The statistical significance of differences in evolutionary rate between major taxonomic groups is evaluated using conventional chi-square techniques on stratigraphic range data. Romer's (1966) compilation of stratigraphic ranges of fossil mammals is used to determine whether orders differ significantly from each other in generic origination and extinction rates. The evolutionary histories of 2180 genera (primarily Cenozoic in age) are analyzed. Chi-square testing shows that significantly high or low (P ≥ 0.99) extinction or origination occurs in 15% of the testable cases. Significantly high or low evolutionary turnover in a taxon (orders in this case) we term taxotely. Significantly high turnover rate is equivalent to Simpson's tachytely and significantly low turnover is equivalent to his bradytely.

In the mammal data set, taxotely is largely attributable to the influence of South American endemics. Some of the effect is interpreted as an artifact of biases in the fossil record (or its study) and some is attributed to real biological aspects of mammalian evolution.

The longevity of genera living at the edge of the early Ordovician North American plate is related to their position on the former shelf, that is preserved in richly fossiliferous sections of Spitsbergen. Genera which endure for a long period (SO Myr or more) tend to be confined to shallow-water sites associated with algal mounds at the edge of the carbonate platform (illaenid-cheirurid community type) or deep-water sites with low oxygen concentration, and probably beneath the thermocline (olenid community type). The latter includes “conservative” forms that have survived from the Cambrian. The long ranges of the olenid community type are attributed to the adaptation of only a few genera to a highly specific, stressed environment. The endurance of the illaenid-cheirurid genera is due to the persistence of the tropical shelf-edge habitat, with high predictability of resources, to which the Ordovician forms became adapted early on. The nileid community type, which occurred between the platform edge and olenid-bearing environment, was the site of rapid generic turnover and may have been the source for subsequent recruitment into other environments. The inner shelf also had rapid generic replacement, dominated by a single family, the Bathyuridae. Rapidity of evolution in this site may be due to the spatial heterogeneity of the epeiric environment, as in the Devonian phacopids studied by Eldredge (1974).

Contours of whorl expansion rate (W), distance of the generating curve from the axis of coiling (D) and shape of the generating curve (S) were plotted from data on 988 Jurassic through Cretaceous ammonite species and 205 Jurassic through Tertiary nautilid species. The areas occupied by the ammonites and nautilids are largely nonoverlapping when plotted as WD and DS graphs.

The almost complete absence of overlap in Juro-Cretaceous ammonite and nautilid shell shape distributions is consistent with the view that ammonites and nautilids were dissimilar ecologically, and evolved different shell shapes in response to different adaptational needs. The terminal Cretaceous extinction of the ammonites may have opened up new opportunities for nautilid evolution during the Tertiary, because Tertiary nautilids are dominanted by moderately compressed, hydrodynamically efficient shell shapes which were rarely present among Jurassic and Cretacepus nautilids, but common among ammonites. The restriction of nautilids to a far more limited portion (compared to ammonites) of the theoretically available spectrum of planispiral shell shapes may be due in part to fabricational constraints imposed by the simple nautilid septum and septal suture. Nautilid shell shapes were limited to globular or slightly compressed to depressed shells, which are inherently strong due to pronounced shell wall curvature, and would be strengthened to only a small extent by buttressing from internal septa. Strongly depressed or compressed shell shapes, commonly evolved among ammonoids, had flattened shell regions which are inherently weak, and would be strengthened to a considerable extent by numerous thick, or strongly folded and fluted septa and septal sutures.

In a hyperbaric chamber, a living mature specimen of Nautilus pompilius withstood a hydrostatic pressure of 8.05 MPa (80.5 kg/cm2) equivalent to 785 m deep in the sea. Thereafter it was killed instantly by implosion of the shell. Before implosion, the animal reacted physiologically to increasing pressure. Therefore, the depth of 785 m can be assigned the depth limit of N. pompilius. The result bears on critical interpretations on the paleoecology and paleobiology of extinct nautiloids and ammonoids with similar shells.

Nautilus pompilius at Fiji lives abundantly to about 600 m depth while the shell implodes between 730–900 m when sunk in a cage. From this, and the average parameters of the septum, its tensile strength is calculated to 110–140 MPa. This is markedly higher than the latest value from direct tensile tests (78 MPa). In recent pressure tests by Saunders and Wehman with dry shells from the Philippines, implosion occurred at pressure equivalents to 310–680 m depth, without significant correlation with septal thickness. We attribute this excessive range and non-correlation to structural damage by postnecrotic processes. The recalculated tensile strength from their original data is 56–137 MPa; the higher values are compatible with our values for septal nacre of Nautilus and Spirula (c. 155 MPa). Septal curvature and thickness in orthocones thus remain useful guides to bathymetry.

