Although there is extraordinary interest in the quantitative measurement of species diversity, published statements on the behavior of the components of species diversity are contradictory and lead to opposite conclusions. In this paper, we demonstrate that the confusion is due to two key oversights: (1) whether or not biological sampling is carried out within or between communities; and (2) determination of the statistical distribution underlying a biological community, which is crucial for the evaluation of all of the components of diversity measurement.

The problem of sampling “within” a population or community is basically distinct from the equivalent integration of structure and diversity measurement “between” differing multispecies populations. “Within-community sampling” is defined as a set of biological samples from a statistical population that has a particular statistical distribution or a constant value for the associated parameter(s). As the number of individuals increases along with the number of species, for a log series distribution, the diversity measures of Shannon's H, log series or Fisher's α, and Simpson's Index 1/λ remain constant while the evenness measures of Buzas-Gibson's E and Pielou's J decrease. For a log-normal distribution, J will remain constant while E decreases and α, 1/λ, and H increase. No single measure of evenness remains constant over all statistical distributions, so if constancy as a type of independence is required, the appropriate distribution must first be determined. Each species ensemble is mathematically fixed by the applicable statistical distribution.

In contrast, “between-community sampling” is defined as a set of biological samples from different statistical distributions and/or the same distribution with differing parametric values. If sampling is between communities and S increases while the number of individuals remains constant, then all the other measures considered here increase. The exception is the broken stick, for which E remains constant while H, J, α, and 1/λ increase.

Herein we propose and justify the use of the log-series distribution (with regression on the information decomposition equation) as a null model for determination of community structure and demonstrate that the community structure of a Miocene bed at Calvert Cliffs, Maryland, is a log series by use of this new unified methodology.

Sutural perimeters of 301 Late Jurassic ammonites scale as the 3/8 power of phragmocone volume. This implies that septal surface grows as the ¾ power of body mass, the exponent of Kleiber's law (1932), one of the best-established empirical laws in biology, which is well known to be the scaling exponent of basal metabolic rate. Sutural complexity, as measured by fractal dimensions, emerges from the relationship between sutural perimeter and phragmocone volume, thus supporting the interpretations of septal folding as a mechanism for the increase in septal surface and as demanded by metabolic and physiologic processes (e.g., respiration or body chamber transport). The implications of these results strongly suggest that ammonite septa were involved in more than a simple structural support.

Clymeniid ammonoids appeared during the Late Devonian (Mid-Famennian) and quickly radiated before becoming extinct at the Devonian/Carboniferous boundary. Outwardly indistinguishable from other ammonoids, clymeniids are distinguished internally by their dorsal siphuncle, contrasted to a ventral siphuncle in almost all other ammonoids. Comparisons of a sample of Clymeniida (n = 22 genera), Goniatitida (n = 33), Prolecanitida (n = 12), and Anarcestida (n = 13) indicate that clymeniids fall within the range of other ammonoids in terms of shell geometry and suture complexity, but their siphuncles average two to three times larger and clymeniid shells are approximately 33% thicker than those of other ammonoids. Although a dorsal siphuncle would be about 50% smaller in surface area and volume than if located in a ventral position, the enlarged clymeniid siphuncle partially and, in some cases, fully compensated for this loss. Hydrostatic simulations of 15 clymeniid genera indicate that their thicker (therefore heavier) shells would have resulted in relatively short body chambers (≈280°) and high aperture orientations (≈90°). In static life-position, these orientations would have placed the dorsal clymeniid siphuncle at or near the bottom of the most recently formed chambers, seemingly an ideal location for draining liquid from the chamber. Migration of the siphuncle to the dorsal side of the shell occurs suddenly during early ontogeny (within the first two or three chambers), and mutation of homeotic gene expression is offered as a possible explanation for the sudden shift. A dorsal siphuncle may have resulted in selection for enlarged siphuncles, but this may have incurred loss of strength against hydrostatic pressure (thereby reducing depth limits) and thus rendered the clade more susceptible to the multiple eustatic and anoxic events that marked the end of the Devonian.

Coiled cephalopods constitute a major part of the Paleozoic nekton. They emerged in the Early Ordovician but nearly vanished in the Silurian. The Emsian appearance of ammonoids started a story of evolutionary success of coiled cephalopods, which lasted until the end-Permian extinction event. This story is investigated by using a taxonomic database of 1346 species of 253 genera of coiled nautiloids and 1114 genera of ammonoids. The per capita sampling diversities, the Van Valen metrics of origination and extinction, and the probabilities of origination and extinction were calculated at stage intervals. The outcome of these estimations largely reflects the known biotic events of the Paleozoic. The polyphyletic, iterative appearance of coiled cephalopods within this time frame is interpreted to be a process of adaptation to shell-crushing predatory pressure. The evolution of the diversity of coiled nautiloids and ammonoids is strongly correlated within the time intervals. Once established, assemblages of coiled cephalopods are related to changes in sea level. The general trends of decreasing mean (or background) origination and extinction rates during the Paleozoic are interpreted to reflect a successive stabilization of the coiled cephalopod assemblages. Different reproduction strategies in ammonoids and nautiloids apparently resulted in different modes of competition and morphological trends. Significant morphological trends toward a stronger ornamentation and a centrally positioned siphuncle characterize the evolution of Paleozoic nautiloids.

