The Cretaceous angiosperm radiation offers an opportunity to examine patterns of morphological evolution in terrestrial plants and to compare them with patterns previously observed during radiations of marine animals. Focusing on evolution among angiosperm pollen types, I used average pairwise dissimilarity and total variance to describe changing morphological varieties (disparity) through the Cretaceous and Paleocene in North America. Angiosperm species diversity shows an approximately tenfold increase through this interval, but this taxonomic diversification is not matched by a comparable change in morphological disparity. Partitioning of morphological disparity among major pollen groups shows that most of the variance is contributed by eudicots from the Albian onwards. Constant disparity across the Cretaceous/Tertiary boundary despite decreased taxonomic diversity suggests that the Cretaceous/Tertiary extinction was not selective with respect to the pollen morphological characters analyzed here. The two measures of disparity show similar patterns. The overall pattern is robust to changes in character weighting, indicating that no one set of characters or weighting scheme is driving the pattern. Analyses of older data indicate that the initial burst of disparity in the Aptian could be due in part to analytical time-averaging. The observed incongruence between taxonomic diversity and morphological disparity suggests that morphological evolution in pollen was characterized by larger jumps early and smaller jumps later on, and is similar to that found in several groups of marine invertebrates.

The Cretaceous/Tertiary boundary event exerted a deep influence on the life of the benthic invertebrates in the Danish Basin. The density and taxonomic diversity of most groups fell abruptly and the lowermost Danian strata are almost barren of invertebrates. The echinoderms, and among them in particular crinoids of the family Bourgueticrinidae, are the only group that deviates form this general pattern and show an increase in the strata immediately above the boundary. This exceptional development is accompanied by a heterochronic change in which the largest element of the bourgueticrinid theca, the proximale, is lost by paedomorphosis (neoteny). In the Late Cretaceous bourgueticrinids the proximale is formed during early ontogeny by the incorporation of a columnal element into the theca, and the addition of new columnals stops once the proximale is formed. The paedomorphic change and the elimination of the proximale allow, in principle, columnals to be added throughout life. This new development is probably the result of a selection for longer stems. It is successful from the very beginning and Democrinus maximus, the earliest bourgueticrinid species in the Danish Basin without a proximale, makes up about 90% of the crinoid fauna in the lowermost Danian deposits.

Previous studies have suggested that unbiased random walks may serve as appropriate null hypotheses for the detection of pattern in stratophenetic series. While numerous processes that influence the perceived temporal morphological evolution of a species may yield stratophenetic patterns that conform to the model of a random walk, use of the model as a null hypothesis raises several concerns. First, unbiased random walks are only a subset of a much larger set of random motions, including biased and fractional random walks. Some of these motions could also serve as appropriate null models for stratophenetic patterns. Second, due in part to the fractal nature of random walks, many types of time series begin to resemble random walks statistically as sampling resolution decreases. Therefore, indiscriminate support for unbiased random walks as null hypotheses of stratophenetic pattern leads inevitably to the commitment of Type II errors (incorrect failure to reject a null hypothesis). In this paper we simulate different hypothetical patterns of microevolution using various random walk models and apply the test of the null hypothesis. The frequency of Type II errors increases as stratigraphic completeness decreases, but at a currently unknown rate. Moreover, the test is insensitive to nongradual patterns of anagenesis.

We also demonstrate that a previously published approach is closely related to a standard method of fractal time series analysis and represents a good qualitative test of evolutionary pattern. The statistical variation underlying this method, however, is currently unknown, and further work is required to make it a robust quantitative test.

Conodont element function and feeding mechanisms are of considerable paleobiological importance, yet many details remain poorly understood and speculative. Analysis based on morphology, physical juxtaposition, and patterns of surface damage and microwear on pairs of Pa elements from individuals of Idiognathodus indicates that these elements crushed food by rotational closure, which brought the oral surfaces into complex interpenetrative occlusion. Other molariform conodont elements also functioned in this manner. Occlusion of this complexity is unique among nonmammalian vertebrates, and is all the more surprising given that conodonts lacked jaws. In addition to enhanced understanding of food processing in conodonts, our analysis suggests that many details of conodont Pa element morphology, which underpin taxonomy and biostratigraphy, can now be interpreted in a paleobiological, functional context.

