Detecting Coordinated Stasis by Model Ranking

One of the most intriguing and debated recent proposals in paleoecology is coordinated stasis (Brett and Baird, 1995; Brett et al., 1996, DiMichele et al. 2004), in which assemblages of taxa persist with little or no morphological change. Coordinated stasis (CS) is an observed pattern of stable associations of taxa over time bracketed by abrupt turnovers. It was first proposed in the Silurian/Devonian Appalachian Basin of New York State and has been investigated elsewhere.

We advocate the use of the more modern statistical approach of model ranking, rather than the more familiar hypothesis testing. The CS model of stasis is ranked against all or any plausible models that incorporate changes in taxa distributions. Hypothesis testing methods, including Analysis of Similarities (ANOSIM), is often problematic because the null of no structure is ill-posed. The null of randomness is often simply the hypothesis of uniform distribution on some transformation of the data such as a dissimilarity measure. The null is often rejected in favor of an alternative because the null is simply not a reasonable state of nature.

Model ranking is also more intuitive and informative than hypothesis testing and allows the incorporation of more geological information into the analysis, such as the temporal ordering of samples, typically not preserved in cluster analysis. We argue that the preservation of the ordering of samples is important under the CS hypothesis.

We advocate probability models on the data in place of distance-based models whenever possible. The CS hypothesis, formulated as static taxa distributions over time, with abrupt faunal turnovers, is naturally and simply modeled as a sequence of static multinomial observations with change-points. There is no worry about the effect of choice of distances or dissimilarities, choice of transformations to de-emphasize particularly abundant taxa, or clustering methodology, making our approach considerably simpler to formulate.