Adapting mark-recapture methods to estimating accepted species-level diversity: a case study with terrestrial Gastropoda

Compilation of data

We present a method for estimating accepted species-level diversity, so we must clarify what we mean by “accepted” name. In zoology, accepted names are called valid names; in botany, they are called correct names (Greuter et al., 1996). To qualify as valid or correct, a name must have been published in compliance with the governing code of nomenclature. This is indeed the usage intended in the World Register of Marine Species and MolluscaBase (Horton et al., 2017). There are cases, however, where the accepted name of a taxon is not valid or correct. An example with terrestrial gastropods is Pomatias laevigatus (Webb & Berthelot, 1833): its original name, Cyclostoma laevigatum, is preoccupied by Cyclostoma laevigatum Menke, 1830. As a junior primary homonym, it is permanently invalid, but no replacement name has been established, so it continues to be used. It is a “current” name that is not acceptable, but it is treated as accepted in MolluscaBase. Such names are included in our counts herein.

MolluscaBase is a subset of the World Register of Marine Species (WoRMS Editorial Board, 2021) but expanded from the usual focus of WoRMS to include freshwater, terrestrial and fossil species. It is intended to be an authoritative, continuously updated GSD for Mollusca and thus provides a cornerstone of the taxonomic infrastructure for this phylum (Bieler, Mikkelsen & Giribet, 2013; Bank et al., 2014). Compilation of data in MolluscaBase is based on the standards of WoRMS as stated by Horton et al. (2017). The number of species of Recent terrestrial Mollusca was determined by using the advanced search function in MolluscaBase for Status “accepted”, Rank “Species”, Environment “Yes” for terrestrial and “Any” for other environments, and Flag “Extant, not fossil only”. Various error checks were run to find species erroneously marked as terrestrial or missing the terrestrial flag, including checking all species listed as terrestrial with at least one other environment indicated; those lacking any indication of environment; and searching for species in entirely terrestrial clades such as Stylommatophora, Cyclophoroidea, Helicinoidea or Pomatiidae that were not indicated as terrestrial.

Names used as valid in the ANSP malacology database were extracted in July 2020. Duplicates on the list were removed (e.g., different generic combinations of the same epithet) so that each name appeared on the list once. Each name was assigned a random number using the rand() function in Microsoft Excel. The list of 13,157 names is provided in Table S1. Our first test (completed 11 August 2020) used the first 1,100 names when sorted lowest to highest by the assigned random number. Our second test (completed 27 June 2021) used the second 1,100 names. The samples included 1,100 names so that after exclusions, more than 1,000 names would remain, ensuring large sample sizes. Names from the random samples used in 2020 and 2021 are shown in Tables S2 and S3 respectively.

Two gastropod families were set aside in the estimates: Truncatellidae and Cerionidae. Truncatellidae in ANSP and in MolluscaBase were both updated by the senior author (Rosenberg) from the same literature and so are not independent. Cerionidae are treated as nominal species rather than valid species in the ANSP collection and so do not fulfill a criterion of the test. Other reasons for exclusion were that names were determined to be out of scope (pertaining to species that are exclusively marine or fossil only), not available (e.g., manuscript names) or duplicates. If two different names from ANSP mapped to the same name in MolluscaBase (i.e., they are synonyms), only one match was counted toward m₂ and one name was excluded, to fulfill the expectations of the binomial distribution.

Names from ANSP were assigned to taxonomic groups (Neritimorpha, Cyclophoroidea, Littorinimorpha and Eupulmonata, see Box 1) and geographic regions (Africa, Asia, Australia/New Zealand, Caribbean, Europe, North America, Oceania, South America and Other (for unassigned, e.g., Bermuda, or unknown)) to allow assessment of completeness in MolluscaBase for these groupings. Japan, Indonesia, New Guinea and the Philippines were grouped with Asia; Madagascar, Mauritius and the Canary Islands with Africa; the Azores and Balearic Islands with Europe; the Bahamas with North America; and the Galapagos with South America. Names that appeared in more than one geographic region were assigned to one based on type locality, area of origin (for introduced species) or preponderance of occurrences in one region in the ANSP collection. For simplicity calculations for taxonomy and geography were based on raw numbers (method 1).

