Functionally significant aspects of skull morphology were examined in Eocene miacids and in early members of the modern carnivore families to see if functional craniology might shed light on factors involved in the origin and early evolution of the modern carnivores. No key innovations are apparent at the beginning of the modern carnivore radiation, and an alternative hypothesis to account for that radiation is proposed: the radiation represents the filling of niches vacated by the extinction of several groups of archaic carnivores in the late Eocene. Differences that distinguish modern viverrids, canids, felids, and mustelids from each other today were less pronounced in the Oligocene, when these families first appeared, and provide no insights into possible ecological differences at the family level. However, body size differences among the early members of the modern carnivore families suggest that partitioning of prey resources by size may have been a factor in their initial radiation. Comparison of cranial morphology in Eocene miacids, early members of the modern carnivore families, and living carnivores allows reconstruction of the primitive conditions of carnivore skull morphology and determination of the pathways of morphological transformation that resulted in the diversity of skull morphology seen in modern carnivores.

Using computer simulations and a quantitative method for describing bifurcating structures, the morphology of branching patterns seen in early land plants is analyzed. Four types or models of random branching (regular, geometric, binomial, and poisson) are shown to adequately describe the range of observed branching in most early land plants. Approximately 57% of all randomly generated computer patterns show reiterative branching events (=three successive identical modes of branching). Artificial canalization of reiterative events results in branching patterns structurally analogous with that of ancient fossil plants. Simulated phylogenetic changes among early land plant lineages, based on parsimonious transitions in branching patterns, indicate that most observed trends can be related directly to those seen in randomly generating branching patterns in which “size” is increased. The trimerophyte to progymnosperm trend in changing branching patterns is an exception, since the binomial model describing the progymnosperms has not been simulated by random processes.

While the apparent phylogenetic changes among early land plant groups do not require deterministic explanations, the transition from regular to geometric branching and the “canalization” of reiterative branching patterns may represent a grade level response to selective pressures related to mechanical design and vegetative reproduction.

Calibrating levels of time resolution that are accessible in the fossil record is important in understanding what evolutionary phenomena can be profitably studied using fossils. A model for attritional bone assemblage formation in fluvial deposits, based on observations of taphonomic processes in modern environments, provides order-of-magnitude estimates for time intervals represented in single unit, ‘contemporaneous' vertebrate samples. In order to form units with adequate material for analysis of morphological variation or paleoecological associations, it appears that bones must be spatially concentrated or stratigraphically condensed by sedimentary processes or biological agencies. In many cases this means that significant periods of time will be represented by single unit assemblages. According to predictions from modern environments, carcasses contributed through normal attrition can accumulate in the soil to ‘fossiliferous' densities over time intervals of 102–104 yrs. Attritional channel assemblages include bones from three sources: floodplain land surfaces, floodplain deposits, and the active channel, and represent time intervals on the order of 102–104 yrs. Given additional limitations on the composition of the fossil sample imposed by circumstances of preservation, outcrop availability and collecting strategy, attritional fluvial assemblages probably can be resolved only to 103 years even under the best conditions. Time intervals represented by fossils are not necessarily the same as those represented by sedimentary events in fluvial systems because bones can continue to accumulate and may be concentrated during times of erosion or non-deposition. Fluvial vertebrate assemblages of comparable taphonomic history can be used to document evolutionary changes over periods longer than their finest level of time resolution. While they may not be applicable to questions of punctuated or gradual transitions over shorter time scales, the longer-term patterns should have their own evolutionary significance.

Paleoecologists studying Paleozoic reef-builders have interpreted their growth forms as responses to conditions of depth and turbulence in reef complexes. Comparison of the shapes of Paleozoic stromatoporoids and corals with the growth forms of modern scleractinians has been used to reconstruct Paleozoic conditions. A review of shape zonation on modern reefs indicates that no general pattern is applicable to all reefs and variations in shape are the result of the interaction of many environmental factors with the genetically dictated growth pattern of the coral. In most zones of a reef a wide range of shapes co-exist. The growth forms of corals on modern reefs are not a simple vegetative response to the many environmental parameters that have been shown to influence form, but are constrained by phylogenetic and developmental influences as well as functional ones.

