Scaling laws describe functional relationships between quantities (...
These numbers are very difficult to quantify and could be off by an...
This is the basic equation of power laws.
Key finding of paper: "The most unifying relationship that we obser...
Species richness (S): "Species richness is the number of different ...
That's a very convincing r-squared for the dominance-abundance scal...
Stunning conclusion!
"We estimate that Earth is inhabited by 10^...
Scaling laws predict global microbial diversity
Kenneth J. Locey
a,1
and Jay T. Lennon
a,1
a
Department of Biology, Indiana University, Bloomington, IN 47405
Edited by David M. Karl, University of Hawaii, Honolulu, HI, and approved March 30, 2016 (received for review October 27, 2015)
Scaling laws underpin unifying theories of biodiversity and are
among the most predictively powerful relationships in biology.
However, scaling laws developed for plants and animals often go
untested or fail to hold for microorganisms. As a result, it is unclear
whether scaling laws of biodiversity will span evolutionarily distant
domains of life that encompass all modes of metabolism and scales of
abundance. Using a global-scale compilation of ∼35,000 sites and
∼5.6·10
6
species, including the largest ever inventory of high-through-
put molecular data and one of the largest compilations of plant and
animal community data, we show similar rates of scaling in common-
ness and rarity across microorganisms and macroscopic plants and
animals. We document a universal dominance scaling law that holds
across 30 orders of magnitude, an unprecedented expanse that pre-
dicts the abundance of dominant ocean bacteria. In combining this
scaling law with the lognormal model of biodiversity, we predict that
Earth is home to upward of 1 trillion (10
12
) microbial species. Microbial
biodiversity seems greater than ever anticipated yet predictable from
the smallest to the largest microbiome.
biodiversity
|
microbiology
|
macroecology
|
microbiome
|
rare biosphere
T
he understanding of microbial biodiversity has rapidly trans-
formed over the past decade. High-throughput sequencing and
bioinformatics have expanded the catalog of microbial taxa by or-
ders of magnitude, whereas the unearthing of new phyla is reshaping
thetreeoflife(1–3). At the same time, discoveries of novel forms of
metabolism have provided insight into how microbes persist in vir-
tually all aquatic, terrestrial, engineered, and host-associated eco-
systems (4, 5). However, this period of discovery has uncovered few,
if any, general rules for predicting microbial biodiversity at scales of
abundance that characterize, for example, the ∼10
14
cells of bacteria
that inhabit a single human or the ∼10
30
cells of bacteria and ar-
chaea estimated to inhabit Earth (6, 7). Such findings would aid the
estimation of global species richness and reveal whether theories of
biodiversity hold across all scales of abundance and whether so-
called law-like patterns of biodiversity span the tree of life.
A primary goal of ecology and biodiversity theory is to predict
diversity, commonness, and rarity across evolutionarily distant taxa
and scales of space, time, and abundance (8–10). This goal can hardly
be achieved without accounting for the most abundant, widespread,
and metabolically, taxonomically, and functionally diverse organisms
on Earth (i.e., microorganisms). However, tests of biodiversity theory
rarely include both microbial and macrobial datasets. At the same
time, the study of microbial ecology has yet to uncover quantitative
relationships that predict diversity, commonness, and rarity at the
scale of host microbiomes and beyond. These unexplored opportu-
nities leave the understanding of biodiversity limited to the most
conspicuous species of plants and animals. This lack of synthesis has
also resulted in the independent study of two phenomena that likely
represent a single universal pattern. Specifically, these phenomena
are the highly uneven distributions of abundance that underpin
biodiversity theory (11) and the universal pattern of microbial com-
monness and rarity known as the microbial “rare biosphere” (12).
Scaling laws provide a promising path to the unified un-
derstanding and prediction of biodiversity. Also referred to as power
laws, the forms of these relationships, y ∼ x
z
, predict linear rates of
change under logarithmic transformation [i.e., log(y) ∼ zlog(x)] and
hence, proportional changes across orders of magnitude. Scaling laws
reveal how physiological, ecological, and evolutionary constraints
hold across genomes, cells, organisms, and communities of
greatly varying size (13–15). Among the most widely known are
the scaling of metabolic rate (B) with body size [M; B = B
o
M
3/4
(13)] and the rate at which species richness (i.e., number of
species; S) scale with area [A; S = cA
z
(16)]. These scaling laws
are predicted by powerful ecological theories, although evidence
suggests that they fail for microorganisms (17–19). Beyond area
and body size, there is an equally general constraint on bio-
diversity, that is, the number of individuals in an assemblage (N).
