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Uncertainty in source partitioning using stable isotopes.

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Stable isotope mixing models accurately estimate source proportions by including source variability. New formulas and tools improve precision for ecological and environmental studies.

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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.