Importance of Weighting High-Resolution Proxy Data From Bivalve Shells to Avoid Bias Caused by Sample Spot Geometry and Variability in Seasonal Growth Rate

Abstract

Shells of bivalve mollusks serve as archives for past climates and ecosystems, and human-environmental interactions as well as life history traits and physiology of the animals. Amongst other proxies, data can be recorded in the shells in the form of element chemical properties. As demonstrated here with measured chemical data (10 elements) from 12 Arctica islandica specimens complemented by numerical simulations, mistakes during sclerochronological data processing can introduce significant bias, adding a further source of error to paleoenvironmental or biological reconstructions. Specifically, signal extraction from noisy LA-ICP-MS (Laser Ablation—Inductively Coupled Plasma—Mass Spectrometry) data generated in line scan mode with circular LA spots requires a weighted rather than an arithmetic moving average. Otherwise, results can be in error by more than 41%. Furthermore, if variations of seasonal shell growth rate remain unconsidered, arithmetic annual averages of intra-annual data will be biased toward the fast-growing season of the year. Actual chemical data differed by between 3.7 and 33.7% from weighted averages. Numerical simulations not only corroborated these findings, but indicated that arithmetic annual means can overestimate or underestimate the actual environmental variable by nearly 40% relative to its seasonal range. The magnitude and direction of the error depends on the timing and rate of both seasonal shell growth and environmental change. With appropriate spatial sampling resolution, weighting can reduce this bias to almost zero. On average, the error reduction attains 80% at a sample depth of 10, 92% when 20 samples were analyzed and nearly 100% when 100 samples were taken from an annual increment. Under some exceptional, though unrealistic circumstances, arithmetic means can be superior to weighted means. To identify the presence of such cases, a numerical simulation is advised based on the shape, amplitude and phase relationships of both curves, i.e., seasonal shell growth and the environmental quantity. To assess the error of the offset induced by arithmetic averaging, Monte Carlo simulations should be employed and seasonal shell growth curves randomly generated based on observed variations.