Thomas D. Olszewski

One of the major obstacles in dealing with any form of data derived from fossils is the effects of time-averaging, which are the result of mixing the remains of organisms that did not live contemporaneously. Although this process results in loss of temporal resolution, it also serves to filter out short-term variations. Temporal resolution of a collection depends not only on the range of fossil ages, but also on their frequency distribution. Previous studies of marine molluscs indicate that most shells in an accumulation are relatively young. Such a distribution of shell ages can be fit by an exponential curve (assuming both a constant probability of shell loss and a constant rate of shell addition), which implies that 90% of the shells were added during the last 50% of the time interval represented by the collection. That is to say, differences between two collections can be discerned even if they overlap 50% in time, because the proportion of shells with shared ages is only 10%. Applying the exponential model to previously published data suggests that long-term rates of destruction are controlled by how frequently shells from the taphonomically active zone are re-exposed to rapid destruction. To take advantage of the “noise-filtering” property of time-averaging, samples need to be large enough to catch the full range of environmental variation recorded by an accumulation. A simple probability formula indicates that samples of easily achievable size can give satisfactory time-averaged results depending on the level of confidence and sampling density defined by the researcher.

Age spectra of Mulinia lateralis shells from the top 0–10 cm of the sediment column in Copano Bay, Texas, show three distinct populations: a young population with a highly skewed distribution ranging from 0 to 1 years, a middle-aged population that is more symmetrical ranging from 1 to 10 years with a peak ∼ 4 years, and a small, very old population ranging from 100 to > 10000 years. The young population is interpreted to record the rapid loss of shells from the taphonomically active zone at or near the sediment surface. The middle-aged population is interpreted to record a sequestered population of shells that has had time to accumulate below the taphonomically active zone. Although surface age spectra differ among depositional environments and at different locations, both of these populations are present in all sampled facies at multiple locations within the bay, indicating that the overarching controls on surface age spectra affect the entire bay. The very old surface population is present only in bay-margin sites and is interpreted to represent shells exhumed from eroding Holocene deposits. An 86-cm-long core taken at a bay-margin site near the mouth of the Aransas River contains shells spanning < 1 to 14,000 years but not preserved in stratigraphic order. The lack of stratigraphic order and the presence of distinct breaks in the postmortem age distribution suggest that 67% of shells in the core were recycled from older deposits, resulting in a 2–3 order of magnitude increase in the amount of time averaging in the sediment column relative to surface samples.

Explaining the origin and maintenance of biodiversity is critical for understanding the potential consequences of present-day environmental change on ecological communities, as well as the evolutionary history of ecosystems in the Earth's past. Much effort in theoretical ecology has focused on identifying mechanisms that promote stable coexistence of species at equilibrium. However, in a consumer-resource model of competition along an environmental gradient, high-diversity assemblages have the potential to persist in non-equilibrium states for millions of generations with very little species loss. Species' populations in such competitively accommodated communities show slow drift; if disrupted, they rapidly reorganize into alternative persistent states. Fossil examples of prolonged ecological stability lasting 1-5 Myr punctuated by rapid reorganization (e.g. brachiopods from the Permian Reef of west Texas) suggest that some palaeocommunities represent a record of periodically disrupted transient states rather than stable equilibria. The similarity between the theoretical results reported here and palaeontological data suggests that the maintenance of high-diversity communities, both in the past and present, may reflect long-duration, non-equilibrium transient dynamics. If so, this has implications for the response of such communities to present-day environmental change, as well as for the evolution of lineages in such systems.

Accumulations of dead skeletal material are a valuable archive of past ecological conditions. However, such assemblages are not equivalent to living communities because they mix the remains of multiple generations and are altered by post-mortem processes. The abundance of a species in a death assemblage can be quantitatively modelled by successively integrating the product of an influx time series and a post-mortem loss function (a decay function with a constant half-life). In such a model, temporal mixing increases expected absolute dead abundance relative to average influx as a linear function of half-life and increases variation in absolute dead abundance values as a square-root function of half-life. Because typical abundance distributions of ecological communities are logarithmically distributed, species' differences in preservational half-life would have to be very large to substantially alter species' abundance ranks (i.e. make rare species common or vice-versa). In addition, expected dead abundances increase at a faster rate than their range of variation with increased time averaging, predicting greater consistency in the relative abundance structure of death assemblages than their parent living community.

