Characterizing the dynamics of amino acid racemization using time-dependent reaction kinetics: A Bayesian approach to fitting age-calibration models

Robust estimates of specimen age and associated precision are critical to the study of many palaeobiological and sedimentological processes. While recent work has explored a variety of methods for calibrating the rate of amino acid racemization using paired radiocarbon analyses, and for assessing the precision of age estimates obtained using these models, the calibration models themselves, and the underlying assumptions used to construct them, have not yet been rigorously evaluated. Here we use a Bayesian model fitting procedure to compare three previously proposed calibration functions ("apparent parabolic kinetics" [APK], "simple power-law kinetics" [SPK], and "constrained power-law kinetics" [CPK]), and we propose a new function, "time-dependent reaction kinetics" (TDK), which has a mechanistic basis in first-order reversible kinetics. We then evaluate which of three statistical distributions - normal, lognormal, gamma - best describes the prediction uncertainty associated with each age-calibration function. The Bayesian fitting method outlined here is superior to the least-squares fitting approach commonly used because it allows greater flexibility in modelling this uncertainty and its effects on the precision of age estimates. To facilitate the adoption of this methodology, we provide an analytical script that can be implemented on a variety of computer platforms using freely available software.Regardless of the fitted calibration function, we find that the gamma and lognormal distributions more accurately describe prediction uncertainty than to the normal distribution. Three of the four calibration functions perform well (the exception being APK), but no single function performs best in all situations. In general, TDK and CPK (which we show to be a special case of TDK) yield superior model fits to SPK when d/. l is close to saturation, and moreover provide useful mechanistically-based functions for calibrating amino acid racemization datasets.