Disparity is a measure of the range or significance of morphology in a given sample of organisms, as opposed to diversity, which is expressed in terms of the number (and sometimes ranking) of taxa. At present there is no agreed definition of disparity, much less any consensus on how to measure it. Two possible categories of metric are considered here, one independent of any hypothesis of relationship (phenetics), the other constrained within an evolutionary framework (cladistics).

The Early Cambrian radiation was clearly a period of significant morphologic and taxonomic diversification. However, we question the interpretation of its first generation products as numerous body plans at the highest level. Four phenetic and two cladistic measures have been used to compare disparity among Cambrian arthropods with that in the living fauna. Phenetic methods assessing character-state variability and the amount of morphological attribute space occupied yield similar results for Cambrian and Recent arthropods. Assessments of disparity within a taxonomic framework rely on the identification of particular characters that delineate higher level body plans. This requires a phylogenetic interpretation, a cladistic investigation of hierarchical structure in the data. Both sets of arthropods fall within the same major clades, and within this cladistic framework the amount of character-state evolution in the two groups is comparable. None of these methods identifies markedly greater disparity among the Cambrian compared with the Recent taxa.

Although measures of disparity are applied here to a consideration of the Cambrian radiation, the metrics clearly have a much wider potential for estimating macroevolutionary trends independently from existing taxonomic frameworks. Geometric morphometry is ideal for measuring morphological variety at lower taxonomic levels, but it requires the recognition of homologous landmarks in all the forms under comparison, or the identification of entire homologous structures. Conventional phenetics has much wider application as it can operate on data coded as discrete homologous character states (this facility is also a requirement of cladistics), which are a more appropriate basis for comparing disparity in markedly dissimilar forms.

The number of cell types required for the construction of a metazoan body plan can serve as an index of morphological (or anatomical) complexity; living metazoans range from four (placozoans) to over 200 (hominids) somatic cell types. A plot of the times of origin of body plans against their cell type numbers suggests that the upper bound of complexity has increased more or less steadily from the earliest metazoans until today, at an average rate of about one cell type per 3 m.y. (when nerve cell types are lumped). Computer models in which increase or decrease in cell type number was random were used to investigate the behavior of the upper bound of cell type number in evolving clades. The models are Markovian; variance in cell type number increases linearly through time. Scaled to the fossil record of the upper bound of cell type numbers, the models suggest that early rates of increase in maximum complexity were relatively high. The models and the data are mutually consistent and suggest that the Metazoa originated near 600 Ma, that the metazoan “explosion” near the Precambrian/Cambrian transition was not associated with any important increase in complexity of body plans, and that important decreases in the upper bound of complexity are unlikely to have occurred.

It is now widely recognized that a large number of Cretaceous planktic foraminiferal species are commonly found associated with fully Danian faunas in many K/T boundary sections and deep-sea cores. This “Cretaceous” fauna has traditionally been regarded as representing the reworking of older Cretaceous sediments into younger strata, though recent isotopic data from some species indicates that, at least in these instances, the reworking hypothesis is false. To further test this reworking hypothesis the biogeography of this “Cretaceous” fauna is compared to the underlying uppermost Maastrichtian biogeography and to the biogeography of lowermost Danian planktic foraminiferal faunas. Results show that there is no regular decline in species richness, extinction, or faunal co-occurrence values for this “Cretaceous” fauna at progressively higher (=younger) Danian stratigraphic horizons. Moreover, there is no compelling association between the stratigraphic persistence of this “Cretaceous” fauna and shallow depositional settings. Instead, this fauna is characterized by: (1) a close (and predictive) association between “Cretaceous” and indigenous Danian species richness values throughout the lower Danian, (2) a close numerical and geographic correspondence between Danian speciation and the disappearance of “Cretaceous” species from the Danian fossil record, and (3) a pronounced similarity between changes in the general biogeographic structures of the “Cretaceous” and associated Danian faunas throughout the study interval. These data suggest that the K/T planktic foraminiferal extinction event exhibited a marked geographic structure with low and middle latitude faunas experiencing differentially high extinction rates in the lowermost Danian zones P0 and P1a and high latitude survivor faunas persisting more or less unchanged into the overlying zone, P1b and P1c. Taken together, these results challenge the traditional concept of an instantaneous uppermost Cretaceous planktic foraminiferal mass extinction and its proposed causal connection to bolide impact.

