ECOGRAPHY 25: 273–282, 2002
Size-dependent species-area relationships in benthos: is the world
more diverse for microbes?
Andrey I. Azovsky
Azovsky, A. I. 2002. Size-dependent species-area relationships in benthos: is the
world more diverse for microbes? – Ecography 25: 273– 282.
Using original and literature data on species richness, I compared the species-area
relations for 5 different size classes of the Arctic benthos: macrofauna sensu lato,
polychaetes, nematodes, ciliates and diatom algae. The data pool covered a wide
range of areas from single samples to the whole seas. Both the slopes and intercepts
of the curves depended significantly on the logarithm of the mean body size of the
group. The number of small species (ciliates and diatom algae) showed relatively
higher local diversity but increased more slowly with the area than the number of
larger ones. Thus, both a- and b-components of species diversity of the marine
benthos were size-dependent. As a consequence, the actual relations between number
of species and their physical size are spatially scale-dependent: there are many more
species of smaller size classes in any one local community, but at a global scope the
situation changes drastically. The possible reasons are discussed, including dispersal
efficiency, rates of speciation and size-dependent perception of environmental heterogeneity. Body size is suggested to be the important scaling factor in manifestation of
so-called ‘‘general ecological laws’’.
A. I. Azo6sky ([email protected]), Dept of Hydrobiology, Biological Faculty, Moscow State Uni6., Moscow 119899, Russia.
Interrelations between species diversity, distribution
ranges, and body size have been widely discussed since
Robert May’s provoking publications (May 1978, 1986,
1988). May stated that smaller organisms were usually
found to be more diverse than larger ones due to their
ability to subdivide environment more finely. Plotting
the recorded number of terrestrial species of different
physical size, he found a strong inverse power relation
down to a characteristic size ca 1 cm, but with fewer
species below (May 1978). He interpreted this fact as
arising mainly from insufficient study of the smallest
animals and supposed a huge number of new species
being undescribed yet in these size classes, e.g. nematodes, protozoans, microbes, etc. (May 1988). This
hypothesis was questioned by both ‘‘small-sized’’ and
‘‘large-sized’’ zoologists (while botanists mostly kept
silent).
Most published evidence was based on body size/species number distributions within certain taxonomical
groups such as birds, mammals or insects. These comprehensive (both global or regional) data sets have
usually shown unimodal relations, and smallest bodysize categories turn out to be never the most speciose
(May 1978, 1986, Dial and Marsluff 1988, Fenchel
1993, Brown 1995, Blackburn and Gaston 1996, Owens
et al. 1999). As an example, in extensive study of
grassland insects, Siemann et al. (1996) found strong
power-law relationship between number of species and
total number of individuals, with both values being
maximal at intermediate size classes.
The thesis on high potential of global diversity for
smallest organisms has also been critically reconsidered
recently by protozoologists (Fenchel 1993, Finlay et al.
1996a, b). They concluded that the real number of
known, extant species of free-living ciliates (the beststudied group of protozoa) is close only to 3000– 3500,
and any further significant augmentation (up to a hundred times as may be inferred from May’s extrapola-
Accepted 8 October 2001
Copyright © ECOGRAPHY 2002
ISSN 0906-7590
ECOGRAPHY 25:3 (2002)
273
tion) is unlikely. It contrasts drastically with macroinvertebrates whose global diversity in marine sediments
is evaluated from 500000 (May 1992, Gray 1994) to
several million species (Grassle and Maciolek 1992,
Poore and Wilson 1993).
On the other hand, the local diversity of ciliates is
amazingly high as compared with the global values
(Fenchel 1993, Finlay et al. 1996b, Fenchel et al.
1997, Finlay et al. 1999, Hillebrand et al. 2001). For
example, a 1 cm2 sample from Niva Bay sediments
reveals 33 –48 species and the total number recorded
for the 1 ha-area bay is as much as 146 species (ca 5%
of all free-living ciliates), so that ciliates exceed the
local macrofauna not only in relative but in absolute
diversity as well. Similarly, at the other intensively
studied site, Chernaya Bay of the White Sea, a 1 cm2
sample yields 35 –50 ciliate species, and the total number recorded so far for the locality (ca 0.5 ha) is
slightly over 120 species for ciliates while only 35 for
macrofauna (Azovsky 1989, 1992, Burkovsky 1992b,
Burkovsky et al. 1994). It is in good conformity with
figures reported by Fenchel.
