Probability models for stasis and change in paleocommunity structure

The hypothesis of coordinated stasis (CS) holds that taxa within ecological communities show a pattern of persistence over geologic time (faunal stability). This hypothesis has been examined by looking for evidence of stasis and change in paleocommunity structure based on patterns of taxon abundances obtained from bulk samples of fossil assemblages. Community structure based on taxon counts is often investigated using distance-based clustering methods, employing Analysis of Similarity (ANOSIM) or other multivariate statistical tools. We propose a new method for analyzing trends in community structure by viewing taxon counts from bulk samples as a time series and assess stasis and change based on a probabilistic assessment of the continuity of the species distribution patterns. In this flexible approach, taxon counts from samples ordered in time or space (or grouped by a geologically informed hypothesis) are modeled as a sequence of multinomial or Bernoulli outcomes drawn from an underlying ecological distribution. The optimal model of community structure may then be chosen from a set of hypotheses about those distributions, based on Akaike's Information Criterion, an information-theoretic measure of fit that penalizes likelihood of fitting the data with the number of parameters needed to attain the fit. CS is the model in which the underlying probabilities for each sample are constant across different samples. In other words, the most likely scenario is that all samples are drawn from the same underlying taxon abundance distribution. We propose that this approach is a powerful and flexible method to statistically assess CS, as well as other hypotheses about community structure, and we demonstrate this method using paleoecological data from the literature.