My, how you've grown: A practical guide to modeling size transitions for integral projection model (IPM) applications

Integral projection models (IPMs) are widely used for studying continuously size-structured populations. IPMs require a growth sub-model that describes the probability of future size conditional on current size and any covariates. Most IPM studies assume that this distribution is Gaussian, despite calls for non-Gaussian models that accommodate skewness and excess kurtosis. We provide a general workflow for accommodating non-Gaussian growth patterns while retaining important covariates and random effects. Our approach emphasizes visual diagnostics from pilot Gaussian models and quantile-based metrics of skewness and kurtosis that guide selection of a non-Gaussian alternative, if necessary. Across six case studies, skewness and excess kurtosis were common features of growth data, and non-Gaussian models consistently generated simulated data that were more consistent with real data than pilot Gaussian models. However, effects of "improved" growth modeling on IPM results were moderate to weak and differed in direction or magnitude between different outputs from the same model. Using tools not available when IPMs were first developed, it is now possible to fit non-Gaussian models to growth data without sacrificing ecological complexity. Doing so, as guided by careful interrogation of the data, will result in models that better represent the populations for which they are intended.