Introduction

Fossils provide the only direct evidence concerning the diversity of life through time, and as such they are paramount in studies of evolutionary patterns and rates. Macroevolutionary studies that address such issues typically employ the relatively densely sampled invertebrate fossil record (e.g., Foote and Raup 1996; Cheetham and Jackson 1998). However, several vertebrate groups have well-sampled fossil records whose long-term evolutionary histories have been thoroughly studied by paleobiologists. Among fossil mammals, most work that pertains to macroevolutionary patterns and processes involves either large-scale analyses of terrestrial land-mammals through the Cenozoic (e.g., Foote and Raup 1996; Alroy 2000), detailed examinations of relatively short, densely sampled fossil occurrences (e.g., Clyde and Gingerich 1994; Alba et al. 2001; Wood et al. 2007), or, less commonly, investigations at scales intermediate between these two (e.g., MacFadden 1985). In most cases, these studies have been restricted to taxonomic groups that have been studied extensively and for which considerable diversity or abundance of fossil forms is thought to be present. Evolutionary patterns in the fossil record of relatively poorly sampled groups have been only rarely examined.

One conspicuous group for which macroevolutionary analyses using the fossil record have been rare is bats (Mammalia: Chiroptera). With more than 1100 extant species (Simmons 2005), bats comprise an extraordinary taxonomic diversity that is second only to rodents among living mammals. Phylogenetic investigations of bats have provided some important insights into the evolutionary history of the group, including recent efforts reaffirming bat monophyly and uncovering various hypotheses of microchiropteran paraphyly. In principal, a perfect fossil record would illuminate the correct phylogenetic history of bats; such a record might serve as an independent test of the correctness of various phylogenetic hypotheses. However, few studies of bats have incorporated extinct taxa into phylogenetic analyses, especially in genus- or species-level analyses. Using fossils in systematics will likely become less common as molecular-based systematics continues to proliferate (Hermsen and Hendricks 2008). However, depending on the types of hypotheses being tested, ignoring fossil taxa that contain phylogeny-relevant information not found in extant organisms may limit our potential to completely understand the evolutionary histories of these groups and may even produce misleading results in some instances.

To determine the potential utility of the bat fossil record in illuminating patterns of evolution, an understanding of its quality must be assessed. How accurately does the known fossil record reflect the true evolutionary history of bats? Two conceptual approaches have been used to address this question in other groups of animals. The first is phylogeny-dependent, in which the quality of the fossil record is assessed for a particular phylogeny. Teeling et al. (2005) presented one type of phylogeny-dependent method of assessing the fossil record of bats. They generated Bayesian estimates of divergence dates for each of the 58 branches (internal and terminal) from their maximum likelihood tree. Teeling et al. then compared their molecular divergence estimates with the oldest known fossils from the 58 branches of the tree. They used the differences in ages between the molecular and fossil estimates to calculate a percentage of missing fossil data per branch. The results of their analyses estimated that, on average, 73% of the known fossil record of 58 lineages of bats was missing. Pteropodid bats, long known to have a poorly sampled record, were missing upwards of 98% of their fossil history. The four non-pteropodid superfamilies were missing between 56% and 86% of their fossil record. Thus, the results of the Teeling et al. (2005) study seem to show that the fossil record of bats is quite poor. However, methods like that presented in Teeling et al. (2005) are heavily dependent upon the lineages included and the topology of the phylogeny used. Due to recent volatility in hypotheses of the higher-level phylogenetic relationships of bats (Springer et al. 2001; Jones et al. 2002, 2005; Eick et al. 2005; Gunnell and Simmons 2005; Teeling et al. 2005; Hermsen and Hendricks 2008), there may be some uncertainty in estimating the quality of the fossil record of bats using phylogeny-dependent methods.

