Non-Unique Equilibria in Competitive Communities and Punctuated Ecological Change in the Fossil Record

The fossil record provides critical insight into how ecological communities change over geologic time and the role that biological interactions like competition and predation play, if any, in their long-term history. Recognizing and quantifying the signature of different kinds of interactions on the structure of communities has been an ongoing focus of evolutionary paleoecology. A classical Lotka-Volterra model of interspecific competition among eurytopic species along a continuous, linear environmental gradient results in a dynamic of competitive accommodation: under appropriate conditions, a diverse assemblage of competing species can reach a mathematically stable, non-unique equilibrium from which no species are eliminated by competitive exclusion. This implies that competition does not inherently place a limit on diversity, but rather can provide a means of increasing total biodiversity. These non-unique equilibria are neither chaotic nor oscillatory, but they are sensitive to initial population sizes and are easy to shift to new equilibrium states when perturbed. This dynamic of competitive accommodation along linear gradients suggests an explanation for intervals of long-term community stability punctuated by ecological reorganizations associated with environmental perturbations observed in the fossil record. Using brachiopod data originally collected by Cooper and Grant from the Permian Basin of West Texas, a series of seven distinct stratigraphic clusters defined by taxonomic associations can be recognized that coincide with unconformity-bounded third-order depositional sequences. The stratigraphic clusters emerge despite a high proportion (50-85%) of generic continuity from cluster to cluster. In addition, there is evidence that brachiopod communities were primarily organized along linear environmental gradients. Using estimates of generic overlap (i.e., beta diversity) along the gradients as defined by correspondence analysis, the model predicts that Permian Basin brachiopod assemblages are expected to show a strong degree of competitive accommodation, providing a possible explanation for their high diversity and punctuated pattern of ecological change.