libpspm: A feature-rich numerical package for solving physiologically structured population models

Abstract

For a vast majority of organisms, life-history processes depend on their physiological state, such as body size, as well as on their environment. Size-structured population models, or more generally, physiologically structured population models (PSPMs), have emerged as powerful tools for modelling the population dynamics of organisms, as they account for the dependences of growth, mortality, and fecundity rates on an organism's physiological state and capture feedbacks between a population's structure and its environment, including all types of density regulation. However, despite their widespread appeal across biological disciplines, few numerical packages exist for solving PSPMs in an accessible and computationally efficient way. The main reason for this is that PSPMs typically involve solving partial differential equations (PDEs), and no single numerical method works universally best, or even at all, for all PDEs. Here, we present libpspm, a general-purpose numerical library for solving user-defined PSPMs. libpspm provides eight different methods for solving the PDEs underlying PSPMs, including four semi-implicit solvers that can be used for solving stiff problems. Users can choose the desired method without changing the code specifying the PSPM. libpspm allows for predicting the dynamics of multiple physiologically structured or unstructured species, each of which can have its own distinct set of physiological states and demographic functions. By separating model definition from model solution, libpspm can make PSPM-based modelling accessible to non-specialists and thus promote the widespread adoption of PSPMs.