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Paleoecologists have long sought to obtain estimates of the sizes of extinct populations. However, even in ideal cases, accurate counts of individuals have been hampered by the fact that many organisms disarticulate after death and leave their remains in the form of multiple, separated parts. We here analyze the problem of estimating numbers of individuals from collections of parts by developing a general counting theory that elucidates the major contributing variables. We discover that the number of unique individuals of a particular species that are represented in a fossil collection can be described by an intricate set of relationships among (1) the number of body parts that were recovered, (2) the number of body parts that were possessed by organisms belonging to that species, and (3) the number of individuals of that species that served as the source of the parts from which the paleontological sample was obtained (the size of the “sampling domain”). The “minimum number of individuals” and “maximum number of individuals” methods currently used by paleontologists to count individuals emerge as end members in our more general counting theory. The theory shows that the numbers of individuals of a species that are represented in a sample of body parts is fully tractable, at least in a theoretical sense, in terms of the variables just mentioned. The bad news is that the size of the “sampling domain” for a species can never be known exactly, thus placing a very real limit on our ability to count individuals rigorously. The good news is that one can often make a reasonable guess regarding the size of the sampling domain, and can therefore make a more thoroughly informed choice regarding how to estimate numbers of individuals. By isolating the variables involved in determining the numbers of individuals in paleontological samples, we are led to a better appreciation of the limits, and the possibilities, that are inherent in the fossil record.

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Previous observations about the stable nature of coral-rich assemblages from the Middle Devonian Hamilton Group have led some researchers to invoke the primacy of ecological controls in maintaining biofacies structure through time. However, few analyses have examined the degree to which recurring biofacies vary quantitatively, and none have assessed lateral variability as a benchmark for testing the significance of temporal variability. Thus, the extent to which Hamilton biofacies persist and the mechanism(s) responsible for their hypothesized stability remain contentious. In this study, recurring coral-rich biofacies were evaluated from two stratigraphic horizons within the Middle Devonian Appalachian Basin to examine (1) the extent to which species assemblages persisted within the basin through space and time, and (2) whether ecological interactions may be a plausible mechanism for generating the degree of stasis observed in this case. Variations in species composition and abundance were examined across multiple spatial scales within both sampled coral-rich horizons. This permitted the establishment of a baseline against which temporal differences in biofacies composition and structure could be evaluated. Although successive coral-rich horizons remained taxonomically stable, their dominance structures changed significantly through the 1.5 Myr study interval. Moreover, additional comparisons among older Hamilton coral-rich horizons corroborate our primary results. These findings support a model in which species respond individually to fluctuations in the physical environment, as indicated by the fluidity of their relative abundances geographically and temporally.

In mid-September 2007, 32 paleontologists gathered at the Smithsonian Institution to spend four days discussing research frontiers in paleoecology, particularly at the interface with neoecology. They represented expertise throughout the Phanerozoic and in all major groups of fossilizable organisms. This meeting was timely, given the increasing evidence of the impact of climate change on ecosystems in our modern world. The vast repository of paleoecological data on past environmental change and concomitant ecological responses, observed at many different spatial, temporal, and taxonomic scales, is of potentially great value for understanding and predicting how modern ecosystems will respond to cUmate change. Of particular interest to the participants of this meeting were questions of how ecological data collected at different scales could be reconciled so that our knowledge of ecological change in the past can better inform our understanding of the present and our predictions of how ecosystems will change in the future. Certainly, this is one of the most exciting research frontiers in paleoecology.Data collected for different ecological studies (both paleoecological and neoecological) encompass a wide range of spatial, temporal, and taxonomic scales. Understanding the scales inherent in an ecological research question is critical to designing a sampling protocol that will yield data capable of resolving that question, yet these scales are often not adequately evaluated or presented in published paleoecological reports. Furthermore, for any body of paleoecological research to be rescued from isolation and integrated with other studies, the various scales encompassed by the research questions and data must be understood and reported.The greatest bamer to communicating and collaborating with neoecologists is not that data collected from extant ecosystems are necessarily different or more complete than paleoecological data but, rather, that these two data sets commonly represent or are collected at different scales. If such differences of scale can be understood and quantified, then they can be reconciled and even exploited. This will allow neoecological studies to inform the interpretation of patterns and processes in the fossil record and will permit the use of paleoecological studies to test how ecological and environmental processes have structured the biosphere over extended ' Corresponding author. time intervals (National Research Council, 2005). To facilitate better communication and sharing of data among paleoecologists and neoecologists, we offer the following guide to questions of scale that we recommend be explicitly addressed to the fullest extent possible in any paleoecological research report. We consider the following a checklist-one that we hope will be useful, particularly to those embarking on new research. For those seeking an important research problem to tackle, we end with a list of significant, yet still unresolved, scale-related questions.