We compared phylogenies derived from morphological data for two cheilostome bryozoan genera, Stylopoma and Metrarabdotos, with genetic differences between species (Stylopoma) and the stratigraphic occurrence of fossils (both genera). Correspondence between species of Stylopoma defined by protein electrophoresis and on preservable skeletal morphology is excellent, despite great morphological variability within colonies and the predominance of quantitative over discrete characters. Moreover, agreement between genetic and morphological classifications increased greatly when morphological discrimination was pushed to the limit, despite inability to consistently assign all specimens to species with high confidence. This “splitting” strategy also maximized the correlation between genetic distances and the distances between species in cladistically derived phylogenies.

Fossil and living species of both genera are sufficiently abundant and widespread to provide credible limits for inferred ancestral relationships. Inclusion of fossils in cladistic analyses of Stylopoma increased the consistency of cladistic hypotheses by up to 30% and provided a more effective means of rooting trees than comparison with living species of the most closely related genus (“outgroup”). Moreover, in the case of Metrarabdotos, failure to incorporate stratigraphic information turned the cladogram virtually upside down, so that postulated ancestors first appear in the fossil record 6–16 m.y. after their putative descendants became extinct.

Stratigraphically rooted trees suggest that most well-sampled Metrarabdotos and Stylopoma species originated fully differentiated morphologically and persisted unchanged for > 1 to > 16 m.y., typically alongside their putative ancestors. Moreover, the tight correlation between phenetic, cladistic, and genetic distances among living Stylopoma species suggests that changes in all three variables occurred together during speciation. All of these observations support the punctuated equilibrium model of speciation.

Many areas of paleobiological research require reliable extinction metrics. Branching-and-extinction simulations and data on Phanerozoic marine families and genera are used to investigate the relationship between interval length and commonly used extinction metrics. Normalization of extinction metrics for interval length is problematic, even when interval length is known without error, because normalization implicitly assumes some model of variation in extinction risk within an interval. If extinction risk within an interval were constant, or if it varied but played no role in the definition of stratigraphic intervals, then Van Valen's time-normalized extinction metric would provide a measure of average extinction risk that is effectively unbiased by interval length. When extinction risk varies greatly within an interval and interval boundaries are drawn at times of heavy extinction, extinction metrics that normalize for interval length are negatively correlated with interval length. Despite its intuitive appeal, the per-taxon extinction rate (proportional extinction per million years) is biased by interval length under a wide range of extinction models.

Empirically, time-normalized extinction metrics for Phanerozoic families and genera are negatively correlated with interval length. This is consistent with an extinction model in which many times of very low risk are punctuated by a few times of very high risk which in turn determine stage boundaries. Origination and extinction patterns are similar, but origination intensity varies less among stages than extinction intensity. This observation has at least two plausible explanations: that origination episodes are more protracted than extinction episodes, and that biologic groups do not respond in unison to origination opportunities the way they seem to respond during extinction events. For families and genera, there is enough variation in extinction intensity among stages that stage length can be ignored when studying certain extinction patterns over the entire Phanerozoic.

The well-known decline of global background extinction intensity was caused by the sorting of higher taxonomic groups. Two factors were responsible. First, probabilities of familial origination and extinction in these groups (taxonomic orders) were highly correlated. Groups whose families had high probabilities of origination and extinction tended to have highly volatile diversity paths and, consequently, short life spans. Second, orders with high probabilities of familial origination and extinction were rarely replaced by new high-turnover orders. Thus, because high-turnover orders tended to become extinct without replacement, the global background extinction intensity declined. Since familial origination and extinction probabilities are correlated, global background origination intensity inevitably declined as well. As a consequence of these processes, virtually all groups of organisms now living have low probabilities of familial origination and extinction.

Simulations of branching evolution were used to obtain the expected relationships among probabilities (of origination and extinction), volatilities, and longevities for the entire range of possible probabilities, and these relationships were compared to those obtained from the empirical record. In the simulations, only the probabilities of origination and extinction were specified, so volatilities and clade longevities were determined entirely by the probabilities. The similarity between results obtained by simulation and those obtained by analysis of the empirical record further supports the inference that the observed decline of background extinction (and origination) intensity can be explained largely by the loss of high-probability groups to induced volatility.

The equations for calculating classical confidence intervals on the end points of stratigraphic ranges are based on the restrictive assumption of randomly distributed fossil finds. Herein, a method is presented for calculating confidence intervals on the end-points of stratigraphic ranges that partially relaxes this assumption: the method will work for any continuous distribution of gap sizes, not just those generated by random processes. The price paid for the generality of the new approach is twofold: (1) there are uncertainties associated with the sizes of the confidence intervals, and (2) for large confidence values (e.g., 95%) a rich fossil record is required to place upper bounds on the corresponding confidence intervals. This new method is not universal; like the method for calculating classical confidence intervals it is based on the assumption that there is no correlation between gap size and stratigraphic position. The fossil record of the Neogene Caribbean bryozoan Metrarabdotos is analyzed with the new approach. The equations developed here, like those for classical confidence intervals, should not be applied to stratigraphic ranges based on discrete sampling regimes, such as those typically established from deep-sea drilling cores, though there are exceptions to this rule.