Thus, ciliates and macrofauna show marked distinctions both in local and global diversity patterns. Freeliving ciliates are conventially recognized as cosmopolitan (Borror 1980, Burkovsky 1984). The explanation by Fenchel (1993) and Finlay et al. (1996a, b,
1999) is that ciliates are so small that every species can
essentially get everywhere, and so numerous that local
extinctions are rare. Considering continuous large-scale
dispersal of ciliates, Finlay et al. (1999) went so far to
declare that they ‘‘appear not to have biogeographies’’
(but see Foissner 1999).
However, some questions arise to this point: is microbial diversity moulded principally by the same rules
as biodiversity patterns in general, or is it a peculiar
phenomenon, and different groups of organisms are
governed by different rules, being limited by different
functional constraints? Or, paraphrasing Lawton
(1998: 5) asking ‘‘whether nematodes play the ciliate
game’’, I would like to ask what are the rules for
these games? Whether they are common for all players, or size-dependent, or their own? If the above
tendencies are general, the rate at which species are
accumulating with increments in area should be a
function of body size.
For marine benthos, few overall size-species number
distributions reported do show the inversion as spatial
scale increases, from right-skewed local (within-community) spectra to relatively flat and then to leftskewed global ones (Warwick 1984, Fenchel 1993,
Burkovsky et al. 1994). However, robust numerical
analyses of biodiversity trends are scarce because of
the difficulties in obtaining comparable data for different groups in a range of spatial scales (Lawton 1999).
Here I attempt to fill the gap by comparing the
species diversity of high-latitudinal (arctic and subarc274
tic) marine benthos across both body size and spatial
dimensions. Instead of arbitrary defined size classes, I
have considered the whole taxa which represent such
avowed and long established groups as microphyto-,
microzoo-, meio- and macrobenthos (Burkovsky et al.
1994). The changes in diversity of these groups were
studied at a range of scales from sample to the ocean
using species-area curves.
Material and methods
Data sources
I have considered the species richness of soft-bottom
benthos from the Polar Ocean and some adjoining
regions of the North Atlantic (the North, Norwegian,
and Irish Seas). The following taxa were chosen to
compare: microphytobenthos: diatom algae (Bacillariophyta);
microzoobenthos:
free-living
ciliates;
meiobenthos: nematodes. The macrobenthos was considered entirely (in sensu lato) as combined group of
invertebrate taxa. Besides, the polychaetes were considered in particular. All these taxa commonly dominate in their respective size classes.
The data pool was compiled using information from
many published sources as well as some unpublished
data (both original and provided by colleagues). I
tried to select the data with regard to its methodical
compatibility, whenever possible; and preference was
made to reviews or summarizing synopses.
In all, 68 datasets from 37 sources were used for
macrobenthos, 45 datasets (24 sources) – for polychaetes, 26 datasets (15 sources) – for nematodes, 23
datasets (14 sources) – for ciliates, and 32 datasets (24
sources) – for diatoms. The sources included data on
the full range of depths from intertidal zone to shallow and deep-sea habitats. Among them, the most
data were from the White Sea (35% sets), the North
Sea (24%) and from the Barents and Kara Seas (21%);
and the remainder was from other regions or from the
wider areas including the above-mentioned regions.
The data on the core region (the White, Barents and
Kara Seas) were obtained largely from long-term studies of soft-bottom communities carried out by joined
research team from Moscow State Univ. and P. P.
Shirshov Inst. of Oceanology (see Acknowledgements).
Pooled together, the data represented series of
nested or overlapped sampling areas covering a wide
range of scales: from several cm2 or dm2 (single samples) to thousands of km2 (regional surveys or synopses for whole seas). Areas, unless reported, were
roughly estimated as area of the regions surveyed or
polygons covered by the samples. The full list of the
sources used, with references, can be obtained from
the author.
ECOGRAPHY 25:3 (2002)
3
D = 2
3V/4p,
Statistical analysis
Species-area cur6es
Theoretical grounds for the form of species-area relationship such as hypothetical mechanisms or underlying
abundance distributions are beyond the scope of our
study (see Connor and McCoy 1979, Sugihara 1981,
Williamson 1988, Hart and Horwitz 1991 for
discussions).