Detailed analysis of the stratigraphic ranges of Devonian rugose coral genera within the Old World and Eastern Americas Realms gives new information on faunal extinctions and other bioevents in both realms. Various origination and extinction metrics are calculated from tabulations of occurrences in each stage. The most significant faunal changes were near or at the ends of the Lochkovian and Frasnian stages. The former marks the gradual transition from dominance by Silurian families and genera to the characteristic Devonian coral assemblages; the latter marks the virtual extinction of the Devonian families and genera. Other coral events are related to the two major changes.

The data provide new bases for comparing the histories of the two realms. Most of the events are recorded in both, giving support to previous suggestions that the causes were worldwide. The coral record shows an increase (probably episodic) in environmental deterioration persisting through the Middle Devonian and culminating in extinction at the end of the Frasnian. Eustatic sea level fluctuations may have caused the precursor events and a bolide impact may have caused the end-Frasnian extinction.

The fundamental goal of biochronology is ordering taxonomic first and last appearance events. The most useful biochronologic data are of the form “the first appearance event of one taxon predates the last appearance event of a second taxon” (FAE < LAE). FAE < LAE data sets are unusually reliable because they converge on a unique solution with greater sampling. The fact that the FAE of one taxon i < the LAE of another taxon j always can be inferred either if i is found lower than j in a stratigraphic section, or if i and j co-occur in at least one taxonomic list. Thus, FAE < LAE data accurately synthesize two disparate sources of information: routine biostratigraphic observations and taxonomic lists that may have no stratigraphic context. Appearance event ordination, the new method introduced here, is intended to summarize FAE < LAE data. The algorithm is founded on the following parsimony criterion: arrangements of FAEs and LAEs should always imply FAEi < LAEj when this is known, and otherwise imply LAEj < FAEi whenever possible. The technique differs from others related to correspondence analysis in its use of FAE < LAE data and explicit definition as a parsimony method. The algorithm is even more unique in that it uses different subsets of FAEi < LAEj statements at each iterative step, converging on separate sets of scores for the FAEs and LAEs. After arranging either the FAEs or the LAEs on the basis of their scores, the other set of scores can be discarded and the best arrangement of the remaining events can be inferred directly. An analysis of the Plio-Pleistocene mammalian record in the Lake Turkana region is used to illustrate the method. Biochronologic resolution on the order of 0.2-1.5 m.y. is achieved. The Turkana species lists by themselves demonstrate enough FAEi < LAEj relationships to resolve the basic biochronologic pattern, but stratigraphic information is still of great use.

Biostratigraphic applications of Devonian plant macrofossils are unusual because of the rarity of these fossil plants. Moreover, the taxonomic determination of these plants is too often either arguable or impossible. Here is proposed a biostratigraphic method based on a quantification of individual plant characters and not on determination of whole fossils. The method is the following: (1) each biocharacter found at a given locality receives a score according to whether it is primitive or derived, so that the biocharacter score increases with increasing derivation; (2) the biostratigraphic coefficients of well-dated localities are calculated, the biostratigraphic coefficient of a given plant locality being the mean of all the biocharacter scores of this locality; (3) the scores of these well-dated localities are used to build a reference scale to which localities under investigation will be compared. A detailed example is developed for Early Devonian times. Various plant biocharacters of seven fossiliferous outcrops have been quantified and the subsequent scores of these localities are presented. This example shows that biostratigraphic results obtained by using the quantification method are comparable in precision with dating based on palynological assemblage zones. Evolutionary aspects of the method are also discussed.

