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The improbability of animal phyla with few species

At present there are many animal phyla that contain only a few species. The existence of these small phyla can be used to test assumptions about speciation and extinction in multicellular animals. We first model the number of species in a monophyletic clade with a birth and death process that assumes rates of speciation and extinction are constant. If no new phyla have evolved since the Cambrian and speciation and extinction rates for minor phyla are similar to or greater than those estimated from fossils, then our model shows that the probabilities of minor phyla surviving to the present are small. Random variation in extinction and speciation rates does not improve the chances for persistence. If speciation rates exceed extinction rates at the initial radiation of the clade, but before the clade becomes large, speciation rates come to equal extinction rates and both are low, persistence from before the Ordovician up to the present becomes likely. These models show that if speciation and extinction rates are independent of the number of species in a clade, then conditions before the Ordovician strongly influence today's distribution of species among taxa. We also discuss a model in which speciation and extinction rates depend on the number of species in a clade. This alternative model can account for the persistence of phyla with few species to the present and predicts a short duration for phyla that did not exceed a threshold number of species.