I used here the well-known Arrenhius power function
merely as descriptive model for species accumulation
patterns:
S =cAz,
(1a)
where V is individual body volume (Schwinghamer
1981). Wet or ash-free dry weights were converted to
volumes using specific mass coefficients (Wieser 1960,
Salzwedel et al. 1985, Burkovsky 1992b). Average group
volumes were calculated as geometrical means of the
specific volumes. If only total abundance and biomass of
the group were reported, average individual weight was
calculated dividing biomass by abundance. As seen from
Table 1, individual species differ considerably in size, but
the average group values obtained from different sources
vary no more than 2 –3 times and hence could well be
used as their inherent size characteristics.
(1b)
Results
or, in log-transformed linear form,
log S=log c+z log A,
where A is area, S is total number of species found
there, c and z are regression coefficients. Leaving aside
the discussion about their biological meaning, note that
z (regression slope in (1b)) indicates the rate of species
number increasing with area, and c is a fitting coefficient (intercept in (1b)), or estimated number of species
per ‘‘unit’’ area. For each size group, I estimated c and
z values and their standard errors by linear regression
in form (1b). Since both number of species and area are
measured with error and thus should be treated as
random variables, the ordinary least squares regression
is inapplicable in the case. Therefore, I used reduced
major axis regression, which produces unbiased slope
estimates and permits comparing correctly the parameters for dimensionless (log-transformed) data (Legendre
and Legendre 1998).
Body size e6aluation
To compare the parameters of S-A curves we need size
characteristics of corresponding taxa. There are many
ways to characterize the individual size of organisms:
by mass (wet, dry or ash-free dry weight), volume or
length (Peters 1983). Here I used equivalent spherical
diameter D (in mm):
Consistency of averaging data analysis
Different spatial scales were unequally represented in
available data body. Since some of sets included data on
several (often many) separate samples or stations, the
greatest amount of observations evidently fell on the
smallest areas (up to several square metres). For example, there were ca 500 samples of ciliates from the White
Sea at the disposal, while only few data concerned the
faunas of the largest areas. Thus, the local, most variable
part of data might have the strongest influence on the
results. Such very unbalanced data design may become
a serious problem for regression analysis and is rather
unsuitable for graphical presentation. Substitution the
means for series of raw values could partly solve the
problem (Draper and Smith 1981, Shaw and MitchellOlds 1993). To check validity of the procedure, the
regression analysis for macrobenthos and ciliates was
preliminary performed for both raw and averaged data.
In the latter case, only the mean numbers of species per
sample or station were used for each data set. The results
turned to be consistently similar (Table 2). Neither
slopes nor intercepts estimated from full-length and
averaged data differed significantly. Therefore, only the
averaged data were used hereafter.
Table 1. Equivalent spherical diameter D (mm) for individual species and species assemblages (data compiled from different
sources).
Group
Total macrofauna
Polychaetes
Nematodes
Ciliates
Diatoms
ECOGRAPHY 25:3 (2002)
Range (min-max) for individual
D values
1.24–58.1
1.24–26.7
0.027–2.120
0.0073–0.124
0.0058–0.120
Average D values for the species
assemblages
Range
Mean
3.37–10.5
2.84–4.80
0.08–0.21
0.034–0.091
0.0124–0.0457
8.31
3.37
0.156
0.0486
0.0179
Number of sources
15
12
10
8
7
275
Table 2. Comparison of regressions made on the full data (left) and after averaging the data within the series of samples (right).
R2 is squared correlation coefficient.
Group
Macrofauna
Ciliates
Full-length data
Number of
cases
Slope, z
Intercept,
log c
R
Number of
cases
Slope
Intercept
R2
398
268
0.161 90.012
0.082 90.004
0.892 9 0.098
1.620 9 0.013
0.705
0.768
68
23
0.152 90.009
0.077 90.006
1.079 90.070
1.666 90.037
0.805
0.878
Comparison of species-area curves
The data on all five size groups studied were fitted
well by the log-linear model, although the parameters
estimated varied between the groups (Table 3, Fig.
1a). The smaller organisms, such as ciliates or diatom
algae, do show weaker and less steep increase of species richness with area than the larger ones. The
larger the organisms are, the faster their diversity increases with the area.
