FWGNA > Synthesis
Synthesis
The FWGNA database current as of 19Nov15 contains 12,211 records of 69 freshwater gastropod species (combining subspecies) inhabiting Atlantic watersheds from Georgia to the New York line.

These records have been collected from approximately 9,000 discrete sites, as depicted in the map below (click for a PDF download).

All sample sites 

A PDF file listing these 69 species, ranked by their total number of records in our Atlantic drainage database, is downloadable from the link below:

  • Table 1Freshwater Gastropods of Atlantic Drainages, ranked by incidence.
We first ask whether these 69 species seem to comprise the complete richness of the freshwater gastropod fauna in our study area, or rather if the incidences shown in Table 1 might suggest that some rare species may have been missed.  We then propose an objective system of ranking species by incidence rarity, as a compliment to, if not a substitute for, the subjective systems of "conservation status" ranking currently in vogue.

> Species Richness

Research interest in the species richness demonstrated by ecological communities has a long history, extending as far back as the work of Fisher and colleagues (1943), if not further.  And from an early date it has been understood that a sampling bias is inevitable against rare species, to the point that the rarest species may fail entirely to obtain representation in samples taken under field conditions (Preston 1948). 

Early efforts to estimate the number of rare species missed in sampling programs focused on modeling the “distribution of commonness and rarity” demonstrated by natural communities, extrapolating from such models to a total species richness that might theoretically be expected (reviews by May 1975, 1986).  The data analyzed were typically abundances – the number of individuals collected for each species.  Consensus tended to converge on lognormal models, primarily because such models were generally found to fit real abundance data collected in a great variety of field situations (for freshwater mollusks, see Dillon 2000: 421-428).  There is also some theoretical justification to expect that a lognormal distribution of commonness and rarity might develop from plausible biotic interactions among species in a community (Sugihara 1980, 1989).

A second class of approach to the estimation of species richness is the “rarefaction curve” (Sanders 1968) or “species accumulation curve” (Holdridge et al. 1971).  In the former, the number of species is plotted as a function of the number of individuals in a single sample.  In the latter, the number of species is plotted as a function of incidence, the number of samples in which a species occurs.  In either case, a variety of techniques have been developed to estimate the asymptotic number of species present, and the sample size (or number of samples) required to reach that asymptote (Reviews by Gotelli & Colwell 2001, O’Hara 2005).

Most recently the effort to estimate species richness has shifted to nonparametric approaches, based on information theory.  Such statistics at the Chao2 estimator and ICE have been shown to outperform species accumulation curves, lognormal models, and other parametric approaches in randomization and simulation studies (Brose et al. 2003, Walther & Moore 2005, Gotelli & Colwell 2011). 

We have calculated the bootstrap species richness estimator of Smith & van Belle (1984), the Chao2 statistic (Chao 1984, 1987), and the incidence coverage-based estimator (“ICE”) of Chao et al. (2000) using the software package EstimateS (Version 9.1.0, Colwell 2013).  All three of these statistics returned bootstrap mean = 68, Chao2 mean = 68, and ICE mean = 68, suggesting no evidence that any rare species may have been missed in our sample.

> Lognormal Analysis

Figure 1 shows the incidences of our 69 species, log-2 transformed following the convention of Preston (1948):

Click for larger

The normal distribution fitting these data demonstrates a mean xbar = 4.74 (27 incidences) and standard deviation sd = 3.07 (8.4 incidences), but is slightly skewed to the right (g1 = 0.233) and strikingly platykurtotic (g2 = -0.968) with a significant Shapiro-Wilk W = 0.957 (p = 0.019).  Thus the hypothesis that the incidences of the 69 freshwater gastropod species inhabiting United States Atlantic drainages might fit a lognormal distribution does not seem to be supported.

Rather, Figure 1 suggests a bimodal distribution, with a second peak of very common (high incidence) species.  Dornelas & Connolly (2008) have suggested that multimodality may be a common feature of species abundance distributions when sample sizes are large, the phenomenon perhaps arising from an admixture of species demonstrating different spatial aggregation patterns.

> Incidence Ranks

In recent years a widespread practice has developed of prioritizing species for conservation purposes by a system of “status ranks.”  The nonprofit environmental organization “NatureServe,” for example, prioritizes the worldwide biota globally (G-ranks), nationally (N-ranks) or regionally (S-ranks) into five categories:  1 = critically imperiled, 2 = imperiled, 3 = vulnerable, 4 = apparently secure, and 5 = secure.  The International Union for the Conservation of Nature also uses five ranks: CR = critically endangered, EN = endangered, VU = vulnerable, NT = near threatened and LC = least concern.  A system of four ranks was advocated in the spurious review of Johnson et al. (2013), E = endangered, T = threatened, V = vulnerable, and CS = currently stable.  A review of the many methods by which species have been categorized according to perceived conservation concern has been offered by Munton (1987).

