Using a least-squares optimization procedure to estimate botanical composition based on the alkanes of plant cuticular wax

Abstract

The existing mathematical methods for estimating botanical composition of an animal's diet from the concentrations of plant alkanes in herbage and faecal samples all have significant limitations. These include the need for an arbitrary selection of a subset of alkanes for use in the calculations, the loss of information, or the generation of negative estimates for diet components when more than two species are present. We present a new algorithm for solving the diet composition problem, which overcomes these difficulties and is rapid to compute. This algorithm (known as non-negative least squares-NNLS) is shown to perform as well as previous methods on a set of herbage mixtures of known composition. Issues relating to the estimation of the errors of diet composition estimates are discussed.