ecotoxicology, conservation biology and evolutionary biology, where it has already been applied to problems like the evolution of cannibalism, niche shifts and metamorphosis.