Interpretations of the environments of western Canadian and other mid-Paleozoic reefs have been based on the growth forms of stromatoporoids. The environmental significance of the shapes has been deduced from comparison with the shapes of modern scleractinians, functional morphology, nature of the enclosing sediment, position of growth, position within the reef, and diversity gradients. The validity of these criteria is open to question and considerable doubt remains concerning the significance of the growth forms. The shapes of reef animals are not specific guides to environments of modern reefs and should not be expected to be guides for ancient ones.

The function of lunules in sand dollars is reviewed and it is argued that ambulacral lunules and the anal lunule evolved for quite different purposes. Whereas ambulacral lunules evolved to increase the perimeter of the test for food gathering, this was clearly not the original function of the anal lunule, although in some genera it has become secondarily adapted to this role. Many of the unique features of the anal lunule can be explained if it evolved as an outlet for ciliary feeding currents drawn centripetally into the mouth, without disrupting either oral or aboral currents. This allowed the entire margin of the test to be used for collecting the fine particles sieved through the aboral spine canopy. Anal lunules probably evolved only once, in the Miocene, and the Monophorasteridae and Mellitidae are probably sister groups.

Studies of ontogenetic processes are fundamentally dependent on hypotheses of phylogeny. The model of Alberch et al. (1979) is reformulated in terms of phylogenetics and used to describe how heterochronic ontogenetic processes can be detected in nature. Heterochronic processes producing paedomorphosis can result in morphologies which resemble primitive (retained ancestral) traits; the conditions under which paedomorphic and primitive features can and cannot be distinguished are described. The utility of ontogeny for determination of evolutionary character transformations and character polarity and for detection of convergence and parallelism are considered. The ontogenetic criterion for assessing polarity is independent of hypotheses of phylogeny and may be as effective as outgroup comparison. Ontogenetic analysis may aid in the detection of convergence but not in the detection of parallelism.

The shape and arrangement of cusps and crests and the orientation of wear striations on the cheek teeth of fossil mammals can be used to reconstruct occlusal patterns. Occlusal patterns have been documented previously in a variety of therian mammals and also in triconodonts and docodonts among nontherians. This is the first detailed analysis of patterns of jaw movement and dental function in a member of the highly specialized nontherian order Multituberculata (Allotheria). Ptilodus, a Paleocene multituberculate, appears to have had two cycles of mastication that followed different paths of movement and utilized different sets of teeth. The first cycle, the slicing-crushing cycle, occurred as the large, laterally-compressed fourth lower premolar (P4) sliced orthally into food items held primarily against the fourth upper premolar (P4). Food items sliced in this manner passed down both the labial and lingual sides of P4, forming subparallel striations in valleys between the nearly vertical enamel ridges. The second cycle is the grinding cycle in which the mandible was retracted while the molars were in tight occlusion, thus producing longitudinal striations on the molars. Unlike the pattern in therians, triconodonts, and docodonts, there is no transversely triangular masticatory orbit in the grinding cycle of multituberculates. The generally accepted idea that the labial aspect of P4 in ptilodontoid multituberculates sheared orthally against the lingual aspect of P4 is not supported. Instead, predominantly horizontal striations developed on the posterolabial wear facet of P4, and on a conjoined facet posterolingually on P4 and anterolingually on the first upper molar (M1), indicate that relative movement between these surfaces was largely palinal (i.e., the jaw moved from front to back), rather than orthal and occurred during the grinding cycle of mastication.

In considering the dietary preferences of ptilodontoid multituberculates, it appears that most members were not folivorous. The small size of many species of Ptilodontoidea suggests that they could not have subsisted on a folivorous diet, which is rich in structural carbohydrates. The length of striations on the sides of P4 of Ptilodus, one of the largest of the Ptilodontoidea, indicates that large, hard food items were ingested. The presence of both smooth and highly-striated enamel on homologous dental wear facets in different individuals of Ptilodus mediaevus from a single quarry sample suggests a varied diet. The recent suggestion that ptilodontoids were omnivorous is supported.

