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

Abstract

The differences in life-history traits and processes between organisms living in the same or different populations contribute to determine their ecological and evolutionary dynamics. Recent advances in statistical and computational methods make it easier to investigate individual and group variation in life-history traits. 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 living in Slovenian streams, 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. 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). Tests on data that were not used to estimate model parameters showed that predictions of individual growth trajectories using the random-effects model were accurately predicted (R2 > 0.80 for the best models over more than 500 predictions) starting from one single observation of body size early in life. Model results pointed to size ranks that are largely maintained throughout the lifetime of individuals in all populations.