A critical comparison of integral projection and matrix projection models for demographic analysis

• Published in: Ecological monographs Vol. 91; no. 2; pp. 1 - 30
• Main Authors: Doak, Daniel F., Waddle, Ellen, Langendorf, Ryan E., Louthan, Allison M., Chardon, Nathalie Isabelle, Dibner, Reilly R., Keinath, Douglas A., Lombardi, Elizabeth, Steenbock, Christopher, Shriver, Robert K., Linares, Cristina, Nagarcia, Maria Begoña, Funk, W. Chris, Fitzpatrick, Sarah W., Morris, William F., Peterson, Megan L.
• Format: Journal Article
• Language: English
• Published: Durham John Wiley and Sons, Inc 01-05-2021; Ecological Society of America
• Subjects: Continuity (mathematics); Decision analysis; Demographic variables; Demographics; demography; elasticity; Empirical analysis; Error analysis; Evaluation; Finite element method; Forecasting; Growth rate; integral projection model; Integrals; IPM; lambda; life span; Literature reviews; matrix projection model; Model accuracy; Modelling; Population biology; Population growth; Projection model; Questions; Species diversity; Statistical analysis; structured population
• ISSN: 0012-9615; 1557-7015
• DOI: 10.1002/ecm.1447

Structured demographic models are among the most common and useful tools in population biology. However, the introduction of integral projection models (IPMs) has caused a profound shift in the way many demographic models are conceptualized. Some researchers have argued that IPMs, by explicitly representing demographic processes as continuous functions of state variables such as size, are more statistically efficient, biologically realistic, and accurate than classic matrix projection models, calling into question the usefulness of the many studies based on matrix models. Here, we evaluate how IPMs and matrix models differ, as well as the extent to which these differences matter for estimation of key model outputs, including population growth rates, sensitivity patterns, and life spans. First, we detail the steps in constructing and using each type of model. Second, we present a review of published demographic models, concentrating on size-based studies, which shows significant overlap in the way IPMs and matrix models are constructed and analyzed. Third, to assess the impact of various modeling decisions on demographic predictions, we ran a series of simulations based on size-based demographic data sets for five biologically diverse species. We found little evidence that discrete vital rate estimation is less accurate than continuous functions across a wide range of sample sizes or size classes (equivalently bin numbers or mesh points). Most model outputs quickly converged with modest class numbers (≥10), regardless of most other modeling decisions. Another surprising result was that the most commonly used method to discretize growth rates for IPM analyses can introduce substantial error into model outputs. Finally, we show that empirical sample sizes generally matter more than modeling approach for the accuracy of demographic outputs. Based on these results, we provide specific recommendations to those constructing and evaluating structured population models. Both our literature review and simulations question the treatment of IPMs as a clearly distinct modeling approach or one that is inherently more accurate than classic matrix models. Importantly, this suggests that matrix models, representing the vast majority of past demographic analyses available for comparative and conservation work, continue to be useful and important sources of demographic information.