Observed stratigraphic ranges almost always underestimate true longevities. Strauss and Sadler (1987, 1989) provide a method for calculating confidence intervals on the endpoints of local stratigraphic ranges. Their method can also be applied to composite sections; confidence intervals may be placed on times of origin and extinction for entire species or lineages. Confidence interval sizes depend only on the length of the stratigraphic range and the number of fossil horizons. The technique's most important assumptions are that fossil horizons are distributed randomly and that collecting intensity has been uniform over the stratigraphic range. These assumptions are more difficult to test and less likely to be fulfilled for composite sections than for local sections.

Confidence intervals give useful baseline estimates of the incompleteness of the fossil record, even if the underlying assumptions cannot be tested. Confidence intervals, which can be very large, should be calculated when the fossil record is used to assess absolute rates of molecular or morphological evolution, especially for poorly preserved groups. Confidence intervals have other functions: to determine how rich the fossil record has to be before radiometric dating errors become the dominant source of error in estimated times of origin or extinction; to predict future fossil finds; to predict which species with fossil records should be extant; and to assess phylogenetic hypotheses and taxonomic assignments.

The Quaternary ice ages were paced by astronomical cycles with periodicities of 20–100 k.y. (Milankovitch cycles). These cycles have been present throughout earth history. The Quaternary fossil record, marine and terrestrial, near to and remote from centers of glaciation, shows that communities of plants and animals are temporary, lasting only a few thousand years at the most. Response of populations to the climatic changes of Quaternary Milankovitch cycles can be taken as typical of the way populations have behaved throughout earth history. Milankovitch cycles thus force an instability of climate and other aspects of the biotic and abiotic environment on time scales much less than typical species durations (1–30 m.y.). Any microevolutionary change that accumulates on a time scale of thousands of years is likely to be lost as communities are reorganized following climatic changes. A four-tier hierarchy of time scales for evolutionary processes can be constructed as follows: ecological time (thousands of years), Milankovitch cycles (20–100 k.y.), geological time (millions of years), mass extinctions (approximately 26 m.y.). “Ecological time” and “geological time” are defined temporally as the intervals between events of the second and fourth tiers, respectively. Gould's (1985) “paradox of the first tier” can be resolved, at least in part, through the undoing of Darwinian natural selection at the first tier by Milankovitch cycles at the second tier.

Prominent extinction “events” have been recognized from statistical analyses of marine invertebrate genera represented in Mesozoic and Cenozoic assemblages, contrasting with relatively low “background” extinction intensities measured in terms of a “percentage extinction” index. On a logarithmic scale, the slope of the relationship between time and extinction intensity for background extinctions is shown to be parallel to the slope obtained for most extinction events, characterized by intensities 100.35 above prevailing background levels. Although extinction intensities are variable, this study suggests that the magnitude of the factor(s) primarily associated with most mass extinctions in a 260-m.y. period (N = 9) need not necessarily have been very different from one event to another, an exception being the mass extinction at the end of the Cretaceous.

Convincing hypotheses of the origin of major invertebrate groups are difficult to make in the absence of phylogenetic analyses. In spite of this, several scenarios exist for the origin of the unusual echinoid order Clypeasteroida. I expand upon the most probable of these models by performing a phylogenetic analysis on three clypeasteroid suborders, the enigmatic fossil genus Togocyamus, and the extinct Oligopygoida. This analysis shows that the oligopygoids are the sister group of the Clypeasteroida plus Togocyamus. The latter is here considered a plesion (extinct sister group) to the crown group Clypeasteroida. Within that order, the suborder Clypeasterina is the sister group to the Laganina plus Scutellina. A new classification of all these taxa is presented. The phylogeny is based on 47 characters and incorporates data on external appendages, Aristotle's lantern anatomy, and test structure of irregular echinoids, as well as new information on the morphology of Togocyamus. The earliest clypeasteroids had a lantern similar to that of adult oligopygoids, which in turn inherited their lantern from a cassiduloid-like ancestor that retained the lantern into adulthood. This lantern is absent in adult cassiduloids. Subsequent changes, including modification of the lantern into a crushing mill, extreme flattening of the test, and proliferation of food-gathering tube feet have allowed clypeasteroids to become epifaunal inhabitants of environments characterized by fine, shifting substrates, a habitat previously inaccessible to most other irregular echinoids.