Although the appeal of such systems to the natural resource agencies charged with protection of potentially endangered species is undeniable, such concepts as "threat" or "peril" or "endangerment" are by their nature entirely subjective. And although some connection is almost certainly made between conservation status rank and rarity in the minds of natural resource managers, the relationship has never been formally explored, at least in the case of freshwater snails.  So here we suggest a ranking system based on incidence, offered as a compliment to (if not necessarily as an objective substitute for) the subjective systems of conservation status ranking current in use.

Convention would dictate that some special consideration might be extended to the extreme 5% of any distribution, normally distributed or otherwise.  Thus we suggest that the 5% of the species demonstrating the lowest number of incidences in a biota under consideration be assigned the rank “I-1,” by analogy to the “G1” rank of NatureServe.  The “I” prefix here designates “incidence,” to emphasize that the present ranking system is based on incidence data, rather than subjective impressions of “global imperilment.”

Gaston (1994) has offered an admirable review of the term “rare” in all its various origins and biological usages.  On the basis of clarity, versatility, consistency and ease of use, he has suggested that the term "rare" be defined as “the first quartile of the frequency distribution of species abundances.”  So because we have just set aside the 5% of species with the lowest incidence frequency as I-1, perhaps the 20% of the species remaining in the lowest quartile ought to be designated I-2.  Then a straightforward application of Gaston’s system would suggest that the second quartile (between the rarest set and the median) be designated I-3, and the third quartile I-4, and the fourth (most common) quartile designated I-5.

Note that the quartile division between ranks I-4 and I-5 corresponds to the dip in Figure 1 above, providing some independent rationale for applying Gaston’s system to our freshwater gastropod incidence data.

The vector of I-ranks resulting from application of the system suggested above to the 69 freshwater gastropod species inhabiting our study area is shown in the rightmost ("FWGNA") column of Table 1.  Note that we have rounded to accommodate some natural breaks in our incidence data, such that all six singleton species are included in rank I-1.

We have also divided the distribution of log-2 incidence categories shown in Table 1 above by our five I-ranks.  But notice that the system we are proposing is entirely nonparametric - based upon rank incidence alone.  Although the temptation to fit a lognormal model to data such as these is undeniable, in light of the analysis above we have refrained from assuming a hypothetical distribution of any sort for the assignment of I-ranks.

> Incidence Rarity

Rabinowitz (1981) has famously pointed out that there are seven forms of rarity.  We have no data on population sizes, however, nor any rigorous measure of habitat specificity for our 69 freshwater gastropod species.  Our analysis here has focused entirely upon geographical distributions.  The species found in the most spots are common by our definition, and those in the fewest spots are rare.  This may be termed “incidence rarity.”

Murray et al. (1999) reported that a remarkable 91% of the species in the “tail” of a rank-abundance curve generated from the canopy-forming vegetation of the Australian dry sclerophyll woodland were significantly more abundant elsewhere.  Murray and colleagues called these 91% the “somewhere-abundant” species, to distinguish that group from the 9% that were “everywhere-sparse.”

Similar phenomena have been noted in many animal communities.  Gaston (1994) has reported that the vast majority of the British bird species demonstrating incidence rarity are “vagrants,” which he defines as “not permanent members of the assemblage, do not breed, or do not have self-sustaining populations.”  Gaston notes that other terms that have been applied to describe such species include accidentals, casuals, immigrants, incidentals, strays, tourists and tramps.  Magurran & Henderson (2003) have added the term “occasionals” for rare species in estuarine fish communities.  The literature of plant community ecology includes the terms "peripheral" and "waif."

Similar to the situation described by Murray and colleagues, the data in Table 1 suggest to us two categories of rare species, the “somewhere-abundant” and the “everywhere-sparse.”  But we are not aware of any term in malacology analogous to “vagrant” or “occasional,” probably because such terms imply greater dispersal capability than is ordinarily assumed for freshwater mollusks.

We therefore suggest adopting the botanical term “peripheral” for use in mollusk community ecology to describe the situation where a rare species is “somewhere-else-abundant.”   We formally define a peripheral species as demonstrating less than median incidence in a region under study, but greater than median incidence elsewhere.  And we suggest that all non-peripheral species in a study region be called “core” species.

