Mixed Model Approaches Can Leverage Database Information to Improve the Estimation of Size-Adjusted Contaminant Concentrations in Fish Populations

Abstract

Concentrations of bioaccumulative contaminants in fish increase with their size and age; thus, research and monitoring of these contaminants in fish across space and time can be confounded by size covariation. To account for this, size-standardization of contaminant concentrations within fish samples is a common practice. Standardized concentrations are often estimated using within-sample regression models, also known as power series regression (referred to here as sampling event regressions, or SERs). This approach requires higher sample sizes than mixed effect models (MEMs), which are suited for this application but are not as commonly used. Herein we compare SERs to three MEM approaches; restricted maximum likelihood, Bayesian inference via Markov chain Monte Carlo (MCMC), and approximate Bayesian inference with nested Laplace approximation (INLA). We did this for two contaminants: mercury (Hg), a contaminant known to bioaccumulate, and arsenic (As), where the bioaccumulative potential is less understood. The MEM approaches generated size-standardized concentrations for small populations (e.g., <5 fish) and/or populations that lacked the range of sizes required for SER estimates, with comparable residual and root mean squared error to SER estimates. INLA was determined to be the best method in most cases because it was computationally less intensive than other approaches and showed consistent performance across a range of scenarios with sample-size limitations. Additionally, we provided example code for prediction using the R-INLA package to enable use and application in fisheries’ contaminant monitoring and research.