The identification of randomness and nonrandomness is a perennial problem in evolutionary research. Stochastic thinking in evolutionary biology and paleobiology has solidified the use of a statistical notion of chance, but the idea of chance in evolutionary studies goes beyond statistics. A duality arises from the use of a statistical meaning on the one hand, and a more strictly evolutionary meaning on the other. The former implies a combination of indiscriminate sampling and unpredictability due to multiple causes; the latter codifies independence from adaptation and the directionality imposed by natural selection. Often these meanings are kept separate in evolutionary research, used in isolation according to the empirical situation or the goal of the investigator (recognition of pattern versus process). I argue that evolutionary studies in general and paleobiological studies in particular can benefit from the simultaneous application of statistical and evolutionary notions of chance. Following some background on the notion of chance and its use, I discuss a series of examples in which insight can be gained by explicit consideration of both meanings. Thus, typologies of extinction become clearer when phenomena like wanton extinction are made explicit; exaptive radiations are exposed as an alternative to adaptive radiations; the possible nonadaptive nature of deterministic chaos becomes sensible; the nonrandomness of community-assembly is put into question; parallel taxonomies of sorting rooted in different notions of nonrandomness are suggested as a means of facilitating understanding of relationships across the hierarchy; developmental constraints and self-organization are more easily distinguished from selective constraints; and a new term, “incidentals,” is suggested to refer to both exaptations and nonaptations. Finally, I point to ways in which the dichotomy between chance and necessity can be approached in evolutionary theory, by showing that the dual nature of chance in evolution entails a distinction between functional and structural necessity, and that chance ultimately becomes a unifying concept for a number of criticisms to neo-Darwinism.

A mathematical-computational method for determining the volume, mass, and center of mass of any bilaterally symmetric organism is presented. Cavities within the body of an organism such as lungs are easily accommodated by this method. Sagittal and frontal profiles, obtained from tracings of “fleshed-out” skeletal reconstructions, are used to provide limits for defining transverse slices of the body. Any internal cavities are defined by their own sagittal and frontal profiles. The computations consist of mathematically slicing the body and any cavities into independent sets of transverse laminae and computing their masses, centroids, and moments with respect to the three coordinate axes. Further calculations produce the masses and the (x,y,z) coordinates for the centers of mass of the body, any cavities, and the body + cavities. Predicted body masses of large, extant mammals (elephant, giraffe, hippopotamus, and rhinoceros) are in close agreement with actual body masses. New, lower estimates for body masses of selected large dinosaurs, based on modern skeletal reconstructions, are also presented, along with numerical estimates of their centers of mass. This method is an improvement over earlier ones that relied on measuring displaced volumes of water or sand by scale models to estimate the masses, and suspending models by threads to estimate their centers of mass.

Outline-based morphometric methods have been more or less restricted to the consideration of closed curves and plagued by problems related to the maintenance of close biological correspondence across all forms within a sample. Methods developed herein generalize and extend the eigenshape method of outline analysis along the following lines: (1) consideration of open curves, (2) improvement of interobject correspondence via incorporation of information provided by landmarks, and (3) extension to the analysis of three-dimensional (open and closed) curves. In addition, techniques for using eigenshape results to create models of shape variation and for more consistently assessing the digital resolution necessary to represent an object are discussed and illustrated. These improvements are then placed in context via discussions of previous attempts to extend morphometric outline analysis methods, the relation between landmark and outline-based morphometric methods, the use of morphometric analyses to test biological hypotheses, and the nature of morphometric shape spaces (with special reference to studies of morphological disparity).