Fortunately, the second class of methods for assessing the quality of the fossil record is phylogeny-independent. That is, statistical metrics are applied directly to the fossil data that quantify the quality of the fossil record (Benton 1998; Paul 1998). The method developed by Foote and Raup (1996) allows for one such quantitative analysis of the fossil record for any group independent of phylogeny. By estimating preservation probability, extinction rate, and the stratigraphic duration of taxa, completeness can be calculated deterministically. Completeness is defined as “the proportion of taxa that have left some fossil record,” (Foote and Raup 1996; sensu Valentine 1989), and it therefore serves as a metric for assessing the quality of the fossil record. In this paper we address the quality of the bat fossil record by calculating completeness using the method presented in Foote and Raup (1996). We calculate completeness for Chiroptera as a whole, as well as for the major higher-level bat clades. These calculations allow for a comparison of the fossil record for each of these groups, as well as an assessment of the quality of the fossil record of bats using a method independent of phylogeny.

Materials and methods

Data collection

A database of all known fossil bat genera was compiled from the literature Appendix (1). Genera were tabulated according to their temporal and geographic distribution. Taxonomy followed Simmons (2005), with the exceptions of Perimyotis and Parastrellus, which were considered distinct genera following the recommendations of Hoofer et al. (2006). Miniopteridae was considered to be a distinct family, following recommendations of recent analyses (e.g., Miller-Butterworth et al. 2007). Superfamily membership followed Teeling et al. (2005). Specimens identified as “cf.” (e.g., “cf. Eptesicus indet.”) were considered valid records for recording presence/absence. Pre-Pleistocene fossil bats were assigned to one of fifteen chronostratigraphic stages: Ypresian, Lutetian, Bartonian, Priabonian, Rupelian, Chattian, Aquitanian, Burdigalian, Langhian, Serravalian, Tortonian, Messinian, Zanclean, Piacenzian, and Gelasian. The Pleistocene was tabulated as a single bin. Stages and boundary dates were taken from Gradstein et al. (2004). Correlation of the European Mammal Neogene (MN) system was performed using Agustí et al. (2001) and references therein. Recent genera were tabulated and used for comparative purposes (but not for statistical calculations).

Data analysis

Calculations of completeness were carried out according to the discrete-time and infinite-window method of Foote and Raup (1996). This method requires tabulating the ranges of all taxa (bat genera in this case) according to discrete time intervals (mostly stages or combinations of two to three stages for this study). Our binning strategy attempted to produce bins of roughly equal durations. Thus, we summed several smaller bins into fewer large bins in an effort to combat high variance in the duration of stages in the Cenozoic (older stages tend to be longer than younger). In particular, we grouped all of the middle Miocene, all of the late Miocene, and all of the Plio-Pleistocene together into three bins (instead of the eight stages that fall within these time periods). The range of a taxon preserved in only one time interval is one. Stratigraphic data are tabulated using first and last occurrences, so that the range of a taxon equals the number of time intervals between its first and last occurrences, including the endpoints. Preservation probability R (the probability that a taxon is preserved at least once in an interval) was estimated by using the frequency, f, of taxa with observed ranges of one, two, and three intervals to calculate the range-frequency ratio, FreqRat, as:

$$ R \approx FreqRat = {{f(2)^2 } \mathord{\left/ {\vphantom {{f(2)^2 } {\left[ {f(1)f(3)} \right]}}} \right. } {\left[ {f(1)f(3)} \right]}} $$

Estimated preservation probability must be considered with respect to true durations, so calculating R is insufficient to analyze the quality of the fossil record (Foote and Raup 1996; Alba et al. 2001). Therefore, the probability P 1 (T) that a taxon is preserved at least once given a true original duration T must be calculated:

$$ P_1 (T) = 1 - \left( {1 - R} \right)^T $$

Original durations can be calculated assuming a constant extinction rate q (and exponential distribution of original durations), where q is calculated from the ln-slope of range-frequencies (omitting taxa that occur in only one bin) as the slope with the sign reversed (see Fig. 1). The probability h(T) that the original distribution equals T is calculated as:

$$ h(T) = e^{{ - q\left( {T - 1} \right)}} - e^{- qT} $$

Completeness P p is calculated as the sum, for all original durations (i.e., T = 1-∞), of the product between h(T) (probability of having original duration T) and P 1 (T) (probability of being preserved at least once during an interval given an original duration T) as:

$$ P_p = \sum\limits_{T = 1}^{\infty } {h(T)P_1 (T)} $$

P p was calculated for the pooled data, such that the range of each genus was considered only on a worldwide basis. Thus, P p was considered an estimate of global completeness. To explore the differences among the bat fossil record of various clades within Chiroptera, P p was calculated separately for Pteropodidae, Rhinolophoidea, Emballonuroidea, Noctilionoidea, and Vespertilionoidea (sensu Teeling et al. 2005), with varying degrees of success. A worked example of the statistical calculations, using the vespertilionoid data, is provided in Appendix 2.

