research letter: Species richness, habitable volume, and species densities in freshwater, the sea, and on land

Approximately 0.5–2.0 million eukaryotic species inhabit the seas, whereas 2.0–10.0 million inhabit freshwater or the land. Much has been made of this several-fold difference in species richness but there is little consensus about the causes. Here, I ask a related question: what is the relative density of species in marine and non-marine realms? I use recent estimates of global eukaryotic species richness and published estimates of the areal coverage and depth of habitat for freshwater, marine, and terrestrial biomes. I find that the marine realm harbors ~99.83% of the habitable volume on this planet. Eukaryotic species density of the marine realm is ~3600-fold (i.e., 3-4 orders of magnitude) less than that of non-marine environments. Species–volume relationships (SVRs) help reconcile actinopterygian fish diversity with global primary productivity and emphasize the interacting roles of abiotic and biotic complexity in shaping patterns of biodiversity in freshwater, the sea, and on land. Comparing SVRs of habitats within and across realms may help resolve the factors and interactions that influence species density.


Introduction
Understanding the diversity and distribution of life on Earth has challenged biologists for centuries (e.g., Linnaeus 1758, Wallace 1880). Among the many intriguing questions is: why is species richness so much lower in the sea than on the land (e.g., Hutchinson 1959)? The ocean is more vast than the land, there are more phyla in the sea than on land, and all the phyla but one (Onychophora) have existed far longer as marine than as terrestrial taxa (May 1994). So why are there now only ~0.5-2.0 million eukaryotic species in the sea, yet ~2.0-10 million eukaryotic species on land or in freshwater (Table 1)?
My intent in this paper is not to try to answer this difficult question, nor to sort among the answers that already have been offered. At least, not directly. Rather, I wish to address a related question which common sense suggests to me is important, needs a more transparent and nuanced approach, and is of immediate interest to biogeographers but largely overlooked: what is the relative density of species in marine and nonmarine (i.e. freshwater and/or terrestrial) realms? To rephrase the question in terms of a more familiar concept: what is the relative species richness per unit of habitable volume in marine and nonmarine realms?
By most estimates, there are approximately six times as many species in freshwater and on land than there are in the sea (Table 1). The magnitude of the inequality is emphasized by noting that marine habitats constitute ~71% of the Earth's surface area (e.g., May 1994). Averaged per unit area, eukaryotic species richness is approximately 14 times higher in freshwater and on land than it is in the sea. Beyond any debate surrounding estimates of species richness, this is not a contentious ratio (e.g., see May 1994, Vermeij and Grosberg 2010, Carrete Vega and Wiens 2012. In contrast, estimates of species density vary at least 30-fold, irrespective of the number of species, because published estimates of the relative habitable volume of the marine realm range from ~10 to 300 times the habitable volume of the land Grosberg 2010, Helfman et al. 2009:329, and cited by Carrete Vega and Wiens 2012). Differences in relative species density, incorporating uncertainty in estimates of habitable volume and species richness, may vary ~100-fold or more between marine and non-marine realms.
The substantial uncertainty in estimates of  Pimm and Raven (2000) also estimate ~15% of species are marine. Table 1. Some recent estimates of freshwater, marine, and terrestrial species richness. The percentage of species that are marine is calculated from the numbers provided in the cases that estimates are given in 2 or more columns. The percentage of species that are marine was given in the original publication in the cases that an estimate of species richness is provided in only one column.