To move the curves apart and make them easily
comparable, I expressed the relative species numbers
as a percentage of the global species pools. Although
the accurate evaluation of global species richness of
any large taxonomic group is rather difficult to date
(May 1988, 1994, Wilson 1992), nevertheless some approximate estimates sufficient for this purpose could
be made. So the present recorded total number of
marine benthic diatoms could be roughly considered
as 2200 species (John 1994, Norton et al. 1996),
marine ciliates – 2500 (the mean of recently reported
3500 (Fenchel 1993) and 1500 bona fide species (Finlay 1998)), nematodes – 4000 (Platt and Warwick
1988), polychaetes – 7500 (Jirkov 1989, van der Land
pers. comm.). As for the macrofauna, the gross total
is a matter of keen debates. I suggest the figures
given by Grassle and Maciolek (1992) and Poore and
Wilson (1993) to be too overestimated, and use here
the total of 160000 species described so far (May
1992, 1994) as more conservative reference point. It
must be noted that no importance should be attached
to the exact values. I used them here as a rough scale
only to make the graphs easily comparable by their
slopes, which did not change after such re-scaling
(Fig. 1b).
Both the curve slopes and intercepts estimated by
log-linear regression depended strongly and regularly
on the average body size. These relationships held
true for all the taxa (Fig. 2).
One more interesting result follows from this analysis. Theoretically, if both parameters of species-area
curve do depend log-linearly on body size, all the
curves should meet at one and the same point (see
Appendix 1). So, there is an area which contains similar number of species of every group, from diatoms
to macrofauna. Coordinates of the intersection point
are ca 107 m2 and 210 species, regardless of organ276
Averaging data
2
isms’ size. Of course, this result should only be
treated as statistical tendency rather than the exact
rule. It is rather possible to talk about some area of
‘‘diversity convergence’’, where the curves come close
together (Fig. 1a). Taking the regression errors into
account, this area could be estimated as ranging from
106 to 108 m2 and containing from 140 to 320 species.
Thus, the weaker statement is more pertinent: any
typical region of arctic sea-floor of several km2 is
commonly inhabited by approximately similar number
of species for every size class. The smaller areas contain, on average, more species of small taxa than of
large ones. For example, for a 1 m2 plot the regressions predict 50 –95 diatom species, 35 –62 ciliates,
15– 36 nematodes but only 7 –27 species of macrofauna, including 4 –15 polychaetes. The opposite is
true to the larger areas (hundreds and thousands of
km2).
Discussion
My results confirm the idea that small organisms
have relatively higher local but lower global diversity
than do larger ones. In the series of their remarkable
studies, Fenchel, Finlay and their colleagues obtained
recently the similar results comparing diversity patterns of free-living ciliates and macroorganisms (see
references in the Introduction). In particular, Finlay
(1998) presented the species-area curve for ciliates and
reported the z value of 0.043, which is not far from
our estimates. They discussed it mainly in the context
of the specific features of ‘‘microbes’’. However, I
found these tendencies to be confirmed throughout all
considered spectrum of sizes. Hillebrand et al. (2001)
also found recently that unicellular organisms (diatoms, desmids and ciliates) showed higher local richness but weaker and less steep increase of the richness
with increasing sample size (area or number of individuals) than compared to metazoans. The similar results were obtained for plankton (McGowan 1971,
Allen et al. 1999). Hence it should be treated as a
general rule (at least for benthic species), rather than
the peculiarity of any particular taxa.
Before discussing the results, however, it is necessary first to discuss how flexible they would be in
methodical respect.
ECOGRAPHY 25:3 (2002)
Reliability of the results: methodological aspects
One possible criticism is that the areas observed here
have not actually been completely investigated, so we
do not in fact have data for the full species richness.
There are a number of methodological factors which
could hereafter influence the diversity estimations presented here and thus change the results.
A) Factors which may increase mainly the local
diversity: underestimation of rare or hidden species.
Long-term local persistence of many forms in a rare or
inactive, encysted cryptic state is the common microbial
property (Finlay et al. 1996b, Fenchel et al. 1997).
Careful examination using scanning electron microscopy doubled the local diatom flora of previously
studied small sandy beach of the White Sea, mostly due
to the very small ( B20 mm) forms; while only ca 10%
of them turn to be new for the White Sea and only one
or two species are perhaps new for science (Sapozhnikov pers. comm.). This ‘‘cryptic’’ diversity not only
causes the underestimation of real richness, but would
also reduce the chances of speciation and local extinction of microbial species (Finlay et al. 1999). Proper
data correction for the ‘‘cryptic’’ diversity should lead
to flattering S/A curves (lower z values). Be the problem as it seems, it looks to be less dramatic for macrobenthos. Hence, the difference between slopes is
expected to become even more significant.
