Seriation in Paleontological Data Using Markov Chain Monte Carlo Methods

Given a collection of fossil sites with data about the taxa that occur in each site, the task in biochronology is to find good estimates for the ages or ordering of sites. We describe a full probabilistic model for fossil data. The parameters of the model are natural: the ordering of the sites, the origination and extinction times for each taxon, and the probabilities of different types of errors. We show that the posterior distributions of these parameters can be estimated reliably by using Markov chain Monte Carlo techniques. The posterior distributions of the model parameters can be used to answer many different questions about the data, including seriation (finding the best ordering of the sites) and outlier detection. We demonstrate the usefulness of the model and estimation method on synthetic data and on real data on large late Cenozoic mammals. As an example, for the sites with large number of occurrences of common genera, our methods give orderings, whose correlation with geochronologic ages is 0.95.Synopsis: Seriation, the task of temporal ordering of fossil occurrences by numerical methods, and correlation, the task of determining temporal equivalence, are fundamental problems in paleontology. With the increasing use of large databases of fossil occurrences in paleontological research, the need is increasing for seriation methods that can be used on data with limited or disparate age information. This paper describes a simple probabilistic model of site ordering and taxon occurrences. As there can be several parameter settings that have about equally good fit with the data, the authors use the Bayesian approach and Markov chain Monte Carlo methods to obtain a sample of parameter values describing the data. As an example, the method is applied to a dataset on Cenozoic mammals. The orderings produced by the method agree well with the orderings of the sites with known geochronologic ages.