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

Simone Vincenzi,Alain J Crivelli,Dusan Jesensek

doi:10.1098/rsos.192146

Abstract

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.

Highlights

Understanding the causes of within- and among-population variation in vital rates of organisms, such as their probability of survival, growth, migration, and reproduction, life histories, and population dynamics is a central topic in ecology and evolutionary biology.royalsocietypublishing.org/journal/rsos R
A number of different von Bertalanffy growth functions (vBGF) and Gompertz growth function (GGF) models had basically the same predictive accuracy, and their Akaike information criterion (AIC) computed on the full dataset were fairly close as well
We found that mixed-effects models based on either the von Bertalanffy or Gompertz growth functions were able to largely capture the individual variation in growth among fish living in four distinct freshwater salmonid populations

Summary

Introduction

Understanding the causes of within- and among-population variation in vital rates of organisms, such as their probability of survival, growth, migration, and reproduction, life histories (i.e. how vital rates vary together and the trade-offs among them), and population dynamics (i.e. how the number of individuals in a population changes over time) is a central topic in ecology and evolutionary biology.royalsocietypublishing.org/journal/rsos R. Since the modelling of mechanisms is more informative than curve fitting (e.g. it allows to predict outside of the range of data observed and test hypotheses on the determinants of growth), ideally the parameters of the growth function should describe some of the physiological or life-history processes that affect growth. Depending on their assumptions and parametrizations, growth functions fitted on the same data can provide different—sometimes in disagreement—insights into the growth process [7]

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Discussion

Conclusion