Seven endemic species of skates (Chondrichthyes: Rajidae) represent the only family of elasmobranchs currently known to live in Antarctic continental waters. Many previous authors believed skates colonized Antarctic waters from Patagonia during interglacial periods in the Quaternary. However, recent fossil material collected from the middle Eocene La Meseta Formation of Seymour Island, Antarctic Peninsula, indicates that they may have persisted in Antarctic waters since the Paleogene. Additionally, oceanographic barriers present in the Neogene and Quaternary would have prevented dispersal from southern continents to Antarctica. A revised dispersal scenario, based on skate fossils, biology, paleogeography, and present centers of skate diversity, suggests that skates evolved in the western Tethys and North Boreal seas of western Europe in the Late Cretaceous and early Paleogene and emigrated into Antarctica during the early to middle Eocene via a dispersal corridor along the continental margins of the western Atlantic Ocean. Skates probably populated the Pacific Basin by passing from this dispersal corridor through the Arctic Ocean. Vicariant events, such as opening of the Drake Passage, the development of the Circum-Antarctic Current, and formation of deep and wide basins around Antarctica in the late Paleogene, created barriers that isolated some species of skates in Antarctica and prevented movement of other species of skates into Antarctica from northern areas. Skates are the only group of fishes known to have survived the Oligocene cooling of Antarctica that killed or extirpated the Paleogene ichthyofauna; they persisted by a combination of cold-tolerance, generalized diet, and unspecialized bathymetric and habitat preferences.

More than 300 coots (Fulica americana) became frozen in Spring Lake, Tazewell County, Illinois, on December 1, 1985. This catastrophic event permitted 8 weeks of taphonomic observations, which showed that ice forms a stable substrate which permits terrestrial taphonomic processes to be imprinted on lacustrine deposits. Bird and mammal scavengers attacked coot carcasses in different manners, resulting in distinct disarticulation sequences. Bird scavengers preferentially fed on the head, neck, and breast-wing complex, causing early disarticulation of bones in these areas, late loss of hindlimb joints, and minimal bone damage. In contrast, mammal scavengers concentrated their attention on the hindlimb and tail region, resulting in bone breakage and early disarticulation of these body parts, but late disarticulation of the breast-wing complex. These data demonstrate that scavenger-specific feeding behaviors significantly influence disarticulation patterns early in assemblage formation, while anatomy may exert increasingly greater influence on disarticulation patterns as carasses become less attractive to scavengers. Finally, because taphonomic processes change in intensity and type through time, bone frequency and modification patterns will vary according to the time at which the patterns are arrested by burial. Thus, bone frequency and modification patterns should provide an index to the relative importance of specific biotic agents and of anatomy in fossil disarticulation patterns as well as an estimate of the time between death and burial.

Paleoecologists have long sought to obtain estimates of the sizes of extinct populations. However, even in ideal cases, accurate counts of individuals have been hampered by the fact that many organisms disarticulate after death and leave their remains in the form of multiple, separated parts. We here analyze the problem of estimating numbers of individuals from collections of parts by developing a general counting theory that elucidates the major contributing variables. We discover that the number of unique individuals of a particular species that are represented in a fossil collection can be described by an intricate set of relationships among (1) the number of body parts that were recovered, (2) the number of body parts that were possessed by organisms belonging to that species, and (3) the number of individuals of that species that served as the source of the parts from which the paleontological sample was obtained (the size of the “sampling domain”). The “minimum number of individuals” and “maximum number of individuals” methods currently used by paleontologists to count individuals emerge as end members in our more general counting theory. The theory shows that the numbers of individuals of a species that are represented in a sample of body parts is fully tractable, at least in a theoretical sense, in terms of the variables just mentioned. The bad news is that the size of the “sampling domain” for a species can never be known exactly, thus placing a very real limit on our ability to count individuals rigorously. The good news is that one can often make a reasonable guess regarding the size of the sampling domain, and can therefore make a more thoroughly informed choice regarding how to estimate numbers of individuals. By isolating the variables involved in determining the numbers of individuals in paleontological samples, we are led to a better appreciation of the limits, and the possibilities, that are inherent in the fossil record.