Although there are few rigorous estimates of the relative incidence of freshwater gastropod species outside the present analysis, our reading of the malacological literature suggests to us that over half of the 34 species listed below the median in Table 1 probably demonstrate above-median incidence elsewhere.  Four of these 34 are exotic invasives - Potamopyrgus antipodarium, Pyrgophorus parvulus, Melanoides tuberculata and Pomacea maculata.  The excellent New York survey of Jokinen (1992) suggests to us that the following 7 species are more common to the north of our study area: Valvata tricarinata, Helisoma campanulata, Lymnaea catascopium, Lymnaea elodes, Gyraulus deflectus, Bithynia tentaculata, and Aplexa hypnorum.  Our reading of the North American literature broadly suggests that the following 3 species are probably more common in interior drainages to the west of our present study area: Pleurocera semicarinata, Pomatiopsis lapidaria and Viviparus subpurpureus.  And the Florida survey of Thompson (1999) suggests that the following 5 species are more common further south: Hebetancylus excentricus, Pleurocera floridensis, Biomphalaria havanensis, Pomacea paludosa and Floridobia floridana.   A lower-case “p” has been appended to the incidence ranks of all 19 of these species in Table 1, to indicate their (hypothesized) peripheral status in Atlantic drainages from Georgia through Pennsylvania.

The 19 species we consider peripheral here are distributed evenly across all three of the incidence ranks below median, as follows:

I-1 I-2 I-3 I-4 I-5
Core 3 6 6* 15+2* 18
Peripheral 3 5 11


The 3 core species marked I-1 and the 6 core species marked I-2 are clearly rare, demonstrating incidences in the bottom quartile.  Gaston (1994) coined two terms relevant to the situation regarding the other species tabulated above, however, "pseudo-rarity" and "non-apparent rarity."  The former term would describe the 3 species we have listed as I-1p and the 5 species we have listed as I-2p, because although their incidence would rank them in the bottom quartile of the 69 species in our study area, there is reason to think that they are not rare elsewhere.  Indeed, those 3+5=8 species have displaced 8 species that should have occupied their spots in the bottom quartile.  Thus the 6 core species marked I-3* in Table 1 (without the modifier "p") and the 2 least common of thes species marked I-4* all demonstrate non-apparent rarity.  They are genuinely rare, and deserved to have appeared in the bottom quartile, but their rarity was obscured by the 8 pseudo-rare, peripheral species.

Note that (at least) 9 of the species listed in Table 1 have been considered “invasive,” demonstrating a potential for rapid range expansion in historic times: Bellamya japonica, B. chinensis, Viviparus georgianus, V. subpurpureus, Bithynia tentaculataPomacea maculata, Melanoides tuberculata, Pyrgophorus parvulus and Potamopyrgus antipodarum.  At least two other species may have obtained representation in Table 1 by artificial introduction (Pomacea paludosa and Biomphalaria havanensis), although demonstrating little potential to spread.  We have elected not to treat these species differently.  The first three in the list above have now spread to above-median incidence in Atlantic drainages from Georgia to Pennsylvania, and are hence now considered “core” species by our definition.  Some of the other species may ultimately transfer from marginal to core status, as well.  We do not expect the designations in the far rightmost column of Table 1 to remain static.

Indeed, we expect the opposite.  Our long term plans call for expansion of the FWGNA survey westward, with concomitant augmentation of our database and (doubtless) addition of new species to our faunal list.  The I-ranks currently shown in Table 1 should be considered subject to revision for quite a few years to come.

> Essays

  • Our initial effort to develop a (parametric) theory of commonness and rarity for freshwater gastropods was based on the incidence of 57 species in four states only.  This was published in my blog post of 9Jan12: "Toward the Scientific Ranking of Conservation Status, Part II."
  • I introduced the first nine-state, nonparametric version of this analysis in my blog post of 9Dec13, "What is Rarity?"  That particular essay focused on Gaston's quartile definition.  The 2013 FWGNA database contained 11,471 records from the Atlantic drainages, representing 67 species.
  • I focused on the subjects of "peripheral" species, pseudo-rarity and non-apparent rarity in my follow-up essay of 6Jan14, "Why is Rarity?"
  • The present FWGNA synthesis (12,211 records, 69 species) is an incremental (but not negligible) expansion of our 2013 analysis.  It was announced in my blog post of 19Nov15.