Often referred to as total abundance, N can range from less than
10 individuals in a given area to the nearly 10
30
cells of bacteria
and archaea on Earth (6, 7). This expanse outstrips the 22 orders
of magnitude that separate the mass of a Prochlor ococcus
cell (3·1
−16
kg) from a blue whale (1.9·10
5
kg)andthe26ordersof
magnitude that result from measuring Earth’s surface area at a
spatial grain equivalent to bacteria (5.1·10
26
μm
2
).
Here, we consider whether N may be one of the most powerful
constraints on commonness and rarity and one of the most ex-
pansive variables across which aspects of biodiversity could scale.
Although N imposes an obvious constraint on the number of species
(i.e., S ≤ N), empirical and theoretical studies suggest that S scales
with N at a rate of 0.25–0.5 (i.e., S ∼ N
z
and 0.25 ≤ z ≤ 0.5) (20–22).
Importantly, this relationship applies to samples from different
systems and does not pertain to cumulative patterns (e.g., collector’s
curves), which are based on resampling (20–22). Recent studies
have also shown that N constrains universal patterns of common-
ness and rarity by imposing a numerical constraint on how abun-
dance varies among species, across space, and through time (23, 24).
Most notably, greater N leads to increasingly uneven distributions
and greater rarity. Hence, we expect greater N to correspond to an
increasingly uneven distribution among a greater number of species,
an increasing portion of which should be rare. However, the
strength of the relationships, whether they differ between microbes
and macrobes, and whether they conform to scaling laws across
orders of magnitude are virtually unknown.
Significance
Ecological scaling laws are intensively studied for their predictive
power and universal nature but often fail to unify biodiversity
across domains of life. Using a global-scale compilation of micro-
bial and macrobial data, we uncover relationships of commonness
and rarity that scale with abundance at similar rates for microor-
ganisms and macroscopic plants and animals. We then show a
unified scaling law that predicts the abundance of dominant
species across 30 orders of magnitude to the scale of all micro-
organism s on Earth. Using this scaling law combined with the
lognormal model of biodiversity, we predict that Earth is home to
as many as 1 trillion (10
12
) microbial species.
Author contributions: K.J.L. and J.T.L. designed research; K.J.L. performed research; K.J.L.
and J.T.L. analyzed data; and K.J.L. and J.T.L. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
1
To whom correspondence may be addressed. Email: ken@weecology.org or lennonj@
indiana.edu.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1521291113/-/DCSupplemental.
5970–5975
|
PNAS
|
May 24, 2016
|
vol. 113
|
no. 21 www.pnas.org/cgi/doi/10.1073/pnas.1521291113
Downloaded by guest on February 17, 2021
If aspects of diversity, commonness, and rarity scale with N,then
local- to global-scale predictions of microbial biodiversity could be
within reach. Likewise, if these relationships are similar for microbes
and macrobes, then we may be closer to a unified understanding of
biodiversity than previously thought. To answer these questions, we
compiled the largest publicly availab le microbial and macrobial
datasets to date. These data include 20,376 sites of bacterial, ar-
chaeal, and microscopic fungal communities and 14,862 sites of tree,
bird, and mammal communities. We focused on taxonomic aspects
of biodiversity, including species richness (S), similarity in abundance
among species (evenness), concentration of N among relatively low-
abundance species (rarity), and number of individuals belonging to
the most abundant species (absolute dominance, N
max
). We use the
resulting relationships to predict N
max
and S in large microbiomes
and make empirically supported and theoretically underpinned es-
timates for the number of microbial species on Earth.
Results and Discussion
As predicted, greater N ledtoanincreaseinspeciesrichness,
dominance, and rarity and a decrease in species evenness. Rarity,
evenness, and dominance scaled across seven orders of magnitude
in N at rates that differed little, if at all, between microbes and
macrobes (Fig. 1). We found that richness (S) scaled at a greater
rate for microbes (z = 0.38) than for macrobes (z = 0.24), but still, it
was near the expected range of 0.25 ≤ z ≤ 0.5 (Fig. 1). However, for
agivenN, microbes had greater rarity, less evenness, and more
species than macrobes (Fig. 1). As a result, microbes and macrobes
are similar in how commonness and rarity scale with N but differ in
ways that support the exceptional nature of the microbial rare
biosphere. The most unifying relationship that we observed was a
nearly isometric (i.e., 0.9 < z < 1.0) scaling of dominance (N
max
).
