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Taylor and Francis Group, International Journal of Environmental Analytical Chemistry, 1(92), p. 1-27

DOI: 10.1080/03067319.2010.522236

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Scaling confounds the interpretation of isotopic data

This paper is available in a repository.
This paper is available in a repository.

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Abstract

We demonstrate that delta values (δ) and other relative ratio-based isotopic expressions can vary with the total amount of isotopes present in the system or subject being evaluated. Although these scaling effects are routinely overlooked, interpretive errors such as noting of spurious treatment effects or not detecting significant effects may occur. Algebraic conversions of linear or log-log equations (rare isotope predicted by common or total isotope) that suggest apparently miniscule scaling will fit the observed relationship between isotopic ratios and total or common isotopes. When the ranges of scaling induced differences in isotopic ratios are converted to the equivalent discrimination expressions (Δ) or delta values (δ), differences are within the range that is generally reported in the isotopic literature. Therefore, interpreting observed differences in isotopic ratios may require an evaluation to determine whether treatments directly affect how a rare isotope is accumulated or are associated with differences in denominator size. If effects are direct, points for different treatments fall on different linear and log-log (total isotope vs. rare isotope or common isotope vs. rare isotope) regression lines. Slope differences or derivatives may be more revealing than changes in isotopic ratios and better represent system change in a scaling system. By simply recording total common isotope or total elemental content, standard statistical procedures that evaluate changes in slopes or derivatives can be combined with an ANCOVA to better evaluate isotopic data. In many cases, scaling issues will not interfere with interpretations. In other situations it may be difficult to untangle a combination of ubiquitous scaling, treatment induced scaling and direct treatment effects.