Analysing prehistoric diets by linear programming

Isotopic measurements of skeletal bone, coupled with corresponding measurements of foods that might have been eaten by prehistoric individuals, offer the promise of providing valuable information about their diets. Linear mixing equations relating bone measurements to food measurements for each of several isotopes serve to constrain the percentages of each food that could have been in the diet. Even though it is seldom possible to determine the diet uniquely, it is always possible to set bounds on the percentages of various foods that could have been part of the diet. The more isotopes that have been measured, the tighter will be the bounds. The bounds are determined by means of linear programming. We set up a basic linear model and illustrate the technique with simple examples. Then, using data and implicit mixing equations from Spielmann et al. an extended case demonstrates how linear programming can answer archaeological questions.