Document: DON-3-91-1

Uncertainty in source partitioning using stable isotopes.

PHILLIPS, D.L.* and J.W.GREGG

U.S. EPA, National Health & Environmental Effects Research Laboratory, Corvallis, OR 97333 USA ¹

Abstract:
Stable isotope analyses are often used to quantify the contribution of multiple sources to a mixture, such as proportions of food sources in an animal's diet, C₃ vs. C₄ plant inputs to soil organic carbon, etc. Linear mixing models can be used to partition 2 sources with a single isotopic ratio (e.g., ¹³C) or 3 sources with a second isotopic ratio (e.g., ¹⁵N). For both these cases, we present formulas for calculating variances and confidence intervals for proportion estimates that account for the observed variability in the isotopic ratios for both the sources and the mixture. The source and mixture variances can be separated into sampling and analytical error components. For the 2 source case, sensitivity analyses were performed to test the sensitivity of the standard errors (SE) of the proportion estimates to: (a) the isotopic ratio difference between the sources, (b) source and mixture population standard deviations (SD), (c) sample sizes, (d) analytical SD, and (e) the evenness of the source proportions. The proportion SE's varied inversely with the source isotopic difference, so doubling from a 2 to a 4 difference reduced the SE's by half. The source and mixture population SD's had a substantial linear effect on proportion SE's. However, the population variability of the sources and the mixture are fixed and the sampling error component can be changed only by increasing sample size. The proportion SE's varied inversely with the square root of sample size, so an increase from 1 to 4 samples per population cut the SE in half. Analytical SD had little effect over the range examined since it was substantially smaller than the population SD's. Proportion SE's were minimized when sources were evenly divided, but increased only slightly as the proportions varied. The variance formulas provided will enable quantification of the precision of source proportion estimates. Researchers can halve the uncertainty of estimates either by doubling the difference between sources (e.g., by increasing from 2 to 4) or by quadrupling sample size (e.g., from 1 to 4).

Keywords: stable isotopes, uncertainty, error propagation, mixing model

This abstract is being presented at: 10:30 AM in session:
STATISTICAL ECOLOGY