Adaptation of mark-recapture methods

Although mark-recapture methods and estimating known species diversity have similar mathematical underpinnings, they have different assumptions. Mark-recapture relies on the assumption of “equal catchability” (Seber, 1982; Chao, Pan & Chiang, 2008) but this assumption clearly is not met for estimates of known species diversity. Despite not meeting this standard, estimates of diversity seem not to be greatly affected by departures from it. One area where this bias manifests is that MolluscaBase is virtually complete for species of mollusks named in the last 10 years, since they are easily discovered with searches in Google Scholar, Zoological Record, and ZooBank, whereas ANSP and other collections are weak for these species. Although collections may contain them, they have not yet been identified therein. Since the ANSP collection and MolluscaBase are negatively correlated in this respect, diversity should be overestimated. When recently named species are set aside (method 2), estimates from 2020 decreased by 433 species (1.5%) and from 2021 by 152 species (0.5%) (Fig. 3; Tables 3–4). The magnitude of the effect is inversely correlated to completeness of the enumerations: in 2021, only 5.3% of sampled species led to missing accepted species; in 2020, the corresponding figure was 16.7% (Table 2). Since the estimates from 2021 are within the error bars for the estimates of 2020, the effect is not significant, but it could be significant in cases where the database is less complete.

A different situation is seen when taking abundance into account. When samples from ANSP are divided into three abundance classes (<5, 5–15 and >15 samples corresponding to a name), there is a negligible increase: nine species in 2020 and 12 species in 2021 (Tables 3–4). Rosenberg (2014, table 4) had a similar result with marine mollusks, with estimates increasing by about 0.5% when abundance was taken into account, but with error bars overlapping the raw estimate. Rosenberg’s (2014) procedure was different from the one used here, with stratified sampling across five abundance classes instead of three, so that each group had at least 200 randomly chosen names, but the overall conclusion is the same: abundance has little effect on the estimate of species-level diversity. This makes sense because discoverability of a name has little correlation with abundance of the organism it represents. When a species is named, it is likely picked up in several indexing sources. If it is missed by the research community, it fades from knowledge (see “overlooked names” in Supplemental Information). Organisms known from only one specimen might be cited hundreds of times and their status as accepted species debated. The dinosaur Hadrosaurus foulkii Leidy, 1858, for example, was considered a nomen dubium by Prieto-Márquez, Weishampel & Horner (2006), a conclusion later reversed on further study (Prieto-Márquez, 2011). Yet, one of the most abundant organisms in the world, the cyanobacterium Prochlorococcus marinus, was not named until 1992 (Chisholm et al., 1992) and many abundant species remain unnamed (Leray & Knowlton, 2016).

The methods also differ in that mark-recapture focuses on recaptured individuals, whereas our estimates of diversity focus on species that were not “recaptured”, that is, accepted names missing from MolluscaBase. Since we defined this number to be (1 − m₂), it can readily be converted to m₂ for use in the mark-recapture formulas. Names in m₂ in estimates of diversity, however, should not be thought of as recaptured, because there are names where we cannot tell whether they were recaptured. These correspond to item e in Table 2: “Epithet missing, accepted name uncertain or unknown”. Names in item b in Table 2, “Epithet present, accepted name uncertain or unknown”, appear similar but are not problematic—their status is given in MolluscaBase, because the epithet is present.

The method presented herein provides a means of estimating the number of species currently accepted in a group that does not yet have a complete taxonomic database, but the 95% CIs provided are based only on sampling error. Our best estimate for accepted diversity of terrestrial gastropods in 2021, accounting for potential correlations between the databases, is 28,420 ± 369 species. Additional uncertainty comes from clerical and observational errors. We have controlled for these errors to the degree possible (see Table 5 and Supplemental Data), but they grade into taxonomic uncertainty. Adding in the additional uncertainty from clerical and observational errors of 475 ± 430 (Table 5) yields a rounded estimate of terrestrial gastropod diversity of 28,895 ± 630 species known by the end of 2021 (Fig. 3). The added uncertainty means that the error term represents a range rather than a statistical confidence interval.

