Using a Bayesian Hierarchical Linear Mixing Model to Estimate Botanical Mixtures

In grazing systems, estimating the dietary choices of animals is challenging but can be achieved using plant-wax markers, natural compounds that provide a signature of individual plants. If sufficiently distinct, these signatures can be used to characterize the makeup of a botanical mixture or diet. Bayesian hierarchical models for linear unmixing (BHLU) have been widely used for hyperspectral image analysis and geochemistry, but not diet mixtures. The aim of this study was to assess the efficiency of BHLU to estimate botanical mixtures. Plant-wax marker concentrations from eight forages found in Nebraska were used for simulating combinations of two, three, five and eight species. Also, actual forage mixtures were constructed in laboratory and evaluated. Analyses were performed using BHLU with 2 prior choices for forage proportions (uniform and Gaussian), 2 covariance structures (independent and correlated markers), stable isotope mixing models (SIMM), and nonnegative least squares (NNLS). Accounting for correlations between markers increased efficiency. Estimation error increased when Gaussian priors were used to model forage proportions. Performance of BHLU, SIMM, and NNLS was reduced with the more complex botanical mixtures and the limited number of markers. For simple mixtures, BHLU is a reliable alternative to NNLS for estimation of forage proportions. Supplementary materials accompanying this paper appear online.