When extended to global scales, this dominance scaling law closely
predicts the abundance of dominant ocean bacteria. Using the
lognormal model of biodiversity, published estim ates of global
microbial N, and published and predicted values of N
max
,we
predict that Earth is occupied by 10
11
–10
12
microbial species.
This estimate is also supported by the scaling of S with N.
Scaling Relationships Point to an Exceptional Rare Biosphere. Across
microbial and macrobial communities, increasing N led to greater
rarity, greater absolute dominance, less evenness, and greater spe-
cies richness (Fig. 1 and SI Appendix,Figs.S5–S9). Bootstrapped
multiple regressions revealed that the significance of differences
between microbes and macrobes with regard to rarity and evenness
was dependent on sample size. Larger samples suggested significant
differences but were less likely to pass the assumptions of multiple
regression (Materials and Methods and SI Appendix,Fig.S5). Al-
though based on disparate types of data (i.e., counts of individual
organisms vs. environmental molecular surveys), absolute domi-
nance scaled at similar rates for microbes and macrobes (Fig. 1).
Each relationship was best fit by a power law as opposed to linear,
exponential, or semilog relationships (SI Appendix,TableS1).
Since being first described nearly a decade ago (25), the rare
biosphere has become an intensively studied pattern of microbial
commonness and rarity (12). Although its general form reiterates
the ubiquitously uneven nature of ecological communities, our
results suggest that microbial communities are exceptional in de-
grees of rarity and unevenness. Although artifacts sometimes as-
sociated with molecular surveys may inflate disparities in
abundance or generate false singletons, our findings suggest that
relationships of rarity, dominance, evenness, and richness were
robust to the inclusion or exclusion of singletons and different
percentage cutoffs in sequence similarity (SI Appendix,Figs.S8and
S9). Naturally, the inclusion of unclassified sequences led to higher
taxonomic richness. As a result of this large-scale comparison, we
suggest that the rare biosphere is driven by the unique biology and
Fig. 1. Microbial communi ties (blue dots) and communities of macroscopic plants and animals (red dots) are similar in the rates at which rarity, absolute
dominance, and species evenness scale with the number of individuals or genes reads (N). However, for a given N, microbial communities have greater rarity,
less evenness, and greater richness than those of macroorganisms. Coefficients and exponents of scaling equations are mean values from 10,000 bootstrapped
multiple regressions, with each regression based on 500 microbial and 500 macrobial communities chosen by stratified random sampling. Each scatterplot
represents a single random sample; hulls are 95% confidence intervals.
Locey and Lennon PNAS
|
May 24, 2016
|
vol. 113
|
no. 21
|
5971
ECOLOGY
Downloaded by guest on February 17, 2021
ecology of microorganisms. Examples are the ability of small
populations to persist in suboptimal environments through resilient
life stages, the ability of microbes to disperse long distances and
colonize new habitats, the capacity of microbes to finely partition
niche axes, and the greater ability of asexual organisms to maintain
small population sizes (12).
Predicted Scaling of Species Richness (S). Scaling exponents (z)for
the relationship of species richness (S)toN fell near or within the
predicted range (i.e., 0.25 < z < 0.5) (20–22) (Fig. 1 and Table 1).
Despite variation in the relationship among datasets (SI Appendix,
Fig. S7), the error structure across datasets was largely symmetrical
(SI Appendix,Fig.S5). Across datasets, z varied more greatly for
macrobes (0.07–1. 23) than for microbes (0.20–0. 46), which more
closely resembled the expected relationship (Table 1 and SI Ap-
pendix,Fig.S7). However, pooling all data to make use of the full
range of N and average out idiosyncrasies across datasets provided
a stronger overall relationship and produced an exponent (z = 0.51)
nearly identical to that observed in other empirical studies (20–22).