B) Factors which may increase mainly the global
diversity. Primarily, it may happen due to discovering
many new, locally distributed species in poorly explored
habitats. It should result in steeper S/A curves (higher z
values). This problem is debated mainly in regard to
deep-sea habitats (Grassle and Maciolek 1992, Rex et
al. 1993). However, most of new deep-sea findings
concern the macro- and meiofauna. Ciliates sampled so
far from the abyssal floor are not evidently different
from the shallower fauna (Barnett 1981). As to the
diatoms, any increasing of diversity of these autotrophs
in deep aphotic zone is unlikely. Any potential wealth
of unicellular endemics in other habitats is also questioned (Finlay 1998, Norton et al. 1996). Thus, these
factors should also increase the difference in slopes
between small- and large-bodied taxa.
C) Finally, some factors could have similar effects at
any scale. So, new methods of sampling (e.g., using
smaller-sized mesh sieves or more effective separation
procedures) may yield a noticeable portion of new
species. Being brought into common use, such perfection should proportionally enrich both local and global
diversity estimations and hence should not significantly
modify previously obtained S/A curves. The same is
true to the exercises of taxonomists-‘‘splitters’’ as well
(see also Hillebrand et al. 2001).
It is hard to say how all these factors brought
together can affect the S/A curves. However, if the
above reasoning is correct, the general pattern would be
expected to become just more contrasting.
The biological reasons: is size-dependence caused
by scale-dependence?
Now let us turn to biological interpretation of the
statistical findings. The two empirical relations (Fig. 2a,
b) present two issues to dispute, namely, the size-dependencies of the intercepts (as indicators of local, or
alpha-diversity) and slopes (as measure of beta-diversity). The explanation advanced by Fenchel (and with
which I mainly agree) is the following: ‘‘ … smaller
organisms tend to have wider or even cosmopolitan
distribution, a higher efficiency of dispersal, a lower
rate of allopatric speciation and lower rates of local and
global extinction than do larger organisms’’ (Fenchel
1993: 375). He argues that the higher population density of smaller species is the main factor responsible for
this pattern.
Not ruling it out, I would accentuate here the potential role of spatial scaling. Many hypotheses involve
environmental heterogeneity as the key factor affecting
species diversity (Hart and Horwitz 1991, Douglas and
Lake 1994). As Williamson (1988) and Williamson and
Lawton (1991) argue, species-area plots may be related
to the form of the environmental variability spectra.
Hence, to understand fully the species diversity patterns
we should consider properly how the species measure
their habitat diversity. Higher local diversity of small
organisms could be readily explained by their finegrained perception of the environmental heterogeneity.
Indeed, the spatial scales of distribution patterns of
benthos have been recently found to correlate with
organisms’ body size (Burkovsky et al. 1994, Azovsky
2000, Azovsky et al. 2000).
Table 3. Parameters of log-linear species-area regression for benthos (numbers of cases (datasets) are given at Material and
methods).
Group
Slope, z
Intercept, log c
Diatoms
Ciliates
Nematodes
Polychaetes
All macrofauna
0.0669 0.005
0.0779 0.006
0.1079 0.005
0.115 9 0.013
0.152 9 0.009
1.833 90.035
1.666 9 0.037
1.309 9 0.034
0.845 9 0.105
1.079 9 0.070
ECOGRAPHY 25:3 (2002)
Squared correlation, R2
0.851
0.878
0.949
0.678
0.805
277
Fig. 1. Species-area curves for
Arctic benthos. A) absolute
diversity scale (species
numbers); B) relative scale
(% of total species richness
for the group).