The traditional belief that vertebrae must alternate in position with the segmented body musculature (myotomes) to allow bending of the axial skeleton is evaluated in terms of the patterns of development and structure of gnathostome vertebrae. The key functional parameter allowing lateral bending of the axial skeleton is the intersegmental position of both the neural and haemal arches, not the centrum. The intersegmental position of both the centrum and arches in tetrapods is the result of a secondary association of the centrum with the primary intersegmental position of the neural and haemal arches. The pattern of vertebral ontogeny and structure in primitive gnathostomes suggests that a causal link between sclerotomic resegmentation during amniote development and the presence of intersegmental vertebrae in the adult is spurious and corroborates the hypothesis that the process of resegmentation evolved as a method of redistributing large volumes of sclerotome cells during development. Patterns of vertebral construction in lower vertebrates are related to fast-start performance and the use of the body as a hybrid oscillator during locomotion.

Using a geometric model of shell morphology, it is demonstrated that biconvex brachiopods occupy only a small region of the potential geometric space available to organisms with planispiral exoskeletons composed of two articulated valves. Measurements taken for a sample of 324 genera of the articulate orders Pentamerida, Rhynchonellida, Spiriferida, and Terebratulida were analyzed using a simple geometric model of shell form and ontogeny. The frequency distribution of brachiopod shell morphologies exhibited by the four orders represents the biological optimization of the spatial relationships between area and volume. Biconvex brachiopods develop shells which are designed to minimize shell surface area while maximizing internal shell volume. The means by which optimization is achieved is related directly to the effects of increase in absolute size during ontogeny. The boundaries upon shell geometries utilizable by biconvex brachiopods are determined by (1) limitations of articulation, and (2) limitations of surface and volume.

Models for the areal distribution of marine animals may be formulated in such a way that their validity can be tested statistically. Five such models are described here: in each case the distributions of the individual taxa are made functions of depth of water, oceanicity, and substrate type.

The simplest model proposes that benthic species are substrate-dependent: it can be verified by a series of χ2 tests. Benthic species can also be seriated along an environmental gradient: this second model can be tested by using a Monte Carlo simulation procedure. The third model proposes that planktic species are to some degree stratified in the water column, and hence that their remains are distributed additively in the underlying sediments: tests on modern and sub-fossil data sets indicate that realistic versions of this model are probably valueless for most geological work. The final models are extensions of the additive model: they are used here to demonstrate the importance of selecting an appropriate model and, in particular, of knowing the mode of life of each species before the model is selected.

During the past 20 years, paleobiology has established the foundations of a nomothetic science based upon evolutionary theory. This radical break with a past philosophy based on irreducible historical uniqueness is still impeded by (1) overreliance upon the inductivist methodology that embodied this previous philosophy, and (2) an unadventurous approach to biology that attempts passively to transfer the orthodoxies of microevolutionary theory across vast stretches of time and several levels of a hierarchy into the domain of macroevolution. I analyze the major trends of recent invertebrate paleobiology in the light of these two impediments. The formulation, by paleobiologists and with paleobiological data, of new macroevolutionary theories should end the subservience of passive transfer and contribute, in turn, to the formulation of a new, general theory of evolution that recognizes hierarchy and permits a set of unifying principles to work differently at various levels.

The modern synthesis, as an exclusive proposition, has broken down on both of its fundamental claims: extrapolationism (gradual allelic substitution as a model for all evolutionary change) and nearly exclusive reliance on selection leading to adaptation. Evolution is a hierarchical process with complementary, but different, modes of change at its three major levels: variation within populations, speciation, and patterns of macroevolution. Speciation is not always an extension of gradual, adaptive allelic substitution to greater effect, but may represent, as Goldschmidt argued, a different style of genetic change—rapid reorganization of the genome, perhaps non-adaptive. Macroevolutionary trends do not arise from the gradual, adaptive transformation of populations, but usually from a higher-order selection operating upon groups of species, while the individual species themselves generally do not change following their geologically instantaneous origin. I refer to these two discontinuities in the evolutionary hierarchy as the Goldschmidt break (between change in populations and speciation) and the Wright break (between speciation and trends as differential success among species).

A new and general evolutionary theory will embody this notion of hierarchy and stress a variety of themes either ignored or explicitly rejected by the modern synthesis: punctuational change at all levels, important non-adaptive change at all levels, control of evolution not only by selection, but equally by constraints of history, development and architecture—thus restoring to evolutionary theory a concept of organism.