Diagnosing underdetermination in stable isotope mixing models.

Area of Science:

• Ecology
• Geology
• Archaeology
• Statistical Modeling

Background:

• Stable isotope mixing models (SIMMs) are crucial for quantifying source contributions in mixtures.
• Bayesian SIMMs have advanced, but underdetermination of mixing space limits accurate estimation of source contributions.

Purpose of the Study:

• To develop a statistical method for quantitatively diagnosing underdetermination in Bayesian SIMMs.
• To introduce the β-dependent SIMM as a tool for assessing the identifiability of source contributions.

Main Methods:

• Proposed a novel statistical method, termed β-dependent SIMM, to diagnose underdetermination.
• Applied the method to simulation data and published field data to demonstrate its utility.

Main Results:

• The β-dependent SIMM rigorously quantifies expected underdetermination through β-dependent posterior intervals.
• Identified limitations of ordinary SIMMs in quantifying individual source underdetermination and potential inconsistencies with joint posterior peaks.

Conclusions:

• β-dependent SIMMs serve as a valuable diagnostic tool for addressing underdetermined mixing problems.
• Recommends reporting β-dependent SIMM results alongside ordinary SIMMs for biologically feasible and sound interpretations of stable isotope data.