Uncertainty in source partitioning using stable isotopes

Area of Science:

• Ecology
• Environmental Science
• Isotope Geochemistry

Background:

• Stable isotope analyses quantify source contributions in mixtures, like diet or soil carbon.
• Linear mixing models are used for two- or three-source partitioning based on isotopic signatures (e.g., δ13C, δ15N).
• Current models often neglect source variability, potentially underestimating proportion uncertainty.

Purpose of the Study:

• To develop and present formulas for calculating variances, standard errors (SE), and confidence intervals for source proportions in mixing models.
• To account for variability in both source and mixture isotopic signatures.
• To assess factors influencing the precision of source proportion estimates.

Main Methods:

• Derived variance formulas for two- and three-source linear mixing models.
• Conducted sensitivity analyses on signature differences, standard deviations (SD), sample size, analytical SD, and proportion evenness.
• Developed graphical tools and an Excel spreadsheet for calculations.

Main Results:

• Omission of source variability can lead to underestimation of proportion uncertainty.
• Source proportion SEs decrease with larger isotopic signature differences and increase with higher source/mixture SDs.
• SEs decrease with the square root of sample size and are minimized with even source proportions.

Conclusions:

• The provided variance formulas enable precise quantification of source proportion estimates.
• Understanding the influence of isotopic variability is crucial for accurate ecological and environmental assessments.
• Accessible tools facilitate the application of these improved mixing models.