A Constrained Divisive-Compositional Approach to Micropalaeontological Ecozonation

Abstract

Zonation of stratigraphic successions is a key practice for identifying intervals characterised by stability or, conversely, by palaeoenvironmental changes. Stratigraphically constrained agglomerative algorithms have been commonly adopted to obtain zonation based on quantitative palaeontological data. Here we explore constrained divisive algorithms aiming at obtaining a zonation that meets the principle of maximizing coefficients commonly used to evaluate the effectiveness of clustering algorithms. In particular, a constrained version of Cavalli Sforza’s method was applied, together with an algorithm conceived to maximise, at each division, the average silhouette width of the observations. The results were compared, following the compositional data analysis properties, with those obtained with a commonly adopted agglomerative method. When evaluated on artificial data, the divisive algorithms show stability and a tendency to identify the boundary between intervals at the midpoint of transitions, consistently with common stratigraphic practice. Overall, the application to real micropalaeontological data, consisting of percentages of planktonic foraminifera, provide reasonable zonation patterns with all algorithms considered. For the main partition, the constrained version of Cavalli Sforza’s method provides highest values of Calinski–Harabasz and Hartigan indexes, while the average silhouette width method, as expected, performs better in the evaluation of average silhouette width index as well as of Goodman–Kruskal’s coefficient and cophenetic correlation. One potential issue to consider is the tendency to define single sample intervals as the number of partitions increases