Morphological gradients in graptoloid colonies are explained by the production and diffusion of a morphogen from the sicula distalwards. Size of the thecae is inversely related to the amount of morphogen present. The graduate decrease of morphogen is given by a set of algebraic equations, and its effect on zooid growth is described by a modified Michaelis-Menten relationship. Changes in size of thecae computed on the basis of these equations fit the changes observed in graptolite colonies. Sets of differential equations are also given to describe the rate of morphogen diffusion and some other processes possibly involved in the development of uniaxiate graptoloid colonies. The suggested basic model of these colonies can be completed by a number of additional assumptions; however, computer experiments reveal that such assumptions do not affect the main properties of the model, namely the appearance of graded series of thecae. New evidence for regeneration of the sicular portion of the broken rhabdosome is presented, providing arguments that morphogen was produced by the siculozooid as a single bolus of secretion. Some local exclusions from the regular size gradient are discussed, and tentative explanations are suggested.

The miniaturization of shells, often observed in Mesozoic brachiopods, is analyzed in two species of the well-known genus Homoeorhynchia. We investigated shell development in the context of recent works that consider growth as a function of size, shape, and age. The miniaturization results from heterochronic disturbances during development. Although these shells exhibit a large morphological plasticity, architectural constraints limit their morphogenesis, so that small adult specimens are not exactly reduced replicas of large ones. Adult morphology depends largely on the pattern of rib formation, with miniaturization arising by two different processes affecting this pattern: predisplacement of the appearance of ribs in H. meridionalis and acceleration in H. cynocephala. The first case seems to be a reversible process without evolutionary consequences, but the second occurs within an evolutionary trend. In both cases, the miniaturization seems to be related to environmental influences. Study of the growth pathway of these species allows recognition of basic characters in the morphological variation of populations.

Fossil leaves and palynomorphs represent different phases of the plant life cycle, are studied as systematically independent entities, and are subject to different taphonomic, sampling, and recognition biases in the paleobotanical record. They thus provide parallel, and largely independent, documentation of long-term trends in land plant diversity, and the palynological record may be used as a comparative test of floristic trends inferred from macrofossil evidence. Analyses of relative “species” richness in 91 macrofossil and 860 palynomorph Cretaceous “floras” (assemblages) from between 25° and 65° N paleolatitude show a major mid-Cretaceous increase in the within-flora diversity of angiosperms, from near 0% prior to the Aptian (120 Ma) to 50–80% by the end of the Maastrichtian (65 Ma). This level of diversity is attained rapidly in macrofloras, but more slowly in palynofloras. In the latest Cretaceous, macrofloras and palynofloras both indicate that “pteridophytes,” conifers, and other “gymnosperms” are generally less diverse than angiosperms. In both data sets, “pteridophyte” diversity shows a clear decline through the Cretaceous, whereas conifer diversity shows no marked temporal trend. Broad congruence of these patterns, in spite of different biases in the macrofossil and palynomorph records, indicates that they provide a robust reflection of floristic trends through the Cretaceous. Nevertheless, discrepancies between the patterns do occur and underline the importance of complementary macrofossil and palynological analyses for accurate resolution of long-term vegetational change.

The earliest fossil record of animals has long been an enigma. For nearly a century after the appearance of The Origin of Species, mineralized trilobites were thought to be among the first organisms to appear as fossils, and as they were considered to be complex life forms, a long previous episode of animal evolution seemed to be indicated. Discovery and description of Tommotian and Vendian faunas, with their small shelly and Ediacaran fossils respectively, provided us with an idea of the nature of organisms in strata that are progressively older than the trilobite-bearing beds. Yet in these older assemblages we do not find the sorts of organisms that might be expected to be precursors to the well-known Phanerozoic clades. The puzzle remains.