Fig. 1
figure 1

Natural-log plot of range frequencies for fossil bat genera. Regression line was calculated after excluding genera with frequencies of zero or one bin. The slope of the regression line with the sign reversed equals extinction rate (q = 0.37).

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Results

Preservation probability, extinction rate (Fig. 1), and completeness are presented in Table 1 for all calculations. No calculations were possible for Pteropodidae, Emballonuroidea, or Noctilionoidea. Approximately half of all genera in the database were represented at least once in the fossil record (143/277). Of all extant genera, approximately 35% (71/204) are known as fossils. There are 70 known extinct bat genera. Approximately 72% of the genera had a range of one stratigraphic horizon. Those genera lasting two stages comprised about 6% of the genera, while those lasting three stages accounted for 13% of the data. Every other range-duration contained fewer than 5% of the genera.

Table 1 Calculations of preservation probability, extinction rate, and completeness for all bats (Chiroptera) and the two superfamilies Rhinolophoidea and Vespertilionoidea
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The number of known genera through time for six clades (Chiroptera, Pteropodidae, and the four superfamilies Rhinolophoidea, Emballonuroidea, Noctilionoidea, and Vespertilionoidea) plus a group of genera from all extinct and uncertain families is shown in Fig. 2. For Chiroptera as a whole, generic diversity is currently at its peak, with a relatively high diversity extending back through the Pleistocene. There has been an apparent gradual increase in diversity through time. Fossil Pteropodidae are rare at the genus level, with only three Tertiary occurrences. Rhinolophoidea (Hipposideridae, Megadermatidae, Craseonycteridae, Rhinopomatidae, and Rhinolophidae), the clade that newer studies suggest may share a sister relationship with pteropodid bats (e.g., Jones et al. 2005; Teeling et al. 2005), shows relatively high generic diversity (compared to modern) throughout most of its history, after initially low diversity during the middle Eocene. Diversity in several intervals throughout the Tertiary (e.g., Rupelian, Burdigalian) approaches or surpasses that of the Pleistocene; only Recent rhinolophoid diversity is higher. Emballonuroidea (Emballonuridae and Nycteridae) are present in relatively low generic diversity throughout the Tertiary, with a slight increase in the Pleistocene and a peak in diversity during the Recent. Noctilionoidea (Furipteridae, Miniopteridae, Mormoopidae, Mystacinidae, Myzopodidae, Noctilionidae, Phyllostomidae, and Thyropteridae) are unknown at the genus level until the Burdigalian (late early Miocene), and they maintain a very low diversity throughout the remainder of the Tertiary. Many more genera are known from the Pleistocene, and the Recent contains the highest noctilionoid diversity. Vespertilionoidea, similar to the patterns in other groups, shows a peak in diversity during the Recent. Generic diversity in vespertilionoids is relatively high throughout much of the Neogene; from 10 to 20 genera are known from each stage of the Neogene after the Aquitanian (early Miocene).

Fig. 2
figure 2

Number of fossil bat genera through time. All Recent bat genera are plotted for comparison with fossil forms. Each point corresponds to the middle of the bin it represents (except for the Recent). For both graphs, the x-axis plots time in millions of years ago, and the y-axis plots the number of genera. Note the different scales of the y-axis between the top and bottom graphs.

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Discussion

The global completeness estimate of 12% indicates that the bat fossil record is very poor. In other words, approximately 88% of all bats that lived never left a fossil record. This low completeness figure lends credence to the notion that bats have a poor fossil record, and it suggests that much of the evolutionary history of the group cannot be studied using fossil data. Teeling et al. (2005) found similar results—the origins of 73% of the 58 bat lineages in their analyses were underestimated by the fossil record. Importantly, their results were calculated using phylogeny-dependent methods, so general congruence between their figure and ours probably reflects a real phenomenon; namely, bats have a poor fossil record.

