Linear Unmixing Models: Extensions and Applications to the Estimation of Dietary (Botanical) Mixing Proportions

Estimating feed efficiency in grazing environments is challenging due to difficulties in quantifying food intakes and diet choices in free-grazing animals. The plant-wax marker technique may be a useful tool to redress this problem. While nonnegative least-squares (NNLS) has been widely used to estimate diet composition using plant-wax markers, in some instances it may not be optimal. An alternative class of flexible models, Bayesian hierarchical linear unmixing (BHLU) models, has been widely used to achieve a similar aim in hyperspectral image analysis and geochemistry, but not diet mixtures. Thus, the goals of the current work were i) to determine the efficiency and accuracy of estimates of botanical mixtures and dietary choices obtained by linear unmixing models under a Bayesian framework (BHLU), and ii) to extend and generalize BHLU and NNLS to more realistically reflect and account for animal and other sources of variation. To carry out these objectives analyses of simulated and real data were performed. From these analyses, BHLU was a reliable methodology for the estimation of diet composition using multivariate plant-wax marker data. However, although intended to more appropriately account for variability and nonlinearity in plant-wax marker concentration data, increasing the complexity of the models fitted did not improve estimation accuracy, perhaps due to increased uncertainty as more parameters were estimated. Moreover, simpler models (including NNLS) often outperformed BHLU and its extensions. Still, clear distinction between the performances of the methodologies was equivocal. Further generalizations of BHLU and NNLS to account for covariance among repeated measurements and genetic relationships among animals improved (although marginally) accuracy of estimation, especially when including a relationship matrix. While the results obtained showed that both BHLU and NNLS perform comparably well in many instances, the possibility of including prior knowledge into the estimation of diet composition is an appealing advantage of BHLU methodology