Quantitative or semi-quantitative methods for biostratigraphy are not yet in common use, except for the relatively subjective approach of graphical correlation. Such methods are, however, well developed, and we hope that the inclusion of one method in PAST will help introduce more paleontologists to this field. We have chosen to implement Unitary Associations analysis (Guex 1991) because of its solid theoretical basis and minimum of statistical assumptions.

The data input consists of a presence-absence matrix with samples in rows and taxa in columns. Samples belong to a set of sections (localities), where the stratigraphical relationships within each section are known. The basic idea is to generate a set of assemblage zones (similar to 'Oppel zones') that are optimal in the sense that they give maximal stratigraphic resolution with a minimum of superpositional contradictions. An example of such a contradiction would be a section containing species A above species B, while assemblage 1 (containing species A) is placed below assemblage 2 (containing species B). The method of Unitary Associations is a logical but somewhat complicated procedure, consisting of several steps. Its implementation in PAST does not include all the features found in the standard program, called BioGraph (Savary and Guex 1999), and advanced users are referred to that package.

PAST produces a detailed report of the analysis, including maximal cliques, unitary associations, correlation table, reproducibility matrix, contradictions between cliques, biostratigraphic graph, graph of superpositional relationships between maximal cliques, and strong components (cycles) in the graphs (Guex 1991). It is important to inspect these results thoroughly in order to assess the quality of the correlation and to improve the quality of the data, if necessary. Angiolini and Bucher (1999) give an example of such careful use of the method of Unitary Associations.