Mathematical expressions used in amino acid racemisation geochronology: A review

A variety of mathematical expressions that describe changes over time (t) in the extent of amino acid racemisation (AAR, expressed as the ratio of D- to L-amino acid isomers or epimers) have been used in Quaternary geochronology. The integrated rate equation was first used to estimate fossil age from D/L but its geochronological utility is disadvantaged by uncertainties regarding the conformity of AAR in fossil protein to apparent reversible first-order kinetics for the entire reaction history. 'Non-linear' models have subsequently been used to relate D/L to t. The logarithmic equation successfully applied to Atlantic Coastal Plain research has not achieved widespread application, perhaps due to the regional calibration required if sensitivity to temperature is to be modelled, or the difficulties encountered when extending the model to include fossils with D/Lo0.1. Success producing a linear correlation between D/L transformed with a power function and t has seen this approach emerge as one of the most commonly applied in AAR geochronology in recent years. Like parabola curve fitting, which has been applied to trends in D/L versus t in a variety of fossils and geographic settings, power transformations may not be suitable for geochronological modelling during the latter stages of amino acid diagenesis. Several studies have demonstrated the utility of simple and contingent linear equations for relating D/L to t. Future research should aim to reduce reliance on independent calibration and explore the geochronological benefits of AAR in pools other than the total hydrolysable amino acids.