The Plus ça Change model proposed by Sheldon states that "gradual phyletic evolution is more characteristic of narrowly fluctuating, slowly changing environments, whereas stasis tends to prevail in more widely-fluctuating, rapidly changing environments". According to this model, Triarthrus becki should show gradual phyletic evolution because T. becki lived in a relatively stable, deep water, basinal habitat.

Certain prerequisites are necessary to test the Plus ça Change model. The stratigraphic data must be within a properly controlled temporal framework. In addition, it is necessary to know whether there are ontogenetic or geographic variation effects on the evolutionary succession. Finally, an appropriate quantitative method is required to test the hypothesis.

We have collected 259 cranidia of the Middle Ordovician trilobite, Triarthrus becki from seven sections in the Mohawk River Valley, New York State for stratophenetic study. The cranidia of T. becki were collected from total 30 collections of the Dolgeville Formation, and Flat Creek Shale and Indian Castle Shale of the Utica Group. The collections from 30 stratigraphic levels from the 7 sections were located in within a high-resolution chronostratigraphic framework based on graphic correlation. In addition, we collected T. becki cranidia from the basal C. spiniferus Zone in Quebec, Pennsylvania, and Kentucky that are synchronous with the lower Indian Castle Shale samples in NY.

Landmark-based morphometric analysis was used for this study. Constraints of ontogenetic and geographic variation effects were considered by an ontogenetic standardization process and pair-wise geographic group comparisons in their morphology. We employed two methods to test the Plus ça Change Model: a statistical test against the null model of a random walk (the Monte-Carlo method), and the criterion suggested by Stanley and Yang based on comparison of contemporaneous geographic variation with variation over the time series. The stratophenetic pattern exhibited by T. becki is much more similar to a stabilized dynamic than to the expected pattern of anagenesis predicted by the Plus ça Change Model.