title: Trade-offs between accuracy and interpretability in von Bertalanffy random-effects models of growth.
abstract: Better understanding of variation in growth will always be an important problem in ecology. Individual variation in growth can arise from a variety of processes; for example, individuals within a population vary in their intrinsic metabolic rates and behavioral traits, which may influence their foraging dynamics and access to resources. However, when adopting a growth model, we face trade-offs between model complexity, biological interpretability of parameters, and goodness of fit. We explore how different formulations of the von Bertalanffy growth function (vBGF) with individual random effects and environmental predictors affect these trade-offs. In the vBGF, the growth of an organism results from a dynamic balance between anabolic and catabolic processes. We start from a formulation of the vBGF that models the anabolic coefficient (q) as a function of the catabolic coefficient (k), a coefficient related to the properties of the environment (γ) and a parameter that determines the relative importance of behavior and environment in determining growth (ψ). We treat the vBGF parameters as a function of individual random effects and environmental variables. We use simulations to show how different functional forms and individual or group variability in the growth function's parameters provide a very flexible description of growth trajectories. We then consider a case study of two fish populations of Salmo marmoratus and Salmo trutta to test the goodness of fit and predictive power of the models, along with the biological interpretability of vBGF's parameters when using different model formulations. The best models, according to AIC, included individual variability in both k and γ and cohort as predictor of growth trajectories, and are consistent with the hypothesis that habitat selection is more important than behavioral and metabolic traits in determining lifetime growth trajectories of the two fish species. Model predictions of individual growth trajectories were largely more accurate than predictions based on mean size-at-age of fish. Our method shares information across individuals, and thus, for both fish populations investigated, allows using a single measurement early in the life of individual fish or cohort to obtain accurate predictions of lifetime individual or cohort size-at-age.
authors.affiliation: Center for Stock Assessment Research, Department of Applied Mathematics and Statistics, University of California, Santa Cruz, California, 95064, USA.|Dipartimento di Elettronica, Informazione e Bioingegneria Politecnico di Milano, Via Ponzio 34/5, I-20133, Milan, Italy.
authors.forename: Simone
authors.initials: S
authors.lastname: Vincenzi
authors.affiliation: Station Biologique de la Tour du Valat, Le Sambuc, F-1320, France.
authors.forename: Alain J
authors.initials: AJ
authors.lastname: Crivelli
authors.affiliation: Fisheries Ecology Division, Southwest Fisheries Science Center, National Marine Fisheries Service, NOAA, 110 Shaffer Road, Santa Cruz, California, 95060, USA.
authors.forename: Stephan
authors.initials: S
authors.lastname: Munch
authors.affiliation: Department of Mathematics, University of Bergen, Box 7800, 5020, Bergen, Norway.
authors.forename: Hans J
authors.initials: HJ
authors.lastname: Skaug
authors.affiliation: Center for Stock Assessment Research, Department of Applied Mathematics and Statistics, University of California, Santa Cruz, California, 95064, USA.|Department of Biology, University of Bergen, 5020, Bergen, Norway.
authors.forename: Marc
authors.initials: M
authors.lastname: Mangel
mesh_terms: D000375:Aging; D000818:Animals; D003198:Computer Simulation; D008954:Models, Biological; D014337:Trout / Q000254:growth & development*
keywords: Slovenia; brown trout (Salmo trutta); longitudinal data; marble trout (Salmo marmoratus); model predictions; von Bertalanffy growth function