Methods
To estimate habitable volume, I surveyed the published literature for estimates of areal coverage of biomes and the depth (height) of the habitable environment therein. Although some remotely sensed data relevant to this question are available, key datasets cover only subsets of habitat types or are in early stages of development (e.g. Lefsky 2010;Los et al. 2012). Rather than take an hybrid approach, I chose instead to use published information alone, so that this paper presents an estimate independent of remotely sensed data. The current estimate may in some years from now be corroborated, modified, or refuted by an estimate using remotely sensed data, but as the latter is unlikely to be perfect (Pfeifer et al. 2012), the difference between the two may itself be useful in suggesting the range of possible estimates. More importantly, notwithstanding some error in source estimates of areas and depths (e.g. that due to topographic complexity), the approach taken here is more explicit and detailed than for previously published estimates (Helfman et al. 2009:329, Vermeij andGrosberg 2010, and cited by Carrete Vega and Wiens 2012) so that the basis of future agreement, disagreement, or reanalysis can be clear. I excluded the aerial and endolithic realms because of paucity of information and taxonomic focus. The aerial realm is in general poorly sampled but has no known aerial endemics; the multigenerational inhabitants are primarily microbes (Womack et al. 2010; see also Wilkinson et al. 2012) which perhaps may be conceived as highly heterogeneous 'ghost populations' (sensu Slatkin 2005) of a coupled terrestrial-atmosphericaquatic biogeography. The endolithic realm is inhabited principally by archaea and eubacteria and the extent of subsurface and deep-biosphere habitats is unclear.
The principal sources for estimates of areas are provided in Table 2. Four additional considerations explaining estimates of depth are described in the following paragraphs.
(1) Large-scale geographic variation in habitat depth was incorporated in calculations of habitat volume by recognizing 12 categories of terrestrial habitat closely allied to recognized biomes that are, in part, characterized by reference to their dominant flora (Rosswall and Heal 1975, Campbell et al. 1994:669-676, Purves et al. 1998:1204-1216. (2) The dominant flora in any habitat generally forms a canopy above which few plants protrude far and in which there are occasional gaps (Whitmore 1990:24-28). Thus, the height of the dominant flora was used to approximate canopy height, and the canopy height was used as the proxy for habitat depth, despite the occurrence of fauna above the canopy and flora and fauna below the ground (e.g. Whitmore 1990:61-62, Risser et al. 1981:203). The justification for this is fivefold: i. There are no known aerial holoplankton. All aerial organisms inevitably must land because all, even those that can feed while airborne (e.g. bats, swallows, and robber flies [Allen 1967:135]), are tied to a terrestrial existence by some part of their life-history or by physics. This is true even of microbes (Womack et al. 2010), of which the vast majority of forms found in the air are better described as (sometimes inter-generational) meroplankton.
ii. Tall vertebrates that inhabit short grasslands do not meaningfully exist above the canopy because their nutrition is dependent on the canopy. Moreover, these large animals generally are sufficiently rare that they do not increase by much the habitable volume that is available to their many parasites which, anyway, often have life-stages that are dependent directly upon the vegetation (e.g. Spedding 1971:74). Smaller vertebrates, such as rodents and reptiles, often exist entirely within the canopy (Risser et al. 1981:222).
iii. The fraction of the biota that occurs below ground generally is limited to very shallow sub-Michael N Dawson surface layers which therefore do not contribute significantly to habitat depth. Analysis of over 200 datasets from field sites distributed globally and covering all major biomes indicates ~50% of roots are ≤ 0.1 m deep, and ~85% of roots are < 0.5 m deep (Zeng 2001). The below-ground invertebrate fauna may be diverse and abundant, but similarly is restricted primarily to the shallowest 1-2 decimeters (e.g. Risser et al. 1981:203). iv. The results of this analysis are reasonably insensitive to modest error in the assumptions. Altering the depth of every terrestrial habitat by 1 m would change the total terrestrial habitable volume by 7.3% and change the terrestrial contribution to global habitable volume by ~0.01%. v. The habitable volume of marine sediments also was ignored, in part because this generally is a poorly known marine habitat and, in part, because this counterbalances to some extent the exclusion of terrestrial, below-ground, habitable volume. The analyses are reasonably insensitive to this assumption too; altering the mean depth of the ocean by one to two meters changes the marine habitable volume ≤0.05%.
(4) Inevitably, boundaries between the habitats recognized here are somewhat arbitrary. For example, mixed-grass prairie is the intergradation of true prairie and shortgrass prairie (Risser et al. 1981:14). Similarly, birch-forest tundra (Berg et al. 1975) arguably is equivalent to the Alpine treelimit forest of Koike and Hotta (1996). Resolving these ambiguities is not in the jurisdiction of this analysis. However, these boundaries generally constitute relatively thin transition zones (e.g. Whitmore 1990:15) and, hence, are unlikely to affect significantly these calculations of habitable volume.
