- The Paleontological Society
Paleontologists have a long tradition of the use of mathematical models to assist in describing and understanding patterns of diversification through time (e.g., Raup et al. 1973; Stanley 1975; Sepkoski 1978; Raup 1985; Foote 1988; Gilinsky and Good 1989). This is natural, as the information, phylogenetic and otherwise, that paleontologists work with comes equipped with a temporal dimension, albeit approximate, which endows these phylogenies with information about the tempo of evolution as well as the genealogical relationships among the lineages. Mathematical and statistical modeling are the tools for unlocking the quantitative information in the phylogenies.
Recently, molecular phylogenetics (e.g., Hillis et al. 1996) has created a new source of phylogenies with a temporal dimension, now frequently provided by molecular clocks. Many people have applied mathematical models to these phylogenies as well. Here, I highlight the areas of overlap as well as differences in what the simple models in the two fields have to tell us. To save ink, I will hereafter refer to paleontology as P and molecular phylogenetics as MP.
First I review the use of simple mathematical models to extract information about the tempo of evolution from phylogenies in the fields of P and MP. The same models, or variants thereof—these being the birth, birth-death, and Moran models—are used in the two areas, but there are differences in what they tell us, arising from differences in the nature of the phylogenies themselves. Finally, I address a high-profile assault on this common framework of understanding that has recently been launched.
THE PURE BIRTH PROCESS
This is one of the two simplest mathematical models used in P and MP (the other is the Moran process—discussed below) and, in its stochastic form, was one of the first stochastic processes to have been studied (Yule 1924; Kendall 1948, 1949 …