Expansive Dominance Scaling Law. Although greater N naturally
leads to greater absolute dominance (N
max
) (26), this relationship is
rarely explored and to our knowledge, has not been studied as a
scaling law. We found that N
max
scaled with N at similar and nearly
isometric rates (i.e., 0.9 < z < 1.0)formicrobesandmacrobesacross
seven orders of magnitude (Fig. 1) (R
2
= 0.94). Based on the
strength of this result, we tested whether this scaling law holds at
greaterscalesofN. We used published estimates for N and N
max
from the human gut (27, 28), the cow rumen (29, 30), the global
ocean (nonsediment), and Earth (6, 7, 31, 32). In each case, we
found that N
max
fell within the 95% prediction intervals of the
dominance scaling law (Fig. 2). Although derived from datasets
where n < 10
8
, the dominance scaling law predicted the global
abundance of some of the most abundant bacteria on Earth
[Pelagibacterales (SAR11); Prochlorococcus marinus]withinanor-
der of magnitude of prior estimates (31, 32). As a result, this
dominance scaling law seems to span an unprecedented 30 orders
of magnitude in N, extending to the upper limits of abundance in
nature. The only other biological scaling law that approaches this
expanse is the 3/4 power scaling of metabolic power to mass, which
holds across 27 orders of magnitude (33).
Predicting Global Microbial S Using N and N
max
. Knowing the num-
ber of species on Earth is among the greatest challenges in biology
(34–37). Historically, scientists have estimated global richness (S)
by extrapolating rarefaction curves and rates of accumulation, often
without including microorganisms (36–38). Although estimates of
global microbial S exist, they range from 10
4
to 10
9
,relyoncultured
organisms, precede large-scale sequencing projects, and are often
based on the extrapolation of statistical estimators (e.g., rarefaction
and Chao). These approaches also lack the theoretical underpin-
nings that distinguish extrapolations of statistical estimates from
predictions of biodiversity theory. As an alternative approach to
estimating S, we leveraged our scaling relationships with a well-
established model of biodiversity.
BasedonthescalingofS with N (Fig. 1), we would expect a global
microbial S of 2.1 ± 0.14·10
11
species. However, this risky type of
exercise would extrapolate 26 orders of magnitude beyond the
available data (Fig. 2). Instead, we used the dominance scaling law
and one of the most successful models of biodiversity (i.e., the log-
normal distribution) to make a theoretically underpinned prediction
of global microbial S (35, 39). The lognormal predicts that the dis-
tribution of abundance among species is approximately normal when
species abundances are log-transformed (20). An extension of the
central limit theorem, the lognormal arises from the multiplicative
interactions of many random variables (20, 39). Although historically
used to predict patterns of commonness and rarity, the lognormal
was later derived to predict S using N and N
max
(35). This derivation
of the lognormal led to predictions of S for habitats ranging in size
from a milliliter of water to an entire lake and speculations of S for
theentireocean.
To our knowledge, the lognormal is the only general biodiversity
model that has been derived to predict S using only N and N
max
as
inputs. We used the lognormal to predict microbial S in two ways.
First, we used published estimates of N and predicted the values of
N
max
using our dominance scaling law (Fig. 2). Second, we made
Table 1. Scaling relationship for abundance (N) and different
measures of diversity for microbial and macrobial datasets
Dataset Rarity Dominance Evenness Richness
EMP (n = 14,615) 0.2 (0.30) 1.01 (0.67) −0.44 (0.42) 0.46 (0.42)
MG-RAST (n = 1,283) 0.06 (0.20) 0.98 (0.97) −0.17 (0.32) 0.20 (0.45)
HMP (n = 4,303) 0.14 (0.14) 1.02 (0.70) −0.33 (0.18) 0.29 (0.13)
TARA (n = 139) −0.26 (0.02) 1.02 (0.13) 0.06 (0.00) 0.29 (0.13)
BBS (n = 2,769) 0.16 (0.086) 1.0 (0.54) −0.32 (0.22) 0.32 (0.19)
CBC (n = 1,412) 0.16 (0.39) 1.07 (0.90) −0.35 (0.44) 0.22 (0.48)
FIA (n = 10,355) 0.07 (0.01) 1.34 (0.68) −0.45 (0.27) 0.07 (0.02)
GENTRY (n = 222) 0.46 (0.27) 0.29 (0.038) −0.19 (0.05) 1.24 (0.46)
MCDB (n = 103) 0.07 (0.07) 1.07 (0.91) −0.16 (0.20) 0.09 (0.19)
Values are scaling exponents; coefficients of determination (r
2
)areinparen-
theses. Datasets are the Earth Microbiome Project (EMP), the Argonne National
Laboratory metagenomic server (MG-RAST) rRNA amplicon projects, the Human
Microbiome Project (HMP), the Tara Oceans Expedition (TARA), the North Amer-
ican Breeding Bird Survey (BBS), the Christmas Bird Count (CBC), the Forest In-
ventory and Analysis (FIA), the Gentry tree transects (GENTRY), and the Mammal
Community Database (MCDB). TARA was the only dataset where N ranged over
less than an order of magnitude, leading results for the TARA to be inconclusive.
