Trimineralic abalone shells (Haliotis iris Gmelin, 1791) and X-ray diffractometry: A Bayesian calibration model for resolving complex skeletal mineralogy

X-ray diffractometry (XRD) is commonly used to determine both aragonite:calcite ratio and Mg content (in calcite) in biogenic skeletal carbonate. Bimineral taxa, such as many abalone, combine aragonite and calcite, or sometimes two distinct calcites, in a single skeleton. At least some abalone shells are, however, formed of three discrete carbonate minerals: aragonite, high-Mg calcite, and low-Mg calcite. Here we develop and apply a new system based on a Bayesian calibration model, an extension of the Reference Intensity Ratio method that accommodates heteroskedastic noise, for determining relative proportions in trimineralic biogenic carbonate using XRD patterns. We describe the system, validate and assess the system using biomineral standards, and quantify sources of error. We then use the system to describe mineralogical variation within the sometimes-trimineralic New Zealand black-footed pāua Haliotis iris. All specimens contained aragonite, and most contained low-Mg calcite, with older shell showing decreasing amounts of calcite (presumably due to wear of this external layer). Almost all specimens from Kaikoura contained at least some high-Mg calcite, thus being tri-mineralic. This mixture of three biogenic carbonates is most unusual, so we have used our new method of analysing XRD patterns to estimate the proportions of three co-occurring skeletal carbonate minerals in this marine invertebrate. We also provide the first detailed analysis of uncertainty and precision in XRD analysis of skeletal carbonate mineralogy.