Levandowsky and Corliss (1977) pointed out that
unicellularity limits the potential of specializations that
protists can exhibit, hence the number of species. However, it does not actually look so. Many free-living
ciliates demonstrate rather fine trophic specialization
excelling taxonomists in the knack of microbial species
distinction (Fenchel 1968, Burkovsky 1984). They also
could segregate their spatial niches at scale of meters or
centimeters (Azovsky 1989, Burkovsky 1992a). Diatoms
still further subdivide habitats, preferably occupying
certain loci of sand grains (Miller et al. 1987, Sapozhnikov pers. comm.). So, small-bodied species do not
subdivide the ecospace more coarsely than larger organisms do, but they do it at much finer scale (Azovsky
2000). According to the hypothesis of Hutchinson and
278
MacArthur (1959), most organisms perceive the world
as a two-dimensional mosaic, with a structure which
scales with the typical physical dimension, d, of the
organism. May (1978, 1986) used this assumption to
estimate relative global diversity of different size
classes. The direct extrapolation, without considering
the obvious differences in slopes, z, leads him to the
doubtful forecast of larger overall richness of the
smaller organisms. Here, I imply this scaling reasoning
to the local instead of global diversity estimates, using
intercept value as a-diversity measure (Rosenzweig
1995).
Let us assume that actual ‘‘ecological’’ space is scaled
inversely as d − 2. Combining it with size-dependence of
slope values, z, we do obtain roughly log-linear relation
ECOGRAPHY 25:3 (2002)
between intercept value (a-diversity measure) and
−0.25 power of physical size of organisms (Appendix
2), that is quite close to empirically estimated value of
−0.27 (Fig. 2b). Notice that species-size histograms
presented by Fenchel (1993) for different aquatic communities (his Fig. 2) also have a roughly d − 0.25 decrease. Thus, size-dependent scaling of area per se can
explain the local but not the global diversity patterns.
If, however, small areas provide more potential
niches for small organisms, then what limits their global
diversity? Does nature present so few kinds of niches
for these creatures with so fine niche-partition capabilities (Levandowsky and Corliss 1977)? Fenchel (1993)
attributed it to the low rates of allopatric speciation by
high population density and therefore small distance
and area effects (in terms of the theory of island
biogeography). The low allopatric speciation (and thus
relatively high simpatric speciation) should lead to
rather common co-occurrence of taxonomically related
(e.g. congeneric) species. Indeed, this effect is observed
for ciliates at regional and habitat level but neither at
local nor global (biogeographic) scale (Azovsky 1992,
1996).
The statement about high density of ‘‘microbes’’,
however, is not so obvious. The rare species of ciliates
are not less rare than ones of bivalves. Moreover, the
‘‘actual’’ value of the physical space may differ for
Fig. 2. The relation between parameters of species-area curves
and mean body size (D, mm) for different groups of benthos.
A) curve slopes (z); B) intercerpts (log c). Squared linear
correlations (R2) are shown on the graphs.
ECOGRAPHY 25:3 (2002)
various organisms: a room is more narrow for an
elephant than for a hundred mice. After rescaling, the
relative density (measured as average number of individuals per ‘‘mean body volume’’ unit of the available
space) occurs to be much lower for micro- than for
macroorganisms (Burkovsky et al. 1994).
Another possible explanation of low b-diversity for
small organisms implies finite quantity of potential
niches which is limited by the range of large-scale
heterogeneity on the Earth. In this case, the essence of
the problem may be a potential exhaustibility of habitat
diversity. In other words, if, as Fenchel (1993) states,
the environment appears equally complex to a monkey
in a forest or to a tardigrade in a moss cushion, than
should the forest be more complex to tardigrade, or is
it merely more spacious? I suppose my results underpin
the latter case, at least for marine benthos. Smaller
organisms, being more ubiquitous, perceive the world
as more fine but more repetitive mosaic of habitats.
Thus, the set of microhabitats, or niches, turns to be
principally similar for ciliates both at interstitial in
Denmark and in an Australian crater-lake (Finlay et al.
1999). In mathematical terms, the spatial spectra of
environmental heterogeneity (and hence the species diversity spectra) may be less reddened for smaller organisms (see Williamson and Lawton 1991, Shneider 1994).
Formally, one more explanation could be put forward appealing to the fractal geometry. Fractal properties of a landscape could significantly influence the form
of species-area curve (Williamson and Lawton 1991,
Milne 1997). To generate the above-described relationship we could suppose the environment as multifractal
mosaic of habitats (what is very likely) but with variable fractal dimension dependent on the organism’ size.
This exotic hypothesis seems theoretically suggestive,
but I seriously doubt its biological grounds.
Phylogenetic reasons (e.g., evolutionary age per se)
could also be of some importance (Tchesunov 1981).