Formostdatasets,N
max
scaled almost isometrically with N. For all datasets except
TARA, evenness decreased with N, while rarity increased. For birds and all mi-
crobe datasets, S scaled near the predicted range of 0.25–0.5.
Fig. 2. The dominance-abundance scaling law (dashed red line) predicts the
abundance of the most abundant microbial taxa (N
max
) up to global scales.
The pink hull is the 95% prediction interval for the regression based on 3,000
sites chosen by stratified random sampling (red heat map) from our micro-
bial data compilation. Gray cross-hairs are ranges of published estimates of N
and N
max
for large microbiomes, including Earth (6, 7, 31, 32) (Materials and
Methods, Approximating Ranges of N
max
for Large Microbiomes). The light-
gray dashed line is the 1:1 relationship. The scaling equation and r
2
only
pertain to the scatterplot data.
5972
|
www.pnas.org/cgi/doi/10.1073/pnas.1521291113 Locey and Lennon
Downloaded by guest on February 17, 2021
predictions of S using published estimates of both N and N
max
(6,
7, 31, 32). Assuming that global microbial N ranges from 9.2·10
29
to
3.2·10
30
(6, 7), the lognormal predicts 3.2 ± 0.23·10
12
species when
N
max
is predicted from the dominance scaling law (Materials and
Methods). However, using published estimates for N
max
ranging from
2.9·10
27
to 2.4·10
28
(31, 32), the lognormal model predicts a value of
global microbial S that is on the same order of magnitude as the
richness-abundance scaling relationship (i.e., 3.9 ± 0.05·10
11
species)
(Fig. 3). The general agreement between the lognormal model and
the richness scaling relationship is encouraging given the magnitude
of these predictions.
Our predict io ns of S for large microbiomes are among the most
rigorous to date, resulting from intersections of empirical scaling,
ecological theory, and the largest ever molecular surveys of micro-
bial communities. However, several caveats should be considered.
First, observed S for the Earth Microbiome Project (EMP) differed
greatly depending on whether we used closed or open reference
data (Materials and Methods), where S was ∼6.9·10
4
and 5.6·10
6
,
respectively. In our main study, we used the closed reference data
owing to the greater accuracy of that approach and because 42% of
all taxa in the open reference EMP dataset were only detected twice
or less. Consequently, choices, such as how to assign operational
taxonomic units (OTUs) and which primers or gene regions to use,
need to be made cautiously and deliberately. Second, estimates of S
will be much greater than observed when many species are detected
only once or twice, such as with the EMP. Statistical estimators of S,
such as rarefaction, jackknife, Chao, etc., are driven by singletons
and doubletons (26). Third, it is difficult to estimate the portion of
species missed when only a miniscule fraction of all individuals is
sampled. For example, the intersection of the lognormal model and
the richness scaling relationship suggests that S for an individual
human gut could range from 10
5
to 10
6
species (Fig. 3). However, S
of the human gut samples is often on the order of 10
3
,whereas
N isoftenlessthan10
6
. These sample sizes are vanishingly small
fractions of the gut microbiome, even when many samples are
compiled together. For example, compiling all 4,303 samples from
the Human Microbiome Project (HMP) dataset yields only 2.2·10
7
reads, hardly sufficient for detecting 10
5
–10
6
species among 10
14
cells. Consequently, detecting the true S of microbiomes with large
N is a profound challenge that requires many large samples.
Conclusion
We estimate that Earth is inhabited by 10
11
–10
12
microbial species.
This prediction is based on ecological theory reformulated for large-
scale predictions, an expansive dominance scaling law, a richness
scaling relationship with empirical and theoretical support, and the
largest molecular surveys compiled to date. The profound magnitude
of our prediction for Earth’s microbial diversity stresses the need for
continued investigation. We expect the dominance scaling law that
we uncovered to be valuable in predicting richness, commonness,
and rarity across all scales of abundance. To move forward, biologists
will need to push beyond current computational limits and increase
their investment in collaborative sampling efforts to catalog Earth’s
microbial diversity. For context, ∼10
4
species have been cultured, less
than 10
5
species are represented by classified sequences, and the
entirety of the EMP has cataloged less than 10
7
species, 29% of
which were only detected twice. Powerful relationships like those
documented here and a greater unified study of commonness and
rarity will greatly contribute to finding the potentially 99.999% of
microbial taxa that remain undiscovered.