Calculations from other taxonomic groups, though not directly comparable, typically provide much higher completeness estimates (e.g., P p  = 0.58 for extinct, North American Cenozoic non-volant mammal species [Foote and Raup 1996], and P p  = 0.91 for mammals from the Neogene of Spain and Portugal [Alba et al. 2001]). Such a low completeness value for bat genera relative to these other studies may in part be due to the global nature of this study; local completeness for a restricted stratigraphic section typically results in much higher values (e.g., Cheetham and Jackson 1998). Such studies are usually performed when fossils are sampled densely in regions with few lapses in the rock record (Foote and Raup 1996). Furthermore, choice of taxa may play a role, and bats are probably less easily preserved than other mammals for both anatomical (delicate skeletons) and taphonomic reasons (see discussion below). This effect may be partly responsible for the high proportion of single hits in the data set (72% of all fossil bats occur in just one bin). Foote and Raup (1996) warn that high proportions of single hits may produce very high variances in estimates of original durations, which produce large errors when calculating completeness.

Fossil bats presumably inhabited environments similar to their modern counterparts, which typically are not well sampled in the fossil record. Of the common bat habitats, caves offer some of the best conditions for preservation, and many fossil bats are known from cave and karst deposits (Kowalski 1995). For example, Tertiary bats from the Mediterranean basin typically come from karst deposits (Sigé and Legendre 1983) and many bats from the Miocene Riversleigh Site of Australia apparently come from cave-fill deposits as well (Hand and Archer 2005). Other than caves, many of the best preserved fossil bats come from sedimentary deposits of extinct lakes (e.g., Jepsen 1966; Habersetzer and Storch 1987; Gunnell et al. 2003; Simmons et al. 2008); lacustrine environments provide some of the best conditions for fossilization in the terrestrial realm. Unfortunately, most bats visit lakes only briefly, so their potential for fossilization in these environments usually is very low.

A rather striking result is the general match between the superfamily-level results from Teeling et al. (2005) with those from this study (Fig. 2), though Teeling et al. found consistently higher completeness figures for each clade (Table 1). The rank-order from most to least percent missing from Teeling et al. (2005) is: Pteropodidae, Noctilionoidea, Emballonuroidea, Rhinolophoidea, and Vespertilionoidea. In the present study, completeness was calculated for Rhinolophoidea and Vespertilionoidea (in addition to all Chiroptera). Calculations were not possible for Pteropodidae, Noctilionoidea, or Emballonuroidea because of too little data. As Table 1 shows, the calculations of extinction rate (q) yielded Pearson coefficients of correlation (between the number of stages and the natural log of the frequency of genus occurrences) of 0.51 for Rhinolophoidea and 0.76 for Vespertilionoidea. The higher correlation for Vespertilionoidea may mean that the extinction rate is more reliable as compared to Rhinolophoidea. Furthermore, because the extinction rate is used to calculate completeness, the completeness of Vespertilionoidea may be more robust than it is for Rhinolophoidea.

It is important to note that having too little data to calculate completeness for Pteropodidae, Noctilionoidea, and Emballonuroidea does not, by itself, mean that the fossil records for these three groups are woefully incomplete. Our binning strategy may have been too aggressive in lumping together into the same bin bats that were found in different stratigraphic levels. If these three clades were geologically rather young (middle or late Miocene, for example), then there would not be enough binned intervals to generate a sufficient statistical sample to calculate completeness. However, none of these three clades are young, as shown by their fossil ages (Appendix 1, Fig. 2) and by phylogenetic analyses (Teeling et al. 2005; Gunnell and Simmons 2005). Examining the pattern of fossil occurrences through time (Fig. 2) provides some insight into the quality of the record for each of these groups. When compared to their modern diversity, Pteropodidae and Noctilionoidea seem to have the worst records, while Rhinolophoidea and Vespertilionoidea have the best. If we compare groups of similar modern generic diversity, it seems that Vespertilionoidea has a better record than Noctilionoidea, as does Rhinolophoidea when compared to Emballonuroidea. Completeness values for Rhinolophoidea and Vespertilionoidea were twice that of Chiroptera as a whole (25% versus 12%). So, it is reasonable to expect that groups other than the rhinolophoids and vespertilionoids would have completeness values substantially lower than 12% (though parsing out completeness values for each of these other groups was not possible in the present study).

