UW Aquatic & Fishery Sciences Quantitative Seminar

# Tom Helser

Alaska Fisheries Science Center

**A Bayesian model of radiocarbon ∆14C signatures in fish otoliths: A Probabilistic Tool for Age Validation and Examining Oceanographic Factors Affecting Functional Responses **

## Abstract

Atomic bomb testing during the 1950s and 1960s produced atmospheric radiocarbon, which after a slight delayed response, diffused into the marine environment and became incorporated into fish otoliths alive during that time. In recent years, measured bomb-produced radiocarbon (∆14C) was developed as an age validation tool which compares the ∆14C signature from test specimens to the ∆14C of known age fish (reference chronology). To date, calcium carbonate structures in dozens of animals across different taxa have been measured for ∆14C, but only a handful of true reference chronologies have been developed with which to compare the ∆14C signatures. In addition, a variety of statistical models and methods have been proposed to describe the functional form of radiocarbon chronologies and provide a quantitative means to compare them. However, none have been completely satisfactory in quantifying ageing bias and its uncertainty. We developed a multi-level Bayesian model and used Markov Chain Monte Carlo Simulation to estimate parameters of different functional response models and to derive a statistical framework for hypothesis tests concerning ageing bias. The model incorporates both observation and process errors and provides framework to estimate the probability of ageing bias overall from a given sample but also the probability conditional on the animal’s age. Results presented are based on a comparison of canary rockfish (*Sebastes pinniger*) and Pacific Ocean perch (*Sebastes alutus*) ∆14C data to the Gulf of Alaska halibut reference chronology. Canary rockfish showed a high probability of being under aged with as high as a 95% probability that under aging was occurring by as much as 6 years. In contrast, the mean ageing bias for Pacific Ocean perch was +1.4 years but considerable density of the marginal posterior encompassed zero suggesting the evidence was weak to conclude any bias. Finally, we extended the complexity of the Bayesian model by incorporating over a dozen different ∆14C chronologies from California to the Gulf of Alaska into a hierarchically structured model and tested for the effects of different oceanographic factors on the functional response of the radiometric curves. The index of ocean upwelling was negatively related to the overall magnitude of 14C measured in calcified structures of marine animals while the parameter commonly used to test bias was weakly positively correlated. This suggests the potential for age bias interpretations to be confounded when ∆14C test samples are compared to reference chronologies derived from different oceanographic regions.