Sources of Uncertainty in Biotransformation Mechanistic Interpretations and Remediation Studies using CSIA

Abstract

Compound-specific isotope analysis (CSIA) is a powerful tool to understand the fate of organic contaminants. Using CSIA, the isotope ratios of multiple elements (δ 13 C, δ 2 H, δ 37 Cl, δ 15 N) can be measured for a compound. A dual-isotope plot of the changes in isotope ratios between two elements produces a slope, lambda (Λ), which can be instrumental for practitioners to identify transformation mechanisms. However, practices to calculate and report Λ and related uncertainty are not universal, leading to the potential for misinterpretations. Here, the most common methods are re-evaluated to provide the basis for a more accurate best-practice representation of Λ and its uncertainty. The popular regression technique, ordinary linear regression, can introduce mathematical bias. The York method, which incorporates error in both variables, better adapts to the wide set of data conditions observed for dual-isotope data. Importantly, the existing technique of distinguishing between Λs using the 95% confidence interval alone produces inconsistent results, whereas statistical hypothesis testing provides a more robust method to differentiate Λs. The propensity for Λ to overlap for a variety of conditions and mechanisms highlights the requirement for statistical justification when comparing data sets. Findings from this study emphasize the importance of this evaluation of best practice and provide recommendations for standardizing, calculating, and interpreting dual-isotope data.

Quantification of Lambda (Λ) in multi-elemental compound-specific isotope analysis

“…It can be determined either by simply using the two enrichment factors and the right-hand side of equation 1 on one hand, or from regression analysis in a dual-isotope plots with isotope data of one element versus data of another element in the same compound ( Figure 1). Lambda values were obtained in many studies (Ojeda et al, 2019, Palau et al, 2017, Rosell et al, 2007, Rodriguez-Fernandez et al, 2018, Rodriguez-Fernandez et al, 2018, Dogan-Subasi et al, 2017, Cretnik et al, 2013, Audi-Miro et al, 2013, Palau et al, 2014, Lian et al, 2019, Badin et al, 2016, Mogusu et al, 2015, Ponsin et al, 2019, McKelvie et al, 2009, Pati et al, 2012 from the regression analyses in dual-isotope plots (i.e., ratios of one isotope as a function of another isotope as delta values; Figure 1A).…”

“…The slope of the dual-isotope plot (Lambda, ) reflects changes of the isotope ratios of each element, which can be specific to a reaction mechanism, and thus inform about transformation processes in the laboratory or in the field. (Vogt et al, 2016, Elsner, 2010 Several studies (Masbou et al, 2018, Huntscha et al, 2014, Lian et al, 2019, Bouchard et al, 2018, Vogt et al, 2016, Elsner, 2010, Ojeda et al, 2019 refer to  using the simple definition in eq. 1, which is written here as an example for hydrogen vs carbon d values (eq.…”

“…Apart from those two different conventions for plotting isotope data, different methods of linear regression were proposed to obtain . These include the ordinary linear regression (OLR), the reduced major axis regression (RMA), and the York linear regression, which have been compared recently (Ojeda et al, 2019).…”

A modified method to calculate dual-isotope slopes for the natural attenuation of organic pollutants in the environment

“…(iii) Calculating Λs and its uncertainty by dual-isotope plots that use regression with York method (Ojeda et al 2019). Plotting dual-isotope, OLR only minimizes the sum of squares of one type of isotope signature set as y-variable, without considering the measurement error of another one.…”

“…While measurement errors are inherent to both variables and neither of them could be ignored. Λyork is obtained by regressing measured data through the York method that incorporates uncertainty in both isotope measurements (Ojeda et al 2019), then Λyork as a more appropriate estimation of Lambda than ΛOLR was proposed.…”