MODELING THE DENSITY OF FOSSILS FROM CROSS-SECTION EXPOSURES: AN EXAMPLE FROM THE ORDOVICIAN OF THE ARROW CANYON RANGE, NV

Collecting accurate density data for deposits with low-concentrations of fossils can prove challenging. Paleontologists are often tasked with reconstructing bed density from cross sections, especially when beds are not exposed in plan view. In these situations, low-concentration and patchy fossil material can easily be underestimated or missed completely. While this problem can be addressed through bulk sampling at high-frequency intervals, this method is not always practical. Bulk sampling might be impeded by lithology, restricted or regulated by volume, or the locality might be too remote to transport bulk samples.

While several models do an excellent job of modeling the accumulation of fossil concentrations from sedimentation rate, no model exists to estimate the density of fossil material within a bed from cross-section exposure. Fortunately, geospatial modeling issues like this have long been considered in mathematics realm, and we can build off of existing thought experiments and basic geometry to create a workable model for paleontological applications. For example, the Buffon-Laplace Needle Problem (first suggested by Buffon, 1777 and later refined by Laplace, 1812, 1820) models the probability that a tossed needle of length l will land on at least one line, given a floor with a grid of equally spaced parallel lines distances a and b apart, with l > a,b. These types of models can be adapted to modeling the occurrence of fossil material within a shellbed by counting cross-section occurrences.

Here we present a model using simple geometry to calculate the density of fossil material within a bed from cross section counts. Our model is adapted from Buffon's studies and calibrated against a unique Ordovician biofacies comprised of oncoids, macluritid gastropods and receptaculitids. The varied modes of exposure of this biofacies in the Arrow Canyon Range of Southern Nevada provide an ideal dataset with which to calibrate this model. Within a 120m stratigraphic interval, fossil material is commonly exposed in large, meter-scale bedding planes and in cross section, thus providing several "snapshots" of fossil distribution on the seafloor.