Finally, I note that the numbers of species and the areas of habitats change with time (e.g.

Results
The estimated total habitable volume available to freshwater organisms is 272,605 km 3 . The total habitable volume available to terrestrial organisms is about 2,025,315 km 3 . The total habitable volume available to marine organisms is approximately 1,367,000,000 km 3 (Table 2).

Species density
The marine environment provides approximately 99.83% of the habitable volume on this planet. The terrestrial and freshwater environments together provide the remaining ~0.17% of the habitable volume: ~0.15% terrestrial plus ~0.02% freshwater. This estimate of the terrestrial habitable volume is close to the lower bound (0.33%; Helfman et al. 2009:329) of previously published estimates (see Carrete Vega and Wiens 2012). Thus, eukaryotic species density averaged across the marine realm is, using a ratio of 1 marine to 6 non -marine species (Table 1) in 595 times more habitable marine volume (Table 2), approximately 3600 -fold less than the eukaryotic species density of terrestrial and aquatic environments. Given some uncertainty in estimates of species richness and of habitable volume, it seems reasonable to conclude that species density in marine environments is three to four orders of magnitude less than the species density in non-marine environments.

Causes of species density are multi-faceted
Many explanations have been proposed for the differences in species richness of freshwater, land, and sea. For example, the marine realm may be less diverse because it has lower net primary productivity, smaller primary producers (which do not provide cover, and are predated rather than browsed or grazed), less-complex habitats, fewer coevolutionary radiations (particularly no equivalent of angiosperms and insects), slower rates of evolution, larger population sizes, and lesseffective barriers to dispersal, as well as species with less ecological specialization and larger geographical range sizes (Day 1963, Smetacek and Pollehne 1986, Palumbi, 1992, Angel 1993, May 1994, Benton 2001, Carr et al. 2003, Jablonski and Roy 2003, Vermeij and Grosberg 2010, Costello et al. 2011, Webb et al. 2011, Carrete Vega and Wiens 2012; see also Hamner 1995). However, little resolution has been achieved, in part because this is a challenging problem, the appropriate comparative framework is still developing, and there may be no single answer.
The species richness of marine and terrestrial environments often has been contextualized using area (e.g., Angel 1993, May 1994, Carrete Vega and Wiens 2012) reflecting the descriptive power of terrestrial species-area relationships (SARs; MacArthur and Wilson 1967, Triantis et al. 2012). SARs also may describe patterns in marine biodiversity (e.g., Schopf et al. 1977, Dawson and Hamner 2005, Sandin et al. 2008, Dawson 2009). However, simple binary comparison of marine and terrestrial systems inverts the SAR (May 1994) suggesting that area is a reasonable proxy for the mechanisms that cause diversity differences between locations within the terrestrial realm, whereas the approximation breaks down when also considering the sea (and vice versa). The same may be true of comparisons between an island and a smaller area of mainland, or between an ocean gyre and a smaller area of the sea-floor. Deviations from the SAR, like variations on the SAR itself, must indicate something about variation in the underlying processes (Triantis et al. 2012).
