The Pennsylvanian System of north-central Texas records oscillating positions of deltas prograding out over muddy marine shelves, adjacent to more distal clear-water marine areas. Invertebrate faunas in the muddy marine habitat migrated in response to these oscillations. The shell of Glabrocingulum, a common gastropod in mud-bottom faunas, shows no morphological response within a cycle to the change in physical conditions during the approach of a prograding delta over the period of tens of thousands of years. An evolutionary split in the genus is seen at the base of Missourian strata; both species continue together through the Upper Pennsylvanian in this area. This split can only be seen among different cycles of sedimentation, which are separated from each other in time by hundreds of thousands of years represented in the stratigraphic record only by unconformities. The longer-term among-cycle history may not be the result of gradually accumulating change in large parent populations. Divergences may be associated with the abrupt habitat changes that punctuate the fossil record.