Taxonomic databases contain “eclectic species” (Blackburn & Tyler, 1987; Barraclough et al., 2016), discovered with various methods and proposed under a variety of taxonomic traditions and species concepts. Technological advances such as scanning electron microscopy, micro-CT scanning and DNA sequencing mean that the methods used by taxonomists are changing—more data sources are available and methods of analysis grow more powerful. Integrative methods lead to better understanding of taxa (Pante, Schoelinck & Puillandre, 2015; Goulding & Dayrat, 2016), as have debates about species concepts (Padial & De la Riva, 2006). Since it is not possible to revise all the species in large groups simultaneously, current methods will not yet have been applied to some of the component taxa (Gaston, 2008). Also, some species concepts may not be appropriate for various groups—Mollusca for example contains some groups that are parthenogenetic, so their members cannot be treated under the Biological Species Concept. Large taxonomic databases thus will always contain eclectic species. (See Box 2 for an example of the importance of species concepts).

Our method estimates the height of the species naming curve (Box 2), with the error bar shrinking to zero as the database evaluated approaches completion. A species naming curve may show known diversity approaching an asymptote, as with unionoids (Fig. 1), or rapidly increasing as with marine mollusks (Rosenberg, 2014, fig. 1), terrestrial gastropods (Fig. 2), and many other groups of organisms (Bebber et al., 2007; Edie, Smits & Jablonski, 2017). As taxonomic research progresses, the number of species recognized in a group as of a given date may increase or decrease, depending on the flux of names into and out of synonymy. This flux can be shown in a name usage curve (Fig. 1). Alroy (2002), based on North American fossil mammals, proposed a method to take this flux into account in correcting estimates of accepted diversity, but MolluscaBase does not have the detail necessary to implement his method. It might be implemented for freshwater mussels (Unionida) since Graf & Cummings (2021a; 2021b) have captured all taxonomic actions relevant to the group in the MusselP database.

In principle, the range of current values determined by our method could be incorporated into projections of diversity levels that might ultimately be recognized. A rapidly increasing curve like that for terrestrial gastropods indicates that many species remain to be discovered, but trying to extrapolate an upper limit is likely to be futile since the error bars become very large (Bebber et al., 2007; Gaston, 2008). Estimates are even less reliable as additional assumptions are made. Appeltans et al. (2012), for instance, incorporated synonymy rates, rates of discovery, and projected tens of thousands of cryptic species yet to be discovered in trying to estimate the scale of global marine diversity. They concluded that previous estimates greatly exceeding one million marine species were “highly unlikely”. Yet, Leray & Knowlton (2016) gave credence to estimates greater than one million because DNA-based approaches show many more lineages than projected by Appeltans et al. (2012). According to Fišer, Robinson & Malard (2018), the increasing ability to detect cryptic species and the history of lineages constitutes a paradigm shift. Korshunova et al. (2019) have argued, however, that increasing ability to make fine scale morphological and molecular distinctions means that degree of crypticity is a continuum, so that it is misleading to refer to cryptic species. These views are concordant, however, in illustrating how increasing technological abilities and theoretical understanding increase our ability to detect species, but they also make it harder to predict an endpoint.

Global diversity of recent terrestrial gastropods

Most mollusk species are still discovered and described under a morphological species concept, although many groups of mollusks exhibit non-adaptive or morphostatic radiation (Gittenberger, 1991; Davis, 1993; Falniowski, 2018). “Cryptic” or morphostatic species have been documented in marine (Meyer, Geller & Paulay, 2005; Fassio et al., 2020), freshwater (Wilke et al., 2010; Falniowski et al., 2020) and terrestrial mollusks (Köhler & Burghardt, 2016; Moussalli & Herbert, 2016; Liew et al., 2014). Descriptions of new species and subspecies of mollusks often do not define their taxonomic concepts (Rosenberg, Moretzsohn & García, 2009) and different schools of thought may have different underlying concepts of taxa (Rosenberg & Ludyanskiy, 1994; Graf, 2007). Molluscan subspecies can be particularly problematic. Many named prior to the geographic subspecies concept (Mayr, 1942; Wilson & Brown, 1953) were sympatric with the nominate subspecies. Modern authors encountering subspecies that are sympatric either synonymize them if they intergrade or treat them as distinct species if they do not (e.g., Rosenberg & Muratov, 2006; Mason et al., 2020). Rosenberg & Muratov (2006) provided guidelines for evaluating older names, since many of the taxa they treated in compiling the Jamaican terrestrial fauna had not been considered since the 1930s or before. Names are taxonomic hypotheses that can be reevaluated as needed when a researcher considers whether a name already exists for a taxon (Gittenberger, 1993; Rosenberg, 1993). A taxonomic hypothesis that has been tested and supported provides a better basis for decision making than one that has not been (Gaston & Mound, 1993). (See Supplemental Data under “species concepts” for examples with Cerion.)