Mechanistic explanations for differences in freshwater, marine, and terrestrial diversity therefore should be sought within a diverse and integrated framework. Such a framework should include, at least, functions of species adaptations and between-species interactions, which are the purview of niche theory, and their rates of dispersal, speciation, and extinction, which are in the realm of island biogeography theory (Hortal et al. 2009). The dimensions of the environment also may be important. For example, the similar spe-   Purves et al. (1998Purves et al. ( :1117Purves et al. ( , 1207Purves et al. ( -1216; b additional sources, Campbell et al. (1994:670-676), Whitmore (1990:10-36), Raven and Johnson (1992:518-528). c estimated as intermediate between midgrass and treelets. d Aquatic environments occupy approximately 0.02% of the volume occupied by marine environments (Garrison, 1996(Garrison, :4-6, 2010; freshwater as a percentage of marine volume estimated by Gleick (1996) 2 is ~0.01%. e Angel (1993), Garrison (1996Garrison ( :4-6, 2010 gives ocean volume as 1,370 million km 3 . Surface area of Earth = 5.086x10 8 km 2 , areas of marine environments from Garrison (1996Garrison ( :6, 91-121, 2010 cies richness of freshwater and marine actinopterygians (Table 1) has been used to discount primary productivity, which is two orders of magnitude lower in freshwater than in the sea, as an explanation for why there are relatively so few fish in the sea per unit area (Carrete Vega and Wiens 2012). Instead, Carrete Vega and Wiens (2012) favored greater dispersal distances of marine taxa and less physical structure in the seas as providing fewer opportunities for speciation, a long-standing hypothesis (e.g., Palumbi 1992Palumbi , 1994, although dispersal distances show considerable overlap for freshwater, marine and terrestrial taxa (Kinlan andGaines 2003, Dawson andHamner 2008). A more nuanced perspective suggests that, in fact, differences in productivity may play a role. Primary productivity in freshwater systems (0.4 PgC/year, Amthor et al. 1998) subsidized by up to 20% (Lennon 2004, but see Bianchi 2011) of terrestrial productivity (54.5 PgC yr -1 , Nemani et al. 2003) is approximately one-fifth (i.e. 11.3 PgC yr -1 ) that of marine systems globally (56.4 PgC yr -1 , Field et al. 1998 [of which ~6-11 PgC yr -1 is coastal, see Falkowski et al. 1998]). Per unit of habitable volume, available primary productivity is ~1000-fold higher in freshwater than in the sea. Per unit of habitable volume, actinopterygian species density is, in fact, quite similar: ~5000-fold higher in freshwater than in the sea. Thus, differences in productivity-coupled with differences in environmental heterogeneity, habitat complexity, dispersal ability, energetics, rarity and numerous other factors sufficient to generate the remaining five-fold or more opportunities for speciation in freshwater-could explain gross modern differences in actinopterygian species richness between freshwater and the sea. While dispersal ability and the structure of the physical environment probably are relevant (Carrete Vega and Wiens 2012, and many others), the evidence suggests that productivity and other factors are important too (e.g. Vermeij and Grosberg 2010). For example, the costs of moving in different environments (Vermeij & Grosberg 2010) must interact with the distribution and density of resources with consequences for the extent and magnitude of the com-munity economy (e.g. Polis et al. 1997), its efficiency, and thus species density. Differences in species density within and among other freshwater, marine and terrestrial taxa also must have multiple causes, the strengths and interactions of which appear to differ from those affecting actinopterygian fish diversity. For example, the ratio of gastropod species richness in freshwater, the sea, and on land is ~4:30:30, close to the respective ratios for primary productivity 11:56:44 (including the aforementioned subsidy) and habitable areas ~1:70:29 (only ~0.1% of gastropods are pelagic, so this ratio also approximates differences in habitable volume for reproductive populations of gastropods). Another example, the high diversity of marine hydrozoans, with catalogued species richness for freshwater:marine:land of ~40:3500:0 (Table 1) could indicate a large effect of habitable volume (freshwater:marine:land = 1:5015:7) mitigated somewhat by primary productivity (11:56:44), but consideration of their biology suggests that functional constraints likely play an important role. Thus, approaches that explore geographical extent and ecological dimensions may improve statistical fits with patterns of, and increase knowledge about causes of, variation in species richness (e.g. Triantis et al. 2003), including deviations from simple correlation with area or evolutionary time (Rabosky et al. 2012; Table 3).
