Choosing the right sigmoid growth function using the unified‐models approach

Abstract

Growth of the young is an important part of the life history in birds. However, modelling methods have paid little attention to the choice of regression model used to describe its pattern. The aim of this study was to evaluate whether a single sigmoid model with an upper asymptote could describe avian growth adequately. We compared unified versions of five growth models of the Richards family (the four‐parameter U‐Richards and the three‐parameter U‐logistic, U‐Gompertz, U‐Bertalanffy and U4‐models) for three traits (body mass, tarsus‐length and wing‐length) for 50 passerine species, including species with varied morphologies and life histories. The U‐family models exhibit a unified set of parameters for all models. The four‐parameter U‐Richards model proved a good choice for fitting growth curves to various traits – its extra d‐parameter allows for a flexible placement of the inflection point. Which of the three‐parameter U‐models was the best performing varied greatly between species and between traits, as each three‐parameter model had a different fixed relative inflection value (fraction of the upper asymptote), implying a different growth pattern. Fixing the asymptotes to averages for adult trait value generally shifted the model preference towards one with lower relative inflection values. Our results illustrate an overlooked difficulty in the analysis of organismal growth, namely, that a single traditional three‐parameter model does not suit all growth data. This is mostly due to differences in inflection placement. Moreover, some biometric traits require more attention when estimating growth rates and other growth‐curve characteristics. We recommend fitting either several three‐parameter models from the U‐family, where the parameters are comparable between models, or only the U‐Richards model.