Brinkmann (1929) argued that phyletic evolution in the Jurassic ammonite Kosmoceras is sufficiently linear that the amount of time missing at diastems can be estimated by the magnitude of morphologic jumps at those horizons. Brinkmann's unpublished raw data have been re-analyzed in order to evaluate the association between evolutionary jumps and physical breaks. All horizons in Brinkmann's 1400 centimeter stratigraphic section have been tested for morphological jumps. Up to 40 statistically significant morphological jumps exist in the section, the actual number depending on the sample interval used. A few of these correspond to the jumps found by Brinkmann and a few coincide with diastems. However, the correspondence between morphological jumps and physical breaks is not as consistent as was thought by Brinkmann. Furthermore, it is argued that the association between physical and biological discontinuities is not dependent on linear evolution but rather is the expected condition wherever phyletic evolution occurs. Due to the irregularity and unpredictability of evolutionary change in Kosmoceras, morphologic jumps cannot be used to assess the amount of time missing at diastems.

Colonies of the fossil bryozoan Archimedes and erect, spiralled species of the living bryozoan Bugula consist of wedge-shaped systems of radially diverging, bifurcated branches that extend from a helical axial margin. Morphology of these colonies may be simulated using few growth rules. These include 1) radius of the central helical margin (RAD), 2) rate of climb of central helical margin (ELEV), 3) radial angle between successive branches that originate from the central helical margin (ANG), 4) radial growth of all branches, 5) angle between branches and axis of central helical margin (BWANG), 6) distance between three adjacent, radially diverging branches at which the central branch bifurcates into two branches equally spaced between the two side branches (XMIN), and 7) placement of a spacing bar at base of newly bifurcated branches. In addition, size constraints on the simulations must be stipulated.

Simulations are begun at a proximal point along the central helix where a radial branch originates and are “grown” in repetitive steps by extending the central helical margin a distance distally, determined by ANG, then censusing established branches for XMIN in order to bifurcate appropriate branches and extend others in several short growth increments, etc. Growth of branches ceases at stipulated maximum width, and growth of the entire simulation ceases at stipulated maximum height.

The presence of a helical inner margin marked by uniformly spaced bifurcations generates the spiralled shape, i.e. ELEV must be a positive number. Values of RAD, ELEV (not zero), ANG and BWANG determine form of the spiral; the other growth rules apply to bifurcated unilaminate branch systems in general.

The range of observed colony forms and hypothetical morphospace of Archimedes may be simulated by varying BWANG, XMIN, and ELEV. RAD was kept constant, as its variation would be redundant with XMIN and ELEV. Variation in ANG affects near-helix morphology, but its influence is undetectable beyond this zone. Variability within colonies may be simulated by assigning to each variable a standard deviation with mean-centered randomly chosen values for each decision.

Alleles, individuals, and species are all examples of entities possessing variation in the properties that underlie natural selection: branching (reproduction), persistence (survivorship), and heritability of characters. This suggests that the logic embodied in the theory of natural selection can be abstracted from its usual application to the level of individuals to encompass selection operating among any biological entities for which these essential properties can be meaningfully defined. This approach leads to a unified perspective of adaptation, selection, and fitness at all levels. Expanded versions of the Price covariance selection equations provide a convenient and useful conceptual vehicle for this discussion. The advantages of a hierarchical approach are twofold: it permits exploration of concepts and ideas across levels by analogy, and it focuses attention upon the mechanisms that account for different evolutionary dynamics at each level rather than obscuring these biologically unique properties with argument by extension from a single “special” level.

We point out that the choice of a single measure of evolutionary change restricts the context in which “other level” processes will be perceived. We illustrate the limited forms in which higher and lower level selection can be recognized from the unique perspective provided by any given level through extensions of Price's formula.

An exploration of the implications of such an approach leads us to the assertion that the development of a unified theory of evolution demands the recognition and incorporation of hierarchical structure as a conceptual foundation.