Notice that among the groups considered here, the
smallest-bodied ones are also the more ancient. The
largest forms as bivalves, gastropods, echinoids, are all
the modern-diversified (Benton 1997). One corollary is
that species turnover over geological time is lower for
small organisms (Nanney 1985). Taking into account
the reproduction rates, the relative temporal difference
(measured in generations) becomes still much more
impressive. It would be quite interesting to extend our
analysis to the other two common meiobenthic groups,
Foraminifera and Harpacticoidae. Formally both belong to meiofauna, but the first one is interposed between nematodes and polychaetes on the mean body
size axis, while the second – between ciliates and
nematodes. At the same time, foraminifers, being protozoa, are rather evolutionary ancient, while harpacticoids are relatively young. So, to test the hypothesis we
should compare the z values for these groups: whether
they are according to their body size or the age?
279
Conclusion
Many various mechanisms have been proposed to explain benthic diversity, operating at different spatial
and temporal scales (Rex et al. 1993, May 1994). Our
results suggest that these scales, in their turn, can be
allometrically rescaled by the same way for various
taxa. Recurring to the question asked in Introduction,
the rules of diversity game are specified by body size of
the players. It also may be an example of cross-scaling
regularity linking together the ‘‘micro’’ and ‘‘macroecological’’ laws (Lawton 1999, Azovsky 2000). The possible explanations include scale of perception of
environment, speciation/extinction rates, metabolic
trade-offs, and/or evolutionary age. However, the question of whether the spatial scaling or evolution is more
important seems to be too speculative. All these factors
are closely related and interlaced, and I believe that
further comprehensive consideration of the problem
should apparently incorporate them all together.
Acknowledgements – I thank I. V. Burkovsky, M. V. Chertoprood, N. V. Kucheruk, V. O. Mokievsky, and F. V. Sapozhnikov for providing me their unpublished data. I also thank V.
O. Mokievsky, H. Hillebrand and B. Finlay for stimulating
discussions, and O. V. Maximova for her linguistic help. This
work was supported by the Russian Fund for Basic Researches (grants Nos 00-04-49175 and 99-05-69369).
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Appendix 1. Consider two species-area curves
described by power function:
S1 = c1Az1,
(1a)
S2 = c2Az2,
(1b)
or, after double logarithmic transformation,
log S1 = log c1 + z1 log A;
log S2 = log c2 + z2 log A;
where S1, S2 are number of species for groups (size
classes) 1 and 2; A is area; z1, z2 are slopes, and c1, c2
are intercepts. At their meeting point,
S1 = S2 = S,
c1Az1 = c2Az2
so,
log A = (log c1 − log c2)/(z2 − z1).
(2)
Assuming the log-linear size-dependence of both slope
and intercept values in accordance with Fig. 2, we get
for the group with body size d1:
log c1 = co + c log d1,
z1 = zo + z log d1
(3a)
and similarly for the second group with body size d2:
log c2 = co + c log d2,
z2 = zo + z log d2.
(3b)
Substituting (3a, b) into (2), we get an area at the
intersection point:
A= antilog( −c/z),
(4a)
and, from (1a) or (1b), an expected number of species
at the point:
S =antilog(c0 − cz0/z).
(4b)
Position of intersection point is independent from body
size, hence all the curves, which satisfy the conditions
(3a, b), meet at the same point with coordinates given
by (4a, b).
281
Appendix 2. Assume that organisms ‘‘measure’’ the
environment in units proportional to their individual
body size, d, so that the ‘‘ecological area’’ of a plot with
‘‘geometrical’’ area A is A/d2. Then, the conventional
species-area relation (1) may be re-written in the form:
we get the following expression for intercept:
log c − 2z0 log d −2k(log d)2.
(5)
Substituting the above obtained estimates for zo and k
in (5), we get:
S=c(A/d2)z,
intercept= log c−0.25 log d − 0.066(log d)2.
or, after logarithmic transformation,
log S=(log c −2z log d)+z log A,
where the term in brackets is intercept. Supposing the
slope is log-linearly depended on body size:
z=z0 +k log d,
282
Neglecting the relatively small quadratic term, we
finally obtain that intercepts of the species-area curves
should approximately linearly decrease as 1/4 of log
(body size). Note that eq. (5) predicts also the decrease
of local diversity for smallest organisms (below 10 mm,
e.g. prokaryotes, flagellates, etc.).
ECOGRAPHY 25:3 (2002)