Auburn University, Department of Geosciences, Auburn, AL, 36849, USA.
Auburn University, Department of Mathematics and Statistics, Auburn, AL, 36849, USA.
Talanta. 2021 May 1;226:122113. doi: 10.1016/j.talanta.2021.122113. Epub 2021 Jan 27.
Measuring changes in the stable isotope ratios of multiple elements (e.g. ΔδC, ΔδCl, and ΔδH) during the (bio)transformation of environmental contaminants has provided new insights into reaction mechanisms and tools to optimize remediation efforts. Dual-isotope analysis, wherein changes in one isotopic system are plotted against another (to derive an interpretational parameter expressed as Λ), is a key tool in multi-element isotopic assessment. To date, most dual-isotope analyses use ordinary linear regression (OLR) for the calculation, which can be subject to regression attenuation and thus an inherent artifact that depresses slope values, expressed as Λ. Here, a series of Monte Carlo simulations were constructed to represent common data conditions and variations within dual-isotope data to test the degree of bias when deriving Λ using OLR compared to an alternative regression technique, the York method. The degree of bias was quantified compared to the modeled or "true" Λ value. For all simulations, the York method provided the least bias in slope estimates (<1%) over all data conditions tested. In contrast, OLR produced unbiased estimates only under a limited set of conditions, which was validated through a mathematical model proof. Both the mathematical model and simulations show that bias of at least 5% in OLR occurs when the extent of enrichment in the x-variable (X) is equal to or less than ≈15 times the 1σ precision in the isotope measurement (σ), for both Cl/C and C/H plots. The results give practitioners tools to evaluate whether bias is present in data and to estimate the extent to which this negatively impacts the interpretations and predictions of remediation potential for new and previously published datasets. This study demonstrates that integration of such robust statistical tools is essential for dual-isotope interpretations widely used in contaminant hydrogeology but relevant to other disciplines including environmental chemistry and ecology.
测量环境污染物（bio）转化过程中多种元素稳定同位素比值的变化（例如 ΔδC、ΔδCl 和 ΔδH），为反应机制提供了新的见解，并为优化修复工作提供了工具。双同位素分析是一种关键工具，其中一个同位素系统的变化与另一个同位素系统的变化进行对比（以得出表示为 Λ 的解释参数），该分析用于多元素同位素评估。迄今为止，大多数双同位素分析使用普通线性回归（OLR）进行计算，这可能受到回归衰减的影响，从而产生固有伪影，从而降低斜率值，表示为 Λ。在这里，构建了一系列蒙特卡罗模拟来代表常见的数据条件和双同位素数据中的变化，以测试使用 OLR 推导 Λ 与替代回归技术（约克方法）相比时的偏差程度。与模型化或“真实”Λ值相比，量化了偏差程度。对于所有模拟，在所有测试的数据条件下，约克方法提供的斜率估计偏差最小（<1%）。相比之下，OLR 仅在有限的条件下提供无偏差的估计，这通过数学模型证明得到了验证。数学模型和模拟都表明，当 x 变量（X）的富集程度等于或小于测量同位素的 1σ 精度（σ）的约 15 倍时，OLR 会产生至少 5%的偏差，对于 Cl/C 和 C/H 图都是如此。结果为从业者提供了评估数据中是否存在偏差的工具，并估计了这种偏差对新数据集和以前发表的数据集的修复潜力的解释和预测的负面影响程度。本研究表明，整合这种稳健的统计工具对于在污染物水文地质学中广泛使用的双同位素解释至关重要，但也与环境化学和生态学等其他学科相关。
