INTRODUCTION

Identifying accurate measures of diversity is a task that preoccupies paleontologists and neontologists alike. Across extinct and extant studies, biological diversity may equate only in terminology but not in biological actuality (i.e., species, alpha diversity, generic richness). The interplay between these deep time and recent diversity studies, however, has generated a wealth of literature in the past 30 years (Jablonski 1999) and has spurred a profusion of ideas about diversity over time that carry both macroecological and conservational implications ( Jackson and Johnson 2001; Jackson et al. 2001). At a fundamental level, the value of any measure of diversity, for paleontologists, directly relies on how well we think our measures of diversity separate biological signal from noise (Raup 1976b).

Traditionally, paleontologists use taxonomic counts, i.e., a tally of the number of fossil taxa (often families or genera) from a given time, as quantitative measurement of biological diversity across geologic time (Sepkoski 1997). Ideally, generic counts reflect the actual number of genera per time interval, but many biases can distort measured diversity from the actual diversity of any time interval (Raup 1976a; Sepkoski 1997). Moreover, for any given taxon, there are specific and, possibly, a limited number of factors that bias measures of diversity through geologic time. These factors arise directly from organismal behavior, life history, taphonomy, and morphology, and vary widely from group to group. Some studies in the paleontological literature use generic compilations within a higher taxon to reflect actual evolutionary trends in a broad fashion, despite apparent biases and distortional issues (Benton et al. 2000; Foote and Sepkoski 1999), whereas other studies seek to develop statistical techniques that account for various biases at broad temporal scales (i.e., 10⁶ yr; Miller and Foote 2003; Peters and Foote 2001)

Our study of generic diversity through geologic time differs from previous work in both scale and taxonomic focus: we use cetaceans (a specific clade with a distinct and known temporal and spatial origin) as an exemplar taxon to assess specific issues associated with generic diversity estimates at a scale smaller than that of Phanerozoic marine diversity (Jablonski and Sepkoski 1996). By using genera as the primary units, we aim to circumvent problems associated with large-scale analytical and taxic paleobiological studies (eg., Adrain and Westrop 2000; Sepkoski 1978). Because our study examines generic richness within a single mammalian order through time, we can attain an acceptable and qualitative level of consistency with taxonomy and nomenclature. Although some Linnean ranks may not have biological equivalence in actuality (Mishler 1999), given the current practice of descriptive paleontological research, generic counts provide reliable data at the highest practical taxonomic resolution for analyzing changing diversity through geologic time.

Cetacea originated in the late early Eocene as mostly terrestrial mammals with a few characteristics for aquatic predation and sensation (Gingerich and Uhen 1998). By the late Eocene, basilosaurid archaeocetes had become obligate marine cetaceans, and their fossils from both hemispheres suggest that they achieved a cosmopolitan distribution in the world's oceans (Uhen 1998). After the radiation of Eocene archaeocetes, cetacean evolutionary history can be simply summarized by the origin of Neoceti, in the Oligocene and their diversification during the middle Miocene (Fordyce and de Muizon 2001). Notwithstanding this widely accepted view of cetacean history, the potential effects on apparent cetacean diversity (including potentially biasing factors) have been identified in broad terms (Barnes et al. 1985; Fordyce 2003b and others) but these effects, particularly the potentially biasing factors, have remained largely unaddressed in specifics and in categorization. We address these potential sources of bias herein.

Increases bias

One source of increased diversity bias may arise from naming new taxa based on limited, non-diagnostic fossils. Potentially, different parts of the same cetacean can be given different names. In paleontology, this process, called taxonomic inflation, results in multiple names being applied to what is actually a single taxon. Taxonomic inflation appears to be most acute in taxa with a sparse and fragmentary fossil record. Also, taxonomic inflation can arise from a literal reading of the taxonomic literature without some form of taxon vetting, which can conflate diversity estimates with taxonomic practice (Alroy 2002; White 2003). In this study, we attenuate the effect of potential over-splitting by strictly counting only genera instead of species.

Taxonomic inflation could still be a problem if genera being counted are based on species named with non-diagnostic type specimens. To prevent further burdening cetacean literature with an abundance of taxa named from fragmentary material (e.g., isolated periotics and teeth), Barnes (1977) proposed to limit new species descriptions only to specimens with diagnostic cranial, periotic and post-cranial elements. Despite this wise advice (even if it had been followed since the time it was offered), many non-diagnostic cetacean genera have persisted in the literature. In this study, genera represented by type species with poor type specimens were designated nomina dubia and left out of the taxonomic counts. It is important to note that for some taxa, describing new taxa represented solely by complete specimens may bias diversity in the opposite manner (Donovan 2001). Incomplete, but diagnostic type specimens are common in vertebrate paleontology, and thus, they are very important to include in this kind of analysis.

Another potential source of apparent diversity is a lack of comparison of the type specimens leading to an overcount of the number of named taxa. Counting genera instead of species should help overcome this problem, but it may persist even on the generic level. The inability to directly compare type specimens of different species is particularly problematic for Cetacea because of the large size of many specimens. Logistically, it is difficult to compare cetacean type specimens side by side when the specimens are as large as a researcher, and especially so when key specimens are on different continents. Current research practices, such as distributing casts of critical type specimens, publishing informative figures, and reproducing descriptive monographs using modern electronic media are all helping to make cetacean specimens more comparable.

Another source of increased diversity bias may result from counting taxa in time intervals that are excessively long. As Foote (2000) noted, the varying duration of different time intervals can distort diversity counts significantly, particularly if some time intervals vary greatly in length. This problem can be minimized by using the finest time scale possible, as well as using time intervals that are evenly divided. Ideally, the length of each time interval would be less than the duration of the taxa being counted, and taxa would occur in multiple time intervals. This type of idealized pattern would allow researchers to use taxa that are boundary crossers for counts of diversity rather than those that are confined to the time interval alone, a procedure recommended by Foote (2000) to avoid problems of variations in interval length. Unfortunately, many cetacean genera are based on single occurrences, and most cetacean genera are confined to a single time interval, so the use of boundary crossers would be inappropriate for measuring cetacean diversity.

Decrease bias

Generic diversity counts may be lowered by lack of available fossil-bearing rock. We assessed this factor by measuring geologic map area to see if available rock correlated with generic diversity (see Crampton et al. 2003 for a recent application of this approach). Similarly, the presence of fossils and the lack of collection effort may decrease generic counts. We thus examined the uniformity of collecting effort (quantified by publication data) in time and space (Raup 1977; Sheehan 1977). In parallel with collecting effort, non-preservation and/or destruction of fossils may similarly decrease diversity counts, and we thus also assessed this biasing factor by determining the uniformity of preservation biases in time and space. Finally, informative paleontological data are hard won: the stepwise progress of information from field discovery to publication (summarized in White and Folkiens 2000) can stop at any point in the sequence of field, museum, laboratory, or publication preparation. The presence of unpublished specimens can become "phantoms" of diversity in an analogous manner to ghost lineages in phylogenetic analyses. Our study also includes assessments of unstudied and undescribed cetacean genera to determine if study effort is uniform in time and space (see Jablonski et al. 2003).