Determining Individual Variation in Growth and Its Implication for Life-History and Population Processes Using the Empirical Bayes Method

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.

Individual, spatial and inter-sex variation in somatic growth: a study of Piaractus mesopotamicus (Characiformes: Serrasalmidae), a long-distance freshwater Neotropical migratory fish

“…Implementing models that take into account the growth trajectory of individuals in a population has provided a better understanding of the source variation in the growth parameters, as the pattern that emerges at the population level is derived from processes generated at the individual level (Alós et al, 2010;Vincenzi et al, 2014;DeAngelis, Grimm, 2014). Furthermore, the use of an approach at the individual level is more appropriate since individual variation is controlled by considering the growth trajectory of each specimen.…”

“…From an ecological point of view, somatic growth is an important feature in the life history of individual fish because it is related to such vital characteristics as fertility, sexual maturity, survival and body size -factors that determine individual fitness and, ultimately, the persistence of a population (Stearns, 1976;Dmitriew, 2011;Vincenzi et al, 2014). Fish retain growth records in various calcified structures, such as scales, otoliths, and vertebrae.…”

“…Among these above-mentioned structures, the otolith is considered the most appropriate structure for analysis due to lack of absorption of growth increments . Factors affecting growth rate and hence annular deposition within otoliths include genetic variability, 2 e160097 [2] sexual dimorphism, population density, inter-annual variability, and seasonal and spatial variation in resource availability (Henryon et al, 2002;Rypel, 2007;Arantes et al, 2010;Williams et al, 2012;Vincenzi et al, 2014). However, these factors do not act alone, as there is a complex interaction between them (Dieterman et al, 2012).…”

“…Each individual is born with a particular genetic make-up that to some extent controls its growth profile, but physical and biological processes modify the on-going growth rate of an individual (Shelton et al, 2013;Vincenzi et al, 2014). Traditional growth models (i.e., a single observation of length-at-age data per individual) clearly ignore such individual variability because they do not consider the growth trajectory of each individual in the population, and estimates of somatic growth parameters are usually described by "average" population parameters.…”

“…Traditional growth models (i.e., a single observation of length-at-age data per individual) clearly ignore such individual variability because they do not consider the growth trajectory of each individual in the population, and estimates of somatic growth parameters are usually described by "average" population parameters. Recent studies emphasize the importance of including intrapopulation variation in growth models so as to reduce bias in parameter estimation (Pilling et al, 2002;Dieterman et al, 2012;Shelton et al, 2013;Vincenzi et al, 2014). This is important because individuals in a population do not have similar growth parameters.…”