In this paper we model the process of taxonomic evolution as a Galton-Watson branching process in discrete time and, using maximum likelihood, develop methods to estimate the probabilities of origination, persistence, and extinction of fossil taxa. We use the methods to estimate the probabilities of origination, persistence, and extinction of families (1) within 135 orders of marine invertebrate organisms, (2) within 12 phyla, and (3) within all marine invertebrate life (independently of the suprafamilial classification).
Most orders, including the arcoid bivalves, the dentaloid scaphopods, the orders of chitins, and many others, have relatively low probabilities of familial origination and extinction. The various ammonoid and trilobite orders, and some others, have high probabilities of origination and extinction. Among the phyla, the Archaeocyatha have the highest probabilities of familial origination and extinction, and the Annelida the lowest, with the more typical phyla of shelly organisms clustering near the high end of the probability scale. The Porifera and Protozoa also have low probabilities but not as low as the Annelida. The estimated origination and extinction probabilities for families within all marine invertebrate life are 0.470 and 0.452 per stage, respectively, values that are at the high end of the probability scale. We have also estimated the probabilities of ultimate extinction (extinction of all families) of the supertaxa.
By analyzing the changes of the diversity during each stratigraphic stage separately, we have also determined the trajectories of the estimated origination and extinction probabilities for families within all marine invertebrate life. The estimated origination probability is relatively high in association with the expansion of the Cambrian and Paleozoic evolutionary faunas and declines to more normal levels for the remainder of the Phanerozoic. The trajectory of the estimated extinction probability is from nearly zero early in the Phanerozoic to more normal levels later, showing clearly defined peaks in association with the five Phanerozoic mass-extinction events. The terminal Cretaceous mass extinction is the only one of the five that was not preceded by a monotonic decline of origination probability or by a series of stages with low origination probability. It appears to have been a unique, singular event.
Because the mathematical theory we employ as a model corresponds so closely to the processes of taxonomic evolution as we understand them, we believe that the theory provides a reasonable model of biological reality.