LEAST-SQUARES ESTIMATION OF DIET COMPOSITION FROM N-ALKANES IN HERBAGE AND FECES USING MATRIX MATHEMATICS

It is possible to estimate diet composition from an analysis of n-alka nes in the faeces of ruminant animals. For instance, to estimate the p roportion of two species in a diet, two equations are constructed usin g the known concentrations of two different n-alkanes in the herbage a nd in the animal's faeces. These two equations are solved for the two unknown quantities of the diet components. Two problems exist with thi s method. First, it is often the case that we have estimated concentra tions of more than two different n-alkanes. This can lead to a problem in deciding which two n-alkanes to use to construct the simultaneous equations. The choice of this pair of n-alkanes is arbitrary in its se lection and wasteful of other useful information. The second problem i s that sometimes the solution to the simultaneous equations yields non sensical answers, such as a negative proportion of one species in the diet. In addition to making it difficult to estimate dietary proportio ns, estimating digestibility becomes impossible. In this paper, we pre sent a technique which provides an estimate of the dietary proportions . This estimate uses information on all the n-alkanes available, and i t has a very desirable property of being a least squares estimate. We also present a method for determining the least squares estimate subje ct to the constraint that all proportions must be non-negative. We pro vide examples for estimating the proportions of grass and clover in th e diet of sheep and the digestibility of those diets.