On the probability of ancestors in the fossil record

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Abstract
Three homogeneous models of species origination and extinction are used to assess the probability that ancestor-descendant pairs are preserved in the fossil record. In the model of cladogenetic budding, a species can persist after it branches and can therefore have multiple direct descendants. In the bifurcation model, a species branches to give rise to two distinct direct descendants, itself terminating in the process. In the model of phyletic transformation, a species gives rise to a single direct descendant without branching, itself terminating in the process. Assuming homogeneous preservation, even under pessimistic assumptions regarding the completeness of the fossil record, the probability of finding fossil ancestor-descendant pairs is not negligible. Even if all species of Phanerozoic marine invertebrates in the paleontologically important taxa had the same probability of preservation, on the order of 1%-10% or more of the known fossil species would be directly ancestral to other known fossil species. However, this is likely to be an underestimate, since the probability of finding ancestor-descendant pairs is enhanced by taxonomic, temporal, and spatial heterogeneities in preservation probability. Moreover, indirect genealogical relationships substantially increase the probability of finding ancestor-descendant pairs. The model of budding, the only one in which an ancestor can persist after a branching event, predicts that half or more of extant species have ancestors that are also extant. Thus, the question of how to recognize ancestor-descendant pairs must be carefully considered.

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