Bias and uncertainty of δ¹³CO₂ isotopic mixing models

Abstract

Patterns in the isotopic signal (stable C isotope composition; δ¹³C) of respiration (δ¹³C_R) have led to important gains in understanding the C metabolism of many systems. Contained within δ¹³C_R is a record of the C source mineralized, the metabolic pathway of C and the environmental conditions during which respiration occurred. Because gas samples used for analysis of δ¹³C_R contain a mixture of CO₂ from respiration and from the atmosphere, two-component mixing models are used to identify δ¹³C_R. Measurement of ecosystem δ¹³C_R, using canopy airspace gas samples, was one of the first applications of mixing models in ecosystem ecology, and thus recommendations and guidelines are based primarily on findings from these studies. However, as mixing models are applied to other experimental conditions these approaches may not be appropriate. For example, the range in [CO₂] obtained in gas samples from canopy air is generally less than 100 μmol mol⁻¹, whereas in studies of respiration from soil, foliage or tree stems, the range can span as much as 10,000 μmol mol⁻¹ and greater. Does this larger range in [CO₂] influence the precision and accuracy of δ¹³C_R estimates derived from mixing models? Does the outcome from using different regression approaches and mixing models vary depending on the range of [CO₂]? Our research addressed these questions using a simulation approach. We found that it is important to distinguish between large (>1,000 μmol mol⁻¹) and small (<100 μmol mol⁻¹) ranges of CO₂ when applying a mixing model (Keeling plot or Miller–Tans) and regression approach (ordinary least squares or geometric mean regression) combination to isotopic data. The combination of geometric mean regression and the Miller–Tans mixing model provided the most accurate and precise estimate of δ¹³C_R when the range of CO₂ is ≥1,000 μmol mol⁻¹.