A model is proposed, based on examples that have been interpreted as phylogenetic trends, to explain how directional morphological evolution at the species level can arise by heterochrony. The examples illustrated are of Tertiary to Recent rhynchonellide brachiopods, Cambrian olenellid trilobites, living spatangoid echinoids, Tertiary to Recent schizasterid echinoids, Cenomanian ammonites and Silurian monograptids. Morphological discontinuities between species along morphological gradients (which can be recognised both spatially and/or temporally), and temporal morphological stasis within species, are both consistent with the punctuated equilibria model of macroevolution. It is argued that morphological discontinuities have arisen by selection of morphological novelties produced by heterochronic processes. These novelties are preadaptations which allow ecological and, consequently, genetic isolation from ancestral species. Establishment of a heterochronic morphological gradient is only possible given a suitable environmental gradient. The terms “paedomorphocline” and “peramorphocline” are proposed for these heterochronic morphological gradients. Paedomorphoclines and peramorphoclines each comprise a number of species occupying a series of adaptive peaks, which have evolved sequentially through time by selection along an environmental gradient.

The distribution of species abundance (number of individuals per species) is well documented. The distribution of species occurrence (number of localities per species), however, has received little attention. This study investigates the distribution of species occurrence for five large data sets. For modern benthic foraminifera, species occurrence is examined from the Atlantic continental margin of North America, where 875 species were recorded 10,017 times at 542 localities, the Gulf of Mexico, where 848 species were recorded 18,007 times at 426 localities, and the Caribbean, where 1149 species were recorded 6684 times at 268 localities. For Late Cretaceous molluscs, species occurrence is examined from the Gulf Coast where 716 species were recorded 6236 times at 166 localities and a subset of this data consisting of 643 species recorded 3851 times at 86 localities.

Logseries and lognormal distributions were fitted to these data sets. In most instances the logseries best predicts the distribution of species occurrence. The lognormal, however, also fits the data fairly well, and, in one instance, better. The use of these distributions allows the prediction of the number of species occurring once, twice, …, n times.

Species abundance data are also available for the molluscan data sets. They indicate that the most abundant species (greatest number of individuals) usually occur most frequently. In all data sets approximately half the species occur four or less times. The probability of noting the presence of rarely occurring species is small, and, consequently, such species must be used with extreme caution in studies requiring knowledge of the distribution of species in space and time.

Some ungulate species at Upper Pleistocene and Holocene archeological sites in South Africa exhibit catastrophic mortality profiles, while others exhibit attritional ones. The awareness by Stone Age people that some species are especially amenable to driving or snaring probably accounts for the catastrophic profiles. Natural catastrophic death immediately followed by human scavenging is a much less likely explanation because the species samples comprise material lumped from deposits that accumulated more or less continuously over hundreds or even thousands of years during which period there is no reason to suppose the repeated occurrence of natural catastrophes nearby.

The inability of Stone Age people to obtain prime-age adults in species that are not particularly amenable to driving or snaring presumably accounts for the attritional mortality profiles. Although the species that display attritional profiles conceivably were scavenged, the high proportion of very young individuals in the profiles suggests active hunting. Very young individuals are much less abundant in attritional profiles from local non-archeological sites, probably because their carcasses were removed from the record before burial, primarily by carnivore or scavenger feeding. Scavenging would account for the abundance of very young individuals in the archeological sites only in the unlikely event that people could regularly locate carcasses before other predators did.

In general, geomorphic/sedimentologic context is probably the best criterion for determining whether a species characterized by a catastrophic profile in an archeological site was hunted or scavenged. At the majority of known sites, active hunting is suggested. In the case of a species characterized by an attritional profile in an archeological site, the proportion of very young individuals in the sample probably provides the best criterion for distinguishing hunting from scavenging. A relatively high proportion of very young individuals suggests active hunting.

A late Miocene population of Neohipparion cf. leptode from the Love Bone Bed of Florida was found to have 13 discrete annual age classes based on eruption sequences and tooth wear. The large sample size of individuals (minimum number = 229) allowed the estimation of standard population parameters, including age-specific mortality rates. The average age of death for a newborn was 3.5 years, but those individuals that survived the 64% juvenile mortality occurring during the first two years lived an average of 8.0 years. The potential longevity of this species of Neohipparion had not increased beyond that of known samples of Merychippus, despite increased crown height. The paleoenvironment of the collecting site was a wooded grassland savanna with annual wet and dry seasons. The Neohipparion population migrated into the area during the dry season but left in the wet season to give birth away from the collecting site.