Diagnosing underdetermination in stable isotope mixing models.

Yutaka Osada,Ichiro Tayasu,Jun Matsubayashi,Hideyuki Doi

doi:10.1371/journal.pone.0257818

Abstract

Stable isotope mixing models (SIMMs) provide a powerful methodology for quantifying relative contributions of several sources to a mixture. They are widely used in the fields of ecology, geology, and archaeology. Although SIMMs have been rapidly evolved in the Bayesian framework, the underdetermination of mixing space remains problematic, i.e., the estimated relative contributions are incompletely identifiable. Here we propose a statistical method to quantitatively diagnose underdetermination in Bayesian SIMMs, and demonstrate the applications of our method (named β-dependent SIMM) using two motivated examples. Using a simulation example, we showed that the proposed method can rigorously quantify the expected underdetermination (i.e., intervals of β-dependent posterior) of relative contributions. Moreover, the application to the published field data highlighted two problematic aspects of the underdetermination: 1) ordinary SIMMs was difficult to quantify underdetermination of each source, and 2) the marginal posterior median was not necessarily consistent with the joint posterior peak in the case of underdetermination. Our study theoretically and numerically confirmed that β-dependent SIMMs provide a useful diagnostic tool for the underdetermined mixing problem. In addition to ordinary SIMMs, we recommend reporting the results of β-dependent SIMMs to obtain a biologically feasible and sound interpretation from stable isotope data.

Highlights

In animal ecology, the development of a methodology for quantifying trophic interactions between consumers and their dietary sources has a long history [1, 2]
We found that changing error structure parameterization from SIAR to Stock’s model leads to wider ΔBDP but improves the consistency between ordinary and beta-dependent marginal posteriors (S1 Table, S3 Fig in S1 File)
Using the published geese data, we found two problematic aspects of underdetermined mixing problems highlighted by the analysis of β-dependent Stable isotope mixing models (SIMMs)

Summary

Introduction

The development of a methodology for quantifying trophic interactions between consumers and their dietary sources has a long history [1, 2]. Stable isotope mixing models (SIMMs) are popular statistical tools for ecologists to estimate the relative contribution of each dietary source to consumers based on isotopic signatures [3, 4], and used in the other fields such as climatology, oceanography, sedimentology and archaeology [5,6,7]. Using a Bayesian framework, the applicability of SIMMs to complex isotopic mixing spaces of realistic systems has rapidly improved [8]. The improvements include the incorporation of measurement errors [9], isotopic correlations [10], element concentrations [11, 12], dietary routings [13], additional residual errors of unknown sources [12], and hierarchical structures of consumer populations [14] and food-webs [15]. Most of them are applicable as an open-source program [16].

Methods

Results

Conclusion