  In this paper we review recent advances in Stable Isotope Mixing Models
(SIMMs) and place them into an over-arching Bayesian statistical framework
which allows for several useful extensions. SIMMs are used to quantify the
proportional contributions of various sources to a mixture. The most widely
used application is quantifying the diet of organisms based on the food sources
they have been observed to consume. At the centre of the multivariate
statistical model we propose is a compositional mixture of the food sources
corrected for various metabolic factors. The compositional component of our
model is based on the isometric log ratio (ilr) transform of Egozcue (2003).
Through this transform we can apply a range of time series and non-parametric
smoothing relationships. We illustrate our models with 3 case studies based on
real animal dietary behaviour.
