Quantitative analysis of species distribution of the Mississippian Zaphrentites delanouei group from the Vale of Glamorgan, UK

The evolutionary process of anagenesis is thought to control distributions of members of the Zaphrentites delanouei species group, the Tournaisian-Viséan solitary rugose corals, within the Carboniferous Limestone. We present alternative interpretations specific to the Friars Point Limestone Formation, which point to composite evolutionary processes closer to anacladogenesis. We use a Markov Chain Monte Carlo process to organize fossils into matrices representing states of concurrence, where concurrence is the number of species coexisting in each bed. We analyse their distributions according to transitions between states. Data testing by matrix multiplication shows whether stochastic equilibrium or convergence is reached, to determine probabilities of species coexistence. Taking the probabilities from the Markov Chain Monte Carlo process to represent the first generation of a branching process, we proceed to calculate the second to fourth generations. Finally, we model these values in a Galton–Watson process to determine the likelihood of ultimate extinction, and whether the species belong to the same population without immigration or emigration. Results show that the species distribution is both anagenetic (0.725) and cladogenetic (0.275). Therefore, we define the evolutionary process as anacladogenetic with the potential for up to eight species in addition to the six defined in the literature. This represents some evidence for a population unaffected by immigration or emigration, with a high likelihood of ultimate extinction for most localities. We deduce that second or third-generation concurrences are a requisite for survival, even with anacladogenesis. As an environmental corollary, the amplification of extinction rates was exacerbated within a regressive marine system, and our techniques will allow further exploration of evolutionary mechanisms and energy within coral ecosystems.