Much of the Archean record of microbial communities consists of fossil mats and stromatolites. Critical physical emergent properties governing the evolution of large-scale (centimeters to meters) topographic relief on the mat landscape are (a) mat surface roughness relative to the laminar sublayer and (b) cohesion. These properties can be estimated for fossil samples under many circumstances. A preliminary analysis of Archean mat cohesion suggests that mats growing in shallow marine environments from throughout this time had cohesions similar to those of modern shallow marine mats. There may have been a significant increase in mat strength at the end of the Archean.

Diversity (the variety of different types of organisms) of an ecological or paleoecological system reflects processes and history operating across a range of hierarchically related scales. For example, the diversity of a biofacies is the sum of the diversity in all the local patches composing the biofacies, the diversity of a depositional system is composed of all the biofacies composing the depositional system, and the diversity of a biotic province is composed of all the landscapes composing the province. Diversity at a larger scale (γ-diversity) incorporates both the average inventory diversity of units of the next smaller scale (α-diversity) and the compositional differences, or differentiation diversity, among the smaller units (β-diversity). Many familiar means of measuring diversity can be mathematically partitioned to determine the relative contribution of different diversity components at any hierarchical level. When using richness (the number of taxa in an ecological system) as a measurement of diversity, it is necessary to use rarefaction to correct for differences in sample size. The divergence between sample-based and individual-based rarefaction curves of a composite collection (γ-diversity) incorporating all the samples (α-diversity) contributing to a given hierarchical level reflects the degree of non-random compositional difference among the smaller scale units (β-diversity). Alternatively, Shannon's entropy can be partitioned additively: β-entropy equals γ-entropy (based on a composite sample) minus average α-entropy of the constituent samples. A useful property of entropy is that it can be converted to effective richness, the number of taxa that would result in the same entropy value if all were equally abundant. Effective richness can be thought of as a unit conversion from non-intuitive entropy units to more easily understood richness units. Effective richness derived from Shannon's entropy partitions diversity multiplicatively – i.e., β-diversity is the number of compositionally distinct smaller units that contribute to the total diversity at the higher level. Diversity partitioning is rapidly becoming adopted as a tool for directly addressing how the structure of higher-level ecological and paleoecological systems reflects interactions among lower-level units in response to environmental and evolutionary changes.

Paleontologists have identified patterns of stability in the diversity and composition of communities over millions to tens of millions of years within the fossil record. It is unclear, however, what processes are responsible for controlling the stability observed in these communities—for example, local species interactions within communities, local species-environment relationships, immigration of species from the regional biota. This study tests whether the taxonomic composition of local brachiopod paleocommunities occupying a slope environment across a ∼40 km2 region remains temporally uniform over a 5.4 myr interval of time recorded by the Pinery, Rader, Lamar, and Reef Trail Members of the middle Permian (Capitanian) Bell Canyon Formation (BCF). Two third-order sequence boundaries have been previously recognized in this formation, indicating episodes of environmental disruptions related to sea-level fall within the basin that can induce habitat tracking or immigration events from other basins. Presence-absence data analyzed by cluster analysis, ordination techniques, and rank-occurrence plots demonstrate that compositional turnover occurs within the BCF. Change in composition of the Lamar Member paleocommunities documents the replacement of established brachiopods with new taxa, including the immigration of two new brachiopod genera from outside North America, indicating the influence of regional-scale effects on community assembly. The results based on metacommunity models suggest that dispersal plays an important role in the assembly of brachiopod paleocommunities in the Delaware Basin. Results also indicate that fossil communities provide useful information for interpreting placement of sequence boundaries and the magnitude of disruption.