Materials and Methods
Data. Our macrobial datasets comprised 14,862 different sites of mammal, tree,
and bird communities. We used a compilation of data that included species
abundance data for communities distributed across all continents, except Ant-
arctica (40). This compilation is based, in part, on five continental- to global-scale
surveys: United States Geological Survey (USGS) North American Breeding Bird
Survey (41) (2,769 sites), citizen science Christmas Bird Count (42) (1,412 sites),
Forest Inventory Analysis (43) (10,356 sites), Alwyn Gentry’sForestTransectData
Set (44) (222 sites), and one global-scale data compilation: the Mammal Com-
munity Database (45) (103 sites). We limited our Christmas Bird Count dataset to
sites where N was no greater than 10
4
(i.e., the reported maximum N for the
North American Breeding Bird Survey). Above that, estimates of N are not likely
based on counts of individuals. No site is represented more than once in our
data. Greater detail can be found elsewhere (appendix in ref. 40).
We used 20,376 sites of communities of bacteria, archaea, and microscopic
fungi; 14,615 of these were from the EMP (1) obtained on August 22, 2014.
Sample processing, sequencing, and amplicon data are standardized and per-
formed by the EMP, and all are publicly available at qiita.microbio.me/.The
EMP data consist of open and closed reference datasets. The Quantitative In-
sights Into Microbial Ecology (QIIME) tutorial (qiime.org/tu torials/otu_picking .
html) defines closed reference as a classification scheme where any rRNA reads
that do not hit a sequence in a reference collection are excluded from analysis.
In contrast, open reference refers to a scheme where reads that do not hit a
reference collection are subsequently clustered de novo and represent unique
but unclassified taxonomic units. Our main results are based on closed reference
data because of the greater accuracy of that approach and because 13% of all
taxa in the open reference EMP dataset were only detected once, whereas 29%
were only detected twice.
We also used 4,303 sites from the Data Analysis and Coordination Center for
the NIH Common Fund-supported HMP (46). These data consisted of samples
taken from 15 or 18 locations (including the skin, gut, vagina, and oral cavity) on
each of 300 healthy individuals. The V3–V5 region of the 16S rRNA gene was
sequenced for each sample. We excluded sites from pilot phases of the HMP as
well as time series data. More detail on HMP sequencing and sampling protocols
can be found at hmpdacc.org/micro_analy sis/microbiome_analyses.php.
We included 1,319 nonexperimental PCR-targeted rR NA ampl icon sequencing
projects from the Argonne National Laboratory metagenomics server MG-RAST
(47). Represented in this compilation were samples from arctic aquatic systems
(130 sites; MG-RAST ID: mgp138), hydrothermal vents (123 sites; MG-RAST ID:
mgp327) (48), freshwater lakes in China (187 sites; MG-RAST ID: mgp2758) (49),
arctic soils (44 s ites; MG-RAST ID: mgp69) (50), temperate soils (84 sites;
MG-RAST ID: mgp68) (51), bovine fecal samples (16 sites; MG-RAST ID: mgp14132),
human gut microbiome samples not part of the HMP (529 sites; MG-RAST ID:
mgp401) (52), a global-scale dataset of indoor fungal systems (128 sites) (53), and
Fig. 3. The microbial richness-abundance scaling relationship (dashed red
line) supports values of S predicted from the lognormal model using the
published ranges of N and N
max
(gray dots) as well as ranges of N
max
pre-
dicted from the dominance scaling law (blue dots). The pink hull is the 95%
prediction interval for the regression based on 3,000 sites chosen by strati-
fied random sampling (red scatterplot). The scaling equation and r
2
value
are based solely on the red scatterplot data. SEs around predicted S are too
small to illustrate.
