Error-weighted maximum likelihood (EWML): a new statistically based method to cluster quantitative micropaleontological data

The advent of readily available computer-based clustering packages has created some controversy in the micropaleontological community concerning the use and interpretation of computer-based biofacies discrimination. This is because dramatically different results can be obtained depending on methodology. The analysis of various clustering techniques reveals that, in most instances, no statistical hypothesis is contained in the clustering model and no basis exists for accepting one biofacies partitioning over another. Furthermore, most techniques do not consider standard error in species abundances and generate results that are not statistically relevant. When many rare species are present, statistically insignificant differences in rare species can accumulate and overshadow the significant differences in the major species, leading to biofacies containing members having little in common. A statistically based “error-weighted maximum likelihood” (EWML) clustering method is described that determines biofacies by assuming that samples from a common biofacies are normally distributed. Species variability is weighted to be inversely proportional to measurement uncertainty. The method has been applied to samples collected from the Fraser River Delta marsh and shows that five distinct biofacies can be resolved in the data. Similar results were obtained from readily available packages when the data set was preprocessed to reduce the number of degrees of freedom. Based on the sample results from the new algorithm, and on tests using a representative micropaleontological data set, a more conventional iterative processing method is recommended. This method, although not statistical in nature, produces similar results to EWML (not commercially available yet) with readily available analysis packages. Finally, some of the more common clustering techniques are discussed and strategies for their proper utilization are recommended.