Although many previously named molluscan species-group taxa have not been evaluated with modern methods, it is nonetheless possible to predict on a qualitative basis some of the effects of taxonomic revision on taxa that have already been named. As of 16 Aug 2021, MolluscaBase had 2,300 taxa inquirenda, 6,400 subspecies and more than 10,000 synonyms for terrestrial gastropods. MolluscaBase is not as complete in its treatment of synonyms and subspecies as it is for accepted species, but these numbers show that there is considerable potential to add accepted species by clarifying taxa inquirenda and reevaluating synonyms and subspecies. That means the species naming curve (Fig. 2) will increase in height, even without new discovery, since resurrected taxa enter the curve in the year they were named. On a name usage curve (Box 2) in contrast, a name would be counted from when it was named to when it was first synonymized and then reappear in the count in any subsequent interval when it was accepted.

The shape of the species naming curve shows that discovery of terrestrial gastropods is far from complete (Fig. 2), as is true for many other taxa (Bebber et al., 2007; Edie, Smits & Jablonski, 2017). Many mollusks were originally described from shells alone. When modern methods are applied integrating data from shell morphology, anatomy and molecules (Goulding & Dayrat, 2016) new species are often discovered (e.g., Criscione & Köhler, 2013). Solem (1984) predicted that the median range for all land snail species would be “less than 100 km, and quite probably less than 50 km”, which suggests that some regions have not been sampled with sufficient intensity to discover most of their species. On average, more than 200 species of terrestrial gastropods have been named per year since 2009, with rates of discovery currently accelerating. Both revisions of existing names and the trajectory of discovery are pushing the species naming curve higher. Although it is not currently possible to predict an upper limit to accepted species level diversity of terrestrial gastropods, it is clear that our estimate of 29,000 species already accepted is a minimum. It would not be surprising to see accepted diversity reach 50,000 species or more.

Solem (1984) estimated the actual minimum diversity of land snails including species yet to be named as 30,000 to 35,000. The number of accepted species is now approaching that lower bound. Accepted names for Europe, North America and Australia/New Zealand are essentially complete. Among continental areas, Africa had the largest percentage missing, but all of the missing taxa are from North Africa, indicating that accepted names from sub-Saharan Africa are virtually complete. The largest remaining gaps were with island faunas. In the Caribbean the fauna of Cuba and in Oceania that of the Hawaiian Islands are the most diverse and these also account for many of the species missing from MolluscaBase. Completeness for accepted names in MolluscaBase does not indicate that a region is well known, since it may be many years since its fauna was treated.

Recent non-marine mollusks have among the highest extinction rates of any group of organisms (Lydeard et al., 2004; Régnier, Fontaine & Bouchet, 2009). Régnier et al. (2015) estimated that 7–10% of Recent terrestrial gastropods species have gone extinct during the Anthropocene. Small geographic ranges put species at immediate risk of extinction. The criteria for evaluation as endangered on the IUCN Red List include extent of occurrence less than 5,000 km² or area of occupancy less than 500 km². If Solem (1984) is correct in suggesting that the median range size of land snail species is less than 50 km, then more than half of the species fulfill an area criterion for endangered status.

Outlook

Our adaptation of mark-recapture methods to estimating accepted species diversity is applicable to taxonomic databases for other phyla and will enable more sophisticated tests of the completeness of global species databases (GSDs). If our method is applied to paleontological databases, a stratified sampling approach should be used to ensure adequate coverage across geological epochs. If appropriate versions or backups of a database exist, it may be possible to implement our method comparing present to past versions instead of needing to wait for database growth. The result will be better understanding of the completeness of existing GSDs.

As taxonomic coverage in GSDs increases, it will no longer be necessary for researchers to compile their own “graveyards” of names (Gittenberger, 1993) to work on a taxon. As geographic coverage increases, it will be possible to generate faunal lists for regions that lack them. As images of type specimens accumulate it becomes possible to more rapidly access identities of nominal taxa. This will lead to acceleration of research in systematic biology, evolution, ecology and conservation.