Locey and Lennon PNAS
|
May 24, 2016
|
vol. 113
|
no. 21
|
5973
ECOLOGY
Downloaded by guest on February 17, 2021
freshwater, marine, and intertidal river sediments (34 sites; MG-RAST ID:
mgp1829). Using MG-RAST allowed us to choose common parameter values for
sequence similarity (i.e., 97% for species level) and taxa assignment, including a
maximum e-value (probability of observing an equal or better match in a da-
tabase of a given size) of 10
−5
, a minimum alignment length of 50 bp, and
minimum percentage sequence similarities of 95%, 97%, and 99% to the closest
reference sequence in the MG-RAST’s M5 rRNA database (47–54). Below, we
analyze the MG-RAST datasets with respect to these cutoffs and reveal no sig-
nificant effect on scaling relationships. Last, we included 139 “prokaryote-
enriched” samples from 68 pelagic and mesopelagic locations, representing all
major oceanic regions (except the Arctic) gathered by the Tara Oceans expedi-
tion (55). Among the taxa not included in our analyses are reptiles, amphibians,
fish, large mammals, invertebrates, and protists. These taxa were absent, because
large datasets to do not exist for their communities or because redistribution
rights could not be gained for publication.
Quantifying Dominance, Evenness, Rarity, and Richness. We calculated or esti-
mated aspects of diversity (dominance, evenness, rarity, and richness) for each
site in our data compilation. All analyses can be reproduced or modified for
additional exploration by using the code, data, and directions provided at https://
github.com/LennonLab/ScalingMicroBiodiversit y.
Rarity. Here, rarity quantifies the concentration of species at low abundance (26).
Our primary rarity metric was the skewness of the frequency distribution of
arithmetic abundance classes (R
skew
), which are almost always right-skewed
distributions (26). Because of the inability to take the logarithm of a negative
skew, R
skew
was given a modulo transformation. The log-modulo transformation
adds a value of one to each measure of skewness and converts negative values
to positive values, making them all positive and able to be log-transformed. We
also quantified rarity using log-transformed abundances (R
log-skew
) (26). We
present results for R
log-skew
in SI Appendix,Fig.S4.
Dominance. Dominance refers to the abundance of the most abundant species,
the simplest measure of which is the abundance of the most abundant species
(absolute dominance; N
max
) (26). Relative dominance is also a common measure,
and it is known as the Berger–Parker index (N
max
/N = D
BP
). We focus on N
max
in
the main body because of the previously undocumented scaling with N and the
ability to predict S using N, N
max
, and the lognormal model. We also calculated
dominance as the sum of the relative abundance of the two most abundant
taxa (i.e., McNaughton’s dominance) and Simpson’s diversity, which is more
accurately interpreted as an index of dominance (26). We present results for
dominance metrics other than N
max
in SI Appendix,Fig.S3.
Evenness. Species evenness captures similarity in abundance among species (26,
56). We used five evenness metrics that perform well according to a series of
statistical requirements (56), including lacking a strong bias toward very large or
very small abundances, independence of richness (S), and scaling between zero
(no evenness) and one (perfect evenness). These metrics included Smith and
Wilson’sindices(E
var
and E
Q
), Simpson’sevenness(E
1/D
), Bulla’s index (O), and
Camargo’sindex(E′) (26, 56). We present results for E
1/D
in Results and Discussion
and results for the other four metrics in SI Appendix,Fig.S2.
Richness. Richness (S) is the number of species observed or estimated from a
sample. Estimates of S are designed to account for rare species that go un-
detected in unbiased surveys (26). We present results for observed S in the text
along and results for six estimators of S (Chao1, ACE, jackknife, rarefaction,
Margelef, and McHennick) in SI Appendix,Fig.S1.
Approximating Ranges of N
max
for Large Microbiomes.
Cow rumen. The most dominant taxonomic unit (based on 97% sequence sim-
ilarity in 16S rRNA reads) in the cow rumen is typically a member of the Provotella
genus and has been reported to account for about 1.5–2.0% of 16S rRNA gene
reads in a sample (29, 30). Assuming there are about 10
15
microbial cells in the
cow rumen (29, 30) and if these percentages are reflective of community-wide
relative dominance (D
BP
), then N
max
of the cow rumen would be in the range of
1.5·10
14
to 2·10
14
.
Human gut. Deep sequencing of the human gut reveals that the most dominant
taxon (based on 97% 16S rRNA sequence similarity) accounts for 10.6–12.2% of 16S
rRNA gene reads in a sample (6, 28). Assuming these percentages are reflective of
the microbiome at large and that there are about 10
14
microbial cells in the human
gut (5, 28, 46), then N
max
would be in the range from 1.06·10
13
to 1.22·10
13
.