Considering the apparent dual sister-group relationships between Noctilionoidea and Vespertilionoidea on the one hand, and Rhinolophoidea and Pteropodidae on the other (e.g., Jones et al. 2005), the apparent disparity in the quality of their fossil records cannot be attributed to factors affecting all bats. In part, the time available for diversification may have differentially affected clades, considering that the generic-rich noctilionoid family Phyllostomidae may be much younger than either Molossidae or Vespertilionidae that together comprise most of the vespertilionoid diversity. But even in the Miocene—likely after the origin of the first phyllostomid (Jones et al. 2005)—the vespertilionoid record contains much more diversity than the noctilionoid record. So, the disparity in the fossil records may in part be a real phenomenon that can be explained by at least three non-exclusive factors. First, it probably reflects a collector bias, as vespertilionoids and rhinolophoids constitute a disproportionate share of the bat fossils known from Europe and North America, both of which have a rather good sampling of fossil forms (Gunnell and Simmons 2005; Hulva et al. 2007). An increased sampling effort throughout the Old and New World tropics may diminish the problem of a depauperate bat fossil record, at least to some degree. Second, differences in the quality of the fossil record between bat clades could be due to different taphonomic effects. Pteropodids and most noctilionoids today inhabit tropical regions in which environmental conditions offer little hope of becoming fossils. For temperate bats, dominated by vespertilionoids, a large percentage inhabits caves and faces fewer taphonomic impediments to fossilization immediately after death. Finally, the disparity in the fossil record of bat clades could be due to a poor rock record. In this case, it may be that diverse assemblages of poorly represented bat clades were fossilized, but these fossils have been buried or destroyed as a result of subsequent geologic processes. Different bat clades could have experienced high diversity at different points in time, and some of these time periods may have been preferentially lost in the rock record.

While numerous questions cannot be directly addressed with this study (e.g., paleobiogeographic patterns), the results confirm the notion that the genus-level fossil record of bats is poor. As such, it is unclear how incorporating extinct bat genera into phylogenetic analyses would really enhance the resulting phylogenetic hypotheses, though simulations indicate that, even in the face of very high degrees of incompleteness, incorporating fossil data can improve phylogeny estimation (Fox et al. 1999). Some studies have shown a fairly high degree of consistency between phylogenetic analyses that do and do not incorporate extinct forms and their stratigraphic positions (e.g., Norell and Novacek 1992); others have demonstrated that fossils play a critical role in phylogeny estimation (e.g., Gauthier et al. 1988). Unfortunately, fossil bats often are represented by little more than isolated teeth or, at best, mandibular or maxillary fragments (Czaplewski et al. 2008). Though numerous parsimony-informative characters are found in the skull and dentition, many diagnostic characters are found in other parts of the skeleton (e.g., Gunnell et al. 2003; Simmons et al. 2008), and an absence of sufficient material may preclude definitive taxonomic or character assignment. Many important early bats cannot be assigned to genera (or even higher level groups) with any certainty (e.g., Archer 1978; Ducrocq et al. 1993; Tejedor et al. 2005). Such specimens have been omitted from this study, as we await more diagnostic material. However, any estimate of the completeness of the fossil record is predicated on the assumption that taxonomic diagnoses have been made correctly, so this issue may not preferentially bias our results.

Conclusions

This study marks the first phylogeny-independent estimate of the global completeness of the fossil record of bats. The genus-level bat fossil record is estimated to be 12% complete. This figure agrees broadly with phylogeny-derived completeness estimates by Teeling et al. (2005) in confirming the notion that the bat fossil record is poor. Such results indicate that much of the taxonomic and morphologic diversity of bats remains to be uncovered. Despite the depauperate fossil record, important steps in the evolutionary history of bats are recorded in fossils, such as the apparent evolution of flight before high-frequency echolocation in Eocene bats (Simmons et al. 2008). Future work should examine Tertiary deposits from historically under-sampled regions to increase our knowledge of fossil bats and thus improve our understanding of this remarkable group of mammals.