A global database of gastropod sizes from the Permian through the Middle Triassic documents trends in gastropod shell size and permits tests of the suggestion that Early Triassic gastropods were everywhere unusually small. Analysis of the database shows that no specimens of unambiguous Early Triassic age larger than 2.6 cm have been reported, in contrast to common 5– 10-cm specimens of both Permian and Middle Triassic age. The loss of large gastropods is abrupt even at a fine scale of stratigraphic resolution, whereas the return of larger individuals in the Middle Triassic appears gradual when finely resolved. Taphonomic and sampling biases do not adequately explain the absence of large Early Triassic gastropods. Examination of size trends by genus demonstrates that the size decrease across the Permian/Triassic boundary is compatible with both size-selective extinction at the species level and anagenetic size change within lineages. Size increase in the Middle Triassic resulted from the origination of large species within genera that have Early Triassic fossil records and the occurrence of new genera containing large species during the Middle Triassic. Genera recorded from the Permian and Middle Triassic but not the Early Triassic (“Lazarus taxa”) do not contribute to observed size increase in the Middle Triassic. Moreover, Lazarus taxa lack large species and exhibit low species richness during both the Permian and the Middle Triassic, suggesting that they survived as small, rare forms rather than existing at large sizes in Early Triassic refugia. The ecological opportunities and selective pressures that produced large gastropods during most intervals of the Phanerozoic evidently did not operate in Early Triassic oceans. Whether this reflects low predation or competitive pressure, r-selection facilitated by high primary production, or physical barriers to large size remains poorly understood.

The evolution of scutes in thyreophoran dinosaurs, based on Scutellosaurus, Scelidosaurus, Stegosaurus, and several ankylosaurs, began with small rounded or ovoid structures that typically had slight, anteroposteriorly oriented keels. These scutes were elaborated in two general and overlapping ways: they could flare laterally and asymmetrically beneath the keels that mark the anteroposterior axis, and they could be hypertrophied in their distal growth to produce plates, spikes, and other kinds of ornamentation. Stegosaurus plates and spikes are thus primarily hypertrophied keels of primitive thyreophoran scutes, sometimes with elaboration of dermal bone around their pustulate bases. Histologically, most thyreophoran scute tissues comprise secondary trabecular medullary bone that is sandwiched between layers of compact primary bone. Some scutes partly or mostly comprise anatomically metaplastic bone, that is, ossified fibrous tissue that shows incremental growth.

The “plumbing” of Stegosaurus plates was not apparently built to support a “radiator” system of internal blood vessels that communicated with the outside of the plates and coursed along their external surfaces to return heated or cooled blood to the body core. Possibly a purely external system supported this function but there is no independent evidence for it. On the other hand, many of the vascular features in stegosaurian plates and spikes reflect bautechnisches artifacts of growth and production of bone. Surface vascular features likely supported bone growth and remodeling, as well as the blood supply to a keratinous covering. When the gross and microstructural features of the plates and spikes are viewed in phylogenetic context, no clear pattern of thermoregulatory function emerges, though an accessory role cannot be eliminated in certain individual species. It seems more likely, as in other groups of dinosaurs, that the variation of dermal armor form in stegosaurs was primarily linked to species individuation and recognition, perhaps secondarily to inter- and intraspecific display, and rarely to facultative thermoregulation.

Finite element modeling (FEM) has been used to evaluate microstructure-controlled stability of selected eggshells of Indian dinosaurs. Our study suggests that under static load the eggshell microstructure of Megaloolithus cylindricus displays a low magnitude of tensile stress over most of the spherolith. The magnitude of this tensile stress is lower than that displayed in M. jabalpurensis, M. baghensis, and Subtiliolithus kachchhensis. In M. cylindricus, a shell thickness matching the length of the spheroliths prevents the failure of eggshells, whereas in M. jabalpurensis and M. baghensis, which have thinner shells, the development of additional subspheroliths compensates for the relatively higher magnitude of tensile stresses. Extremely thin eggshell in S. kachchhensis shows a still higher magnitude of tensile stresses, thereby making it prone to cracking, but the propagation of cracks is apparently checked and stability reinforced by wider spacing of pore canals.

Marsupial mammals are characterized by a pattern of dental replacement thought to be unique. The apparent primitive therian pattern is two functional generations of teeth at the incisor, canine, and premolar loci, and a series of molar teeth, which by definition are never replaced. In marsupials, the incisor, canine, and first and second premolar positions possess only a single functional generation. Recently this pattern of dental development has been hypothesized to be a synapomorphy of metatherians, and has been used to diagnose taxa in the fossil record. Further, the suppression of the first generation of teeth has been linked to the marsupial mode of reproduction, through the mechanical suppression of odontogenesis during the period of fixation of marsupials, and has been used to reconstruct the mode of reproduction of fossil organisms. Here we show that dental development occurs throughout the period of fixation; therefore, the hypothesis that odontogenesis is mechanically suppressed during this period is refuted. Further, we present comparative data on dental replacement in eutherians and demonstrate that suppression of tooth replacement is fairly common in diverse groups of placental mammals. We conclude that reproductive mode is neither a necessary nor a sufficient explanation for the loss of tooth replacement in marsupials. We explore possible alternative explanations for the loss of replacement in therians, but we argue that no single hypothesis is adequate to explain the full range of observed patterns.