INFERRING THE RATES OF BRANCHING AND EXTINCTION FROM MOLECULAR PHYLOGENIES.

Molecular techniques provide ancestral phylogenies of extant taxa with estimated branching times. Here we studied the pattern of ancestral phylogeny of extant taxa produced by branching (or cladogenesis) and extinction of taxa, assuming branching processes with time-dependent rates. (1) If the branching rate b and extinction rate c are constant, the semilog plot of the number of ancestral lineages over time is not a straight line but is curvilinear, with increasing slope toward the end, implying that ancestral phylogeny shows apparent increase in the branching rate near the present. The estimate of b and c based on nonlinear fitting is examined by computer simulation. The estimate of branching rate can be usable for a large phylogeny if b is greater than c, but the estimate of extinction rate c is unreliable because of large bias and variance. (2) Gradual decrease in the slope of the semilog plot of the number of ancestral lineages over time, as was observed in a phylogeny of bird families based on DNA hybridization data, can be explained equally well by either the decreasing branching rate or the increasing extinction rate. Infinitely many pairs of branching and extinction rates as functions of time can produce the same ancestral phylogeny. (3) An explosive branching event in the past would appear as a quick increase in the number of ancestral lineages. In contrast, mass extinction occurring in a brief period, if not accompanied by an increase in branching rate, does not produce any rapid change in the number of ancestral lineages at the time. (4) The condition in which the number of ancestral lineages of extant species changes in parallel with the actual number of species in the past is derived.