Changes in shape and in the pattern of the reticulate carapace ornament of 63 representative female ostracode specimens of the deep-sea genus Poseidonamicus from 28 Deep Sea Drilling Project sites, extending over a geographic distance of 40,000 miles and a geologic age of 40X10 (super 6) yr, have been analyzed by Resistant Fit Theta-Rho analysis, conventional least-squares Theta Rho analysis, and by inspection of homologies in the fossae of the reticulum. It is possible to demonstrate that a sudden evolutionary change in the architectural framework of the carapace can be the product of mechanical accommodation under stress to more gradual and general changes in carapace shape. Certain geometric imperatives related to these mechanical needs determine morphologic stability and consequently rates of evolutionary change. In the western deep South Atlantic (near the Vema Channel on the Rio Grande Rise), an important evolutionary "punctuational event" seems to have taken place at about 14 Myr, whereas its concomitant, more gradual transformation is traceable in the shallower eastern South Atlantic (Walvis Ridge). This evolutionary event in Poseidonamicus probably reflects the relatively sudden invasion of deep Antarctic Bottom Water through the Vema Channel resulting from the formation of the East Antarctic ice cap, while the more gradual transition in shallower depths of Walvis Ridge represents a temporary transitory refuge. The problems of recognizing allopatric origins of species in the deep sea compared to in situ sudden transitions caused by biomechanical instability are considered.