Bayesian hierarchical modeling of Pacific geoduck growth increment data and climate indices

Growth increment widths from hard structures of marine and freshwater fish and bivalve species are increasingly used to model growth and elucidate relationships with environmental variability. Fully characterizing the intrinsic age-related growth variation among individuals within and between populations, while estimating the extrinsic environmental effects simultaneously, can be challenging. Using the long-lived bivalve Pacific geoduck (Panopea generosa), we develop an integrated approach to analyze the relationship between growth increment data and climate indices using Bayesian hierarchical methods. Fitting models to growth increment data from multiple individuals over two sites, we examined different covariance structures related to random individual effects, long- and short-term environmental effects and unexplained errors. The best fitting hierarchical model accounted for a site-specific mean growth response, individual growth variability through random parameter effects, and site-specific error variances. Extrinsic environmental effects on growth were also significant and included a random year effect and the Pacific Decadal Oscillation (PDO) as a predictor of mean growth across both individuals and sites. Once intrinsic age-related growth was accounted for, PDO accounted for 18% to total variability in growth increment data; geoduck shell size was predicted to increase as a function of larger PDO anomalies. However, the greatest variability in growth increment data was explained by random year effects (∼60–70%), and while largely unexplained, sea surface temperature (SST) is a likely determinant on geoduck growth rates showing a positive growth–SST response.