The question of what causes the observed differences in species density among realms is a coarse version of a more familiar complementary enquiry: what causes differences in species density among locations within (and across) marine and non-marine realms? Integrating these levels has many merits, for example, increasing the number and diversity of samples, enabling comparisons to be chosen to study particular properties, and increasing power to resolve factors and interactions that may affect species diversity (Polis et al. 1997). Whereas there are three recognized realms, there are 26 ecoregions (7 freshwater, 5 marine, 14 terrestrial), 238 major habitat types (53 freshwater, 43 marine, 142 terrestrial) 3 , and thousands of 'islands'-terrestrial, freshwater, and marine-to be compared. The paucity of pelagic marine gastropod species relative to benthic environments is a pattern that also characterizes annelids (Halanych et al. 2007), cnidarians (Daly et al. 2007), foraminifera 4 , microbes (Zinger et al. 2011), and many other marine taxa; it is a pattern paralleled in freshwater lakes (Vander Zanden et al. 2011) and which reaches an extreme when comparing air versus the ground (e.g. Womack et al. 2010, Wilkinson et al. 2012. What is it about benthic habitats, which are smaller than pelagic habitats, that raises or maintains diversity (or, conversely, what is it that inhibits or depletes pelagic diversity)? The open ocean is often likened to a desert, whereas coral reefs surrounded by the ocean are thought of as the rainforests of the sea 5 , although kelp forests are perhaps structurally more similar. By comparing marine and nonmarine organisms in environmentally similar settings, and quantifying environmentally dissimilar settings within and among realms (Dawson & Hamner 2008), we might hope to better understand differences in species density.

Improving and using species density estimates
Estimates of species richness and habitable volume of freshwater, marine, and terrestrial realms remain imprecise, but converging estimates of global species diversity (Table 1) and habitat volume (Helfman et al. 2009, this study) suggest estimates of absolute species densities have a maximum error of several-fold and estimates of relative species densities are accurate to within a few percentage points. While a complete inventory of species richness will take decades or centuries to complete (Bouchet 2006, Costello et al. 2011, Mora et al. 2011, improved estimates of habitable volume and physical complexity of terrestrial habitats are tantalizingly close (e.g., Lefsky 2010, Los et al. 2012. Data describing the densities of other attributes, such as the abundance, ecology, energetics, functional biology, and life-history of organisms may provide some of the most important information, but are in shortest supply (e.g. Jetz et al. 2012) and also are among the most difficult to collect.
It is important to recognize that many terrestrial SARs likely provide implicit support for species-volume relationships (SVRs) because terrestrial habitat depth is small relative to areas species density of freshwater, land, sea K ecoregions 28 * 10 6 2,022 * 10 6 1,800 * 10 6 1.14 K habitats 216 * 10 6 20,511 * 10 6 15,484 * 10 6 1.34 Species richness ~6-8.7 * 10 6 ~0.7-2.2 * 10 6 3.9-8.6 (mean 6.25) Species density (species.km -3 ) ~0.0005-0.0016 2,342-5,099 (mean 3,720) i.e. ~10 3 -10 4 ~2.61-3.79 Table 3. A summary of some biodiversity and physical characteristics of freshwater, marine, and terrestrial environments, and their comparison. Estimates of area and volume from Table 2. Estimates of species richness from Table  1. Number (#) of ecoregions and major habitats from WWF (see footnote 2). K = choros (see Triantis et al. 2003 (Scheiner et al. 2011) even though area is commonly acknowledged to be a proxy for habitat diversity and ecological or evolutionary processes (e.g., Hortal et al. 2009, Triantis et al. 2012; see also Panitsa 2012, but see Triantis et al. 2003). This is an oversight because segregation by depth of habitat is known to enhance diversity (e.g. Losos 2009:340; see also e.g. Brusca and Brusca 2003:506), which may be multiplied through species interactions (e.g., Castro andHuber 2003:268, Novotny et al. 2006). To the extent that habitat is engineered by some organisms, and used and modified by others, there seems to be no obvious evolutionary limit to species richness, or density (Vermeij and Grosberg 2010, see also Emerson andKolm 2005, Hortal et al. 2009). Important characteristics of environments and organisms do not sort by realm (Palumbi 1992, Dawson and Hamner 2008, Pawar et al. 2012, Webb 2012 nor necessarily by taxon (Webb et al. 2011) and vary from place to place (Dawson 2009, Vermeij andGrosberg 2010) and through time (Benton 2001, Vermeij and Grosberg 2010, Rabosky et al. 2012. Resolving the relative contributions of factors that do cause differences in species density within and among realms will require carefully designed comparisons (Dawson and Hamner 2008) that take a nuanced perspective of ecological and evolutionary interactions between abiotic and biotic components of ecosystems (Vermeij and Grosberg 2010).