Global ocean (nonsediment) and Earth. The most abundant microbial species
on Earth has yet been determined. Perhaps, the best genus-level candidates
(based on 97% 16S rRNA sequence similarity) are the marine picocyanobacteria
Synechococcus and Prochlorococcus, with estimated global abundances of 7.0 ±
0.3·10
26
and 2.9 ± 0.1·10
27
, respectively (32). Members of the SAR11 clade (i.e.,
Pelagibacterales) have an estimated global abundance of 2.0·10
28
and may also
be candidates for the most abundant microorganisms on Earth (31). We used
SAR11 as the upper limit for the most dominant microbial sp ecies o n Earth
(i.e., the most abundant species cannot be more abundant than the most
dominant order-level clade). We used 6.7·10
26
–3.0·10
27
as the range for N
max
of
the nonsediment global ocean and 2.9·10
27
–2.0·10
28
as the range for N
max
of
Earth. We used the range from 3.6·10
28
to 1.2·10
29
as the lower to upper range
for the number of microbial cells in the open ocean (7) and from 9.2·10
29
to
3.2·10
30
(6) as the lower to upper range for the number of microbial cells on Earth.
Predictions of S for Large Microbiomes and Earth. We used the methods de-
scribed in Curtis et al. (35) to predict global microbial richness (S) using the
lognormal species abundance model in ref. 39. Curtis et al. (35) used the log-
normal to estimate microbial S in 1 g soil, 1 mL water, and an entire lake, and
then, they speculate on what S may be for a ton of soil (many small ecosystems)
and the entire ocean (many large ecosystems). The lognormal prediction of S is
based on the ratio of total abundance (N) to the abundance of the most
abundant species (N
max
) and the assumption that the rarest species is a sin-
gleton, N
min
= 1. In equation 1 from the work by Curtis et al. (35), according to
the lognormal model, in communities with S(N) species, the number of taxa
that contain N individuals is
S
ð
N
Þ
=
Sa
ffiffiffi
π
p
exp
(
−
a log
2
N
N
O
2
)
,
where a is an inverse measure of the width of the distribution, with SD that is σ
2
(a = [2ln2σ
2
]
−1/2
)andN
O
that is the most common (i.e., modal) abundance class.
In equation 3 from the work by Curtis et al. (35), if it is assumed that the log-
normal species abundance curve is not truncated and therefore, is symmetric
about N
O
, then it can be shown that
N
min
=
N
2
O
N
max
.
The second method for estimating the spread of the lognormal distribution, a,is
by knowing or assuming N
min
. By using equations 1 and 3 from the work by
Curtis et al. (35) and the assumption that S(N
min
) = 1, S can be expressed in
terms of a, N
min
,andN
max
. Curtis et al. (35) reason that S will not be sensitive to
small deviations from the N
min
= 1 assumption and hence, that knowledge of
N
min
, N
max
,andN allows equation 11 from the work by Curtis et al. (35) to be
solved numerically for Preston’s a parameter and subsequently, S to be pre-
dicted using equation 10 from the work by Curtis et al. (35):
SðNÞ=
ffiffiffi
π
p
a
exp
8
<
:
a log
2
ffiffiffiffiffiffiffiffiffiffiffi
N
max
N
min
s
!!
2
9
=
;
.
Curtis et al. (35) show that the above equation can be used to rewrite equation
5inref.35asequation11inref.35:
N
T
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
πN
min
N
max
p
2a
exp
8
<
:
a log
2
ffiffiffiffiffiffiffiffiffiffiffi
N
max
N
min
s
!!
2
9
=
;
exp
(
lnð2Þ
2a
2
)
"
erf
a log
2
ffiffiffiffiffiffiffiffiffiffiffi
N
max
N
min
s
−
lnð2Þ
2a
!!
+ erf
a log
2
ffiffiffiffiffiffiffiffiffiffiffi
N
max
N
min
s
+
lnð2Þ
2a
!!#
.
Equation 11 from the work by Curtis et al. (35) can be numerically solved for a,
which is then used in their equation 10 to solve for S. We coded equations 1, 3,
10, and 11 from the work by Curtis et al. (35) into a Python script that can be
used to recreate the results in the work by Curtis et al. (35) under the functions
“alpha2” to derive a and “s2” to estimate S. In predicting S, we accounted for
variability in N and N
max
by randomly sampling within their published ranges
(SI Appendix, Fig. S14). This sