Determining individual variation in growth and its implication for life-history and population processes using the empirical Bayes method.

Simone Vincenzi,Stephan Munch,Hans J Skaug,Marc Mangel,Alain J Crivelli,Simon A Levin

doi:10.1371/journal.pcbi.1003828

Abstract

The differences in demographic and life-history processes between organisms living in the same population have important consequences for ecological and evolutionary dynamics. Modern statistical and computational methods allow the investigation of individual and shared (among homogeneous groups) determinants of the observed variation in growth. We use an Empirical Bayes approach to estimate individual and shared variation in somatic growth using a von Bertalanffy growth model with random effects. To illustrate the power and generality of the method, we consider two populations of marble trout Salmo marmoratus living in Slovenian streams, where individually tagged fish have been sampled for more than 15 years. We use year-of-birth cohort, population density during the first year of life, and individual random effects as potential predictors of the von Bertalanffy growth function's parameters k (rate of growth) and (asymptotic size). Our results showed that size ranks were largely maintained throughout marble trout lifetime in both populations. According to the Akaike Information Criterion (AIC), the best models showed different growth patterns for year-of-birth cohorts as well as the existence of substantial individual variation in growth trajectories after accounting for the cohort effect. For both populations, models including density during the first year of life showed that growth tended to decrease with increasing population density early in life. Model validation showed that predictions of individual growth trajectories using the random-effects model were more accurate than predictions based on mean size-at-age of fish.

Highlights

A better understanding of growth will always be an important problem in biology
Estimates of parameters For each von Bertalanffy growth function (vBGF) model we tested, we obtained convergence of the algorithm for parameter estimation in ADMB, and the data used for the estimation of the parameters were well predicted by the models
Tests on simulated data sets showed that when individual trajectories are simulated with positive, negative or no correlation r between k and L? at the individual level, the estimated correlation between individual random effects estimated with the Empirical Bayes (EB) method is very close to the true r

Summary

Introduction

Somatic growth is one the most important lifehistory traits across taxa, since survival, sexual maturity, reproductive success, movement and migration are frequently related to growth and body size [1]. Variation in growth can affect the estimation of vital rates and demographic traits, which may translate to incorrect predictions of population dynamics [5,6,7]. The implications of including individual differences in growth in the study of population processes are largely unexplored, in part because of the computational challenges of estimating the determinants and the extent of shared (i.e. among homogeneous groups) and individual (i.e. after accounting for shared component) variation in growth [5,8]. Determining how shared and individual variation in growth emerges may improve predictions of future growth and size of individuals and populations, which is valuable for conservation and management [9,10]. When estimating the effects of size on survival, the Cormack-Jolly-Seber model requires the size of individual to be known on the occasions when the individual was alive but not sampled, or, alternatively, it requires individual growth trajectories [11]

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