Statistical Analysis
With the realization that elemental fingerprints can be used very effectively to separate mixtures of fish coming from different sources, there is increasing demand for statistical software to separate the group mixtures. Discriminant analysis is not a good option here, since the 'priors' parameter is unknown. Here, we've released a working copy of two different methods for use in separating stock mixtures based on elemental fingerprints or other continuous or categorical variables.
A Bayesian stock mixture analysis (mix.Fish) which allows for the simultaneous analysis of both continuous (elemental) and categorical data (genetic, meristic) was described in Smith and Campana (2010). The mix.Fish R package (which includes a sample dataset) is available for free download and was written for R 3.0.1. Mix.Fish for Unix is also available. Installation instructions are provided.
The Integrated Stock Mixture Analysis (ISMA) program (written for the S-Plus environment) was first described in Campana et al. (1999). The ISMA function is a maximum likelihood-based method to analyze an unknown mixture given some known (reference) groups. Below you will find the ISMA function and a companion file which provides operating instructions. To read the function into your Splus session, just enter the following: source("d:\\assess\\scaling\\ISMA.ssc") ... using your appropriate paths, of course.
Note that no matter which method is used for the stock mixture analysis, mixture analyses don't tell you if there are differences among your reference groups to start with. For this, a MANOVA or discriminant analysis is required. The more differentiated your reference groups are (based on the variables you use), the more accurate your classification of your unknown mixture will be.