> References

Brose, U., N. D. Martinez, & R. J. Williams 2003.  Estimating species richness: sensitivity to sample coverage and insensitivity to spatial patterns.  Ecology 84: 2364-2377.
Chao, A. 1984. Non-parametric estimation of the number of classes in a population. Scandinavian Journal of Statistics 11, 265-270.
Chao, A. 1987. Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783-791.
Chao, A., W.-H. Hwang, Y.-C. Chen, and C.-Y. Kuo. 2000. Estimating the number of shared species in two communities. Statistica Sinica 10:227-246.
Colwell, R. K. 2013. EstimateS: Statistical estimation of species richness and shared species from samples. Version 9. User's Guide and application published at: http://purl.oclc.org/estimates.
Dillon, R. T., Jr. 2000.  The Ecology of Freshwater Molluscs.  Cambridge University Press.  509 pp.
Dornelas, M. & S. R. Connolly 2008. Multiple modes in a coral species abundance distribution.  Ecology Letters 11: 1008-1016.
Fisher, R. A., A. S. Corbet, and C. B. Williams 1943. The relation between the number of individuals and the number of species in a random sample of an animal population.  Journal of Animal Ecology 12: 42-58.
Gaston, K. J. 1994.  Rarity.  Chapman & Hall, London.  205 pp.
Gotelli, N. J. & R. K. Colwell. 2001.  Quantifying biodiversity: Procedures and pitfalls in the measurement and comparison of species richness. Ecology Letters 4 , 379-391.
Gotelli, N. J. and R. K. Colwell. 2011.  Estimating species richness. Pages 39-54 in A. E. Magurran and B. J. McGill, editors. Frontiers in Measuring Biodiversity.  Oxford University Press, New York.
Holdridge, L. R., W. C. Grenke, W. H. Hatheway, T. Liang & J. A. Tosi 1971.  Forest Environments in Tropical Life Zones.  Pergamon Press, Oxford.
Johnson, Bogan, Brown, Burkhead, Cordeiro, Garner, Hartfield, Lepitzki, Mackie, Pip, Tarpley, Tiemann, Whelan & Strong 2013.  Conservation status of freshwater gastropods of Canada and the United States.  Fisheries 38: 247- 282.
Jokinen, E. H. 1992.  The Freshwater Snails (Mollusca: Gastropoda) of New York State.  Albany: New York State Museum.  112 pp.
May, R. M. 1975.  Patterns of species abundance and diversity.  Pp 81 – 120 In Ecology and Evolution of Communities (M. L. Cody & J. M. Diamond, eds.)  Belknap, Cambridge, MA.
May, R. M. 1986.  The search for patterns in the balance of nature: Advances and retreats.  Ecology 67: 1115-26.
Munton, P.  1987.  Concepts of threat to the survival of species used in Red Data books and similar compilations.  Pp 72- 95 In The Road to Extinction (R. Fitter & M. Fitter, eds.)  IUCN/UNEP.  Gland, Switzerland
Magurran, A. E. & P. A. Henderson 2003.  Explaining the excess of rare species in natural species abundance distributions.  Nature 422: 714-716.
Murray,  B. R., B. L. Rice, D. A. Keith, P. J. Myerscough, J. Howell, A. G. Floyd, K. Mills & M. Westoby 1999.  Species in the tail of rank-abundance curves.  Ecology 80: 1806-1816.
O’Hara, R. B. 2005.  Species richness estimators: How many species can dance on the head of a pin.  Journal of Animal Ecology 74: 375-386.
Preston, F. W. 1948.  The commonness, and rarity, of species.  Ecology 29: 254-283.
Rabinowitz, D. 1981.  Seven forms of rarity.  Pp 205 – 217 in The Biological Aspects of Rare Plant Conservation (H. Synge, ed.)  Wiley, NY.
Sanders, H. L. 1968. Marine benthic diversity: A comparative study.  American Naturalist 102: 243-282.
Smith, E.P. & van Belle, G. 1984. Nonparametric estimation of species richness. Biometrics 40, 119-129.
Sugihara, G.  1980.  Minimal community structure: An explanation of species abundance patterns.  American Naturalist 116: 770-787.
Sugihara, G.  1989.  How do species divide resources?  American Naturalist 133: 458-463.
Thompson, F. G. 1999.  An identification manual for the freshwater snails of Florida.  Walkerana 10 (23): 1 – 96.
Walther, B. A. & J. L. Moore 2005.  The concepts of bias, precision and accuracy, and their use in testing the performance of species richness estimators, with a literature review of estimator performance.  Ecography 28: 815-829.