Biological and statistical interpretation of size-at-age, mixed-effects models of growth

• Main Authors: Simone Vincenzi, Dusan Jesensek, Alain J. Crivelli
• Format: Article
• Language: English
• Published: The Royal Society 2020-04-01
• Series: Royal Society Open Science
• Subjects: growth; von bertalanffy; gompertz; mixed-effects models
• Online Access: https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.192146

The differences in life-history traits and processes between organisms living in the same or different populations contribute to their ecological and evolutionary dynamics. We developed mixed-effect model formulations of the popular size-at-age von Bertalanffy and Gompertz growth functions to estimate individual and group variation in body growth, using as a model system four freshwater fish populations, where tagged individuals were sampled for more than 10 years. We used the software Template Model Builder to estimate the parameters of the mixed-effect growth models. Tests on data that were not used to estimate model parameters showed good predictions of individual growth trajectories using the mixed-effects models and starting from one single observation of body size early in life; the best models had R2 > 0.80 over more than 500 predictions. Estimates of asymptotic size from the Gompertz and von Bertalanffy models were not significantly correlated, but their predictions of size-at-age of individuals were strongly correlated (r > 0.99), which suggests that choosing between the best models of the two growth functions would have negligible effects on the predictions of size-at-age of individuals. Model results pointed to size ranks that are largely maintained throughout the lifetime of individuals in all populations.