The fossil stickleback, Gasterosteus doryssus, is highly variable for pelvic girdle structure and the number of dorsal spines. Six “sampling pits” were dug at known stratigraphic positions within a continuous section which contains abundant G. doryssus, and the stratigraphic position of each specimen within each pit was determined. The deposit apparently is composed of annual layers (varves), allowing relatively precise conversion of stratigraphic distance to years. The temporal distribution of phenotypes is heterogeneous but can be grouped into two temporally contiguous, nonheterogeneous sets. However, absence of heterogeneity for pelvic phenotypes within the two groups of pits could be an artifact of small sample size. The number of sample pits was insufficient to determine whether the observed phenotypic heterogeneity among pits represents temporal trends. Differences also occurred between mean temporal distributions of stickleback phenotypes within one of the pits located within a nonheterogeneous set of pits. Thus, there is within-pit temporal heterogeneity that is unresolved by between-pit comparisons, although the sampling pits are separated by an average of only about thirty thousand years. Larger time intervals usually used in paleontology may seriously underestimate evolutionary rates because fine scale reversals of evolutionary trajectory are undetected. Temporal variation in G. doryssus provides a system in which most limitations of other fossil systems for measuring the rate of evolution can be circumvented. As in virtually all paleontological studies, spatial variation cannot be entirely eliminated as a potential cause of stratigraphic variation.

During the middle Cretaceous, exceptional ecologic conditions developed in the Tarfayan Basin (SW Morocco) marked by the deposition of marls and limestones, rich in organic matter. The ostracod fauna of the Cenomanian to Coniacian consisted of a few ornamentally stable species. Towards the close of the Turonian, Oertliella? tarfayaensis became dimorphic at the top of its range, the new morph with smooth lateral zones being the undoubted ancestor of Oertliella? chouberti. The multivariate morphometric evolutionary pattern for O.? tarfayaensis fluctuates about a stationary value in a manner which could reflect evolutionary stasis. The passage from the ancestral to the descendant species took between 1 × 105 and 2 × 105 yr. At the multivariate level, the transition could have taken place by random genetic drift with, or without, selective effects. At the univariate level, there is no clear evidence for either of these mechanisms. The phenotype is regionally stable which suggests that a non-genetic origin of the change is unlikely. An alternative model for the speciation event is allopatric speciation in a peripheral isolate and immigration. The Late Turonian morph may have resulted from environmentally cued polymorphism with elimination of the original morph due to a long term ecologic change, possibly connected with an increase in silica in the environment.

In a recent contribution, Rightmire (1981) claims that “No significant trends can be observed” in several characters measured in skulls of Homo erectus. While I sympathize with the frustrating problem of small sample size in hominid finds, one must ask the question: could you ever see a trend, given the quality of your information? If sample size is low, if trends are of relatively small magnitude, and if sample variance is high, one can always safely show that nothing (i.e., stasis) has happened. This form of inference falls into a classic statistical trap: attempting to prove statistical homogeneity. You cannot do it without a concomitant estimate of least significant difference, that is, estimating the magnitude of variation within which you cannot distinguish among estimates of a parameter.

Levinton notes that the number of individuals available to my study of patterns in the evolution of Homo erectus is low, especially when cranial base breadth is considered. If measurements of biauricular breadth are related to stratigraphic age of the fossils using linear regression, the slope obtained is small (−1.52). The confidence interval includes zero, and there is no evidence that a real trend is present. At the same time, the .95 interval is large (±26.81), so slopes differing by even a substantial margin cannot be distinguished. Levinton suggests that this negates a claim for stasis, and I agree that there are grounds for doubt. But by his reasoning, a case for stasis can never be established. While it is true that the occurrence of (very small) trends can never be denied, even if an analysis of many fossils shows a zero slope bracketed by narrow confidence limits, surely these “trends” must be dismissed as insignificant. Given such an outcome, a conclusion of no (directional) change would be quite justified.