A Bayesian hierarchical meta-analysis of fish growth: with an example for North American largemouth bass, Micropterus salmoides

Abstract

Variability in animal growth from one population to another is of keen interest to population ecologists wishing to understand the inherent within species variability and explore meaningful environmental covariates. Yet most studies investigating growth of animals within a population are usually analyzed in isolation from, or at best, compared qualitatively across populations. Here, we introduce statistical methods that permit simultaneous quantitative analysis of the growth of 245 populations of largemouth bass ( Micropterus salmoides) across the North American Continent. Growth in length at age is modeled using a nonlinear mixed effect model and we used Bayesian hierarchical meta-analysis as a natural approach to estimate parameters, investigate growth variability among populations and to elucidate meaningful biological covariates for this species. Growth of M. salmoides across North America varied by more than 120% in terms of maximum attainable size ( L ∞; 36–80 cm) and by more than 88% in terms of instantaneous growth rates ( K; 0.091 to 0.670 per year). Results from this method also confirm the theoretical, but often untested, view that growth parameters L ∞ and K are negatively correlated in fish populations; Bayesian credibility intervals ranged from −0.56 to −0.72 with the posterior mode of −0.65. The Bayesian hierarchical growth model showed less variability in growth parameters and lower correlations among parameters than those from standard techniques used in population ecology suggesting that the absolute value of the correlation between L ∞ and K may be lower than the general perception in the ecological literature, often in the range of −0.8 to −0.9. Finally, growth parameters were negatively correlated with latitude suggesting that population productivity most likely declines the higher in latitude a population is found for this species.