The age of first occurrence of taxa remains an underutilized source of information in phylogenetic analysis. In this paper I develop a method whereby one can measure the fit of the stratigraphic record to an estimated phylogenetic tree. The method works as follows: (1) each of the internal nodes excluding the root node of a phylogenetic tree is visited, (2) the oldest age of first occurrence for the taxa above the node is compared to the oldest age of first occurrence for the sister node, and (3) if the age above the node is the same age or younger than the age below the node, then the node is stratigraphically consistent. A measure of the total fit of the stratigraphic record to the tree is the proportion of nodes that are stratigraphically consistent (expressed as the stratigraphic consistency index, SCI). This measure of stratigraphic fit is sensitive to errors in phylogenetic estimation as well as to missing lineages (or parts of lineages). The significance of the fit of the stratigraphic record to the tree can be determined through a permutation approach that generates the null distribution for SCI under the hypothesis that the stratigraphic fit is no better than would be expected at random. The method is applied to several studies taken from the literature. Almost all published trees had significant SCI values, meaning the trees fit the stratigraphic record quite well. Applications of stratigraphic consistency for determining the confidence that should be placed in a phylogenetic estimate, for determining the root of a tree, and as a modified optimality criterion for estimating phylogenetic trees are discussed.

Morphologic discrimination of species of scleractinian reef corals has long been plagued by a shortage of independent characters and by high ecophenotypic plasticity. Because of these two factors, many species appear to intergrade morphologically. We outline a newly developed protocol for the morphometric recognition of species, which uses size and shape coordinates derived from landmark data. The landmarks consist of spatially homologous points digitized in three dimensions on upper calical surfaces. The approach is more powerful than linear measurements at detecting subtle distinctions among species; and the distinctions are easy to visualize and interpret biologically, which increases the accuracy and resolution of subsequent phylogenetic and large-scale faunal analyses.

As an example, we distinguish morphospecies in collections of Porites made at three Caribbean locations. Size and shape coordinates are analyzed using principal component analysis, average linkage cluster analysis, and a series of iterative discriminant analyses. Positions of different corallites from the same colonies are examined on cluster dendrograms to determine cutoffs for group recognition, and discriminant classifications for different corallites from the same colonies are compared to maximize group assignments. The results yield seven morphospecies, which are generally in 90% agreement with classification of the same animals using allozyme electrophoresis. Measures of corallite size and the relative heights and locations of the pali and septal denticles all reveal unique patterns of variation among morphospecies.

Cantius is an early Eocene adapid primate with an exceptionally well known fossil record. Measurements were recorded to describe the size and shape of upper and lower first molars collected from a measured stratigraphic section in the Clarks Fork Basin of Wyoming. Rates of change of size and shape are quantified by calculating evolutionary rates in standard deviation units per generation (haldanes). Temporal scaling of rates shows that change in size was generated by a significantly nonrandom directional process, while change in shape was generated by a significantly nonrandom stabilizing process. Size change in Cantius is interpreted to be the result of weak directional selection, and shape change is interpreted to be the result of strong stabilizing selection.

Ediacaran fossils are taphonomically similar to impressions of fossil plants common in quartz sandstones, and the relief of the fossils suggests that they were as resistant to compaction during burial as some kinds of Pennsylvanian tree trunks. Fossils of jellyfish are known from siderite nodules and fine-grained limestone, and even in these compaction-resistant media were more compressed during burial than were the Vendobionta. Vendobionta were constructed of materials that responded to burial compaction in a way intermediate between conifer and lycopsid logs. This comparative taphonomic study thus falsifies the concept of Vendobionta as thin soft-bodied creatures such as worms and jellyfish.

Lichens, with their structural chitin, present a viable model for the observed preservational style of Vendobionta, as well as for a variety of other features that now can be reassessed from this new perspective. The diversity of Ediacaran body plans can be compared with the variety of form in fungi, algae, and lichens. The large size (ca. 1 m) of some Ediacaran fossils is reasonable for sessile photosynthetic symbioses, and much bigger than associated burrows of metazoans not preserved. Microscopic tubular structures and darkly pigmented cells in permineralized late Precambrian fossils from Namibia and China are also compatible with interpretation as lichens. The presumed marine habitat of Ediacaran fossils is not crucial to interpretation as lichens, because fungi and lichens live in the sea as well as on land.