Inadequacies in stratigraphic resolution or completeness can make true rates of morphologic change through geologic time impossible to estimate precisely. However, relative rates may be sufficient to test whether the tempo of change within species can account for morphologic differences across species boundaries, and hence to distinguish between gradual and punctuated patterns of evolution. The conditions under which these patterns can be distinguished statistically are explored by simulating varying degrees of within-species rate variability relative to across-species morphologic difference. The statistical methods are then applied to multiple-character morphologic data from closely spaced sequential populations of the Neogene bryozoan Metrarabdotos, using discriminant analysis to compare overall morphologies. In nine comparisons of ancestor-descendant species pairs, all show within-species rates of morphologic change that do not vary significantly from zero, hence accounting for none of the across-species difference. In all cases the ratio of within-species fluctuation to across-species difference is low enough to allow the punctuated pattern to be distinguished with virtual certainty. In at least seven of the cases, ancestor species persisted after giving rise to descendants, in conformity with the punctuated equilibrium mode of evolution.

Much of the controversy concerning the theory of punctuated equilibrium stems from skepticism about the biologic validity of fossil morphospecies, particularly for supposedly simple invertebrate taxa like cheilostome Bryozoa that form the bulk of the fossil record. However, evidence from breeding experiments and protein electrophoresis shows that morphospecific identity of cheilostomes is heritable and that morphospecies are genetically distinct with no indication of morphologically cryptic species. Thus paleontologists can study cheilostome evolution at the species level, and previously demonstrated pattems suggesting punctuated speciation in cheilostomes should be taken at face value.

The possible roles of random genetic change and natural selection in bryozoan speciation were analyzed using quantitative genetic methods on breeding data for traits of skeletal morphology in two closely related species of the cheilostome Stylopoma. The hypothesis that morphologic differences between the species are caused entirely by mutation and genetic drift could not be rejected for reasonable rates of mutation maintained for as few as 10 to 10 generations. Divergence times this short or shorter are consistent with the abrupt appearances of many invertebrate species in the fossil record, commonly followed by millions of years of morphologic stasis. To produce these differences over 10 generations or fewer, directional selection acting alone would require unrealistically high levels of minimum selective mortality throughout divergence. Thus, selection is unnecessary to explain the divergence of these species, except as a means of accelerating the effects of random genetic change on shorter time scales (directional selection), or decelerating them over longer ones (stabilizing selection). These results are consistent with a variety of models of phenotypic evolution involving random shifts between multiple adaptive peaks. Similar results were obtained by substituting trait heritabilities and genetic covariances reconstructed by partitioning within- and among-colony phenotypic variance in place of the values based on breeding data. Quantitative genetic analysis of speciation in fossil bryozoan lineages is thus justified.