A flexible Bayesian method for estimating stratigraphic intervals and their co-occurrence in time

The fossil record is both incomplete and subject to a number of biases with different sources (e.g., preservational, statistical), which hinders making inferences about the past of life on earth. Stratigraphic intervals allow estimate two important quantities from the fossil record of a given lineage, its origination, and extinction times. Many models are available in the literature, although specialising in implementation and therefore resulting in limitations of application. This toolset is extended herein by proposing a flexible method which allows one to estimate origination and extinction times, as well as model preservation potential in flexible ways. The present method is more general than previous alternatives, many of which constitute special cases. A method is presented to represent the stratigraphic interval as a continuous distribution by integrating over parameter uncertainty through the use of the posterior predictive distribution, which represents the stratigraphic interval as a continuous variable in time which already incorporates parameter uncertainty, rather than a bounded interval. It is possible then to combine these distributions using conflation, to build a time probabilistic model for the co-occurrence of these intervals. Empirical examples using the method for estimating the origination and extinction times of palynomorphs and the co-occurrence time for an assemblage of unknown age in the economically important Cerrejon Formation, as well as the origination time of the marine barracudas (family Sphyraenidae), are used for illustrating the potential of the method. It is implemented in the StratIntervals.jl Julia package, which allows a large set of possible prior distributions and MCMC samplers.