A BAYESIAN HIERARCHICAL MODELING PERSPECTIVE ON PALEOCOMMUNITY RECONSTRUCTION AND ANALYSIS

As representatives of paleocommunity structure, fossil assemblage data are plagued by several sources of variation, not only sampling error, but most notably, patchiness. Important notions of community recurrence and geographical extent rely on careful modeling of these data. Without such consideration of scale, evidence for ecological stasis through time, may have been dismissed prematurely on the basis of apparent differences.

The typical metric for a community structure is relative abundance, especially of dominant or ecologically important taxa. A natural model of taxon counts is a multinomial distribution with relative abundances serving as a parameter vector. Two communities are deemed similar if their parameter estimates are statistically indistinguishable, perhaps through a hypothesis test. Yet, in the presence of patchiness, a hypothesis of similarity will nearly always be rejected. The recommended solution is to replicate and pool at a scale to smooth out any patchiness artifacts.

From the point of view of quantitative ecologists, this is an example of nested data – replicates at an outcrop being similar at one scale and outcrops being similar at another scale. Pooling is apt to increase estimator variance because the data arise from different, local distributions causing the similarity hypothesis to be incorrectly rejected. Quantitative ecologists approach these problems using a multilevel or hierarchical model. Such models are straightforward to construct but difficult to estimate without sophisticated software. This is a natural application of Bayesian modeling (e.g., Gelman and Hill, 2007) and is becoming increasingly common in ecology. The key is to relegate variability to its proper level in the hierarchy. Recurrence is assessed at the proper geographic scale once lower level variability has been accommodated.

We illustrate Bayesian hierarchical modeling, estimation and interpretation on several well-known fossil assemblage data sets. In particular, using a data set of Upper Cretaceous shells from (Bennington, 2003), we show that local patchiness can be easily accommodated while determining that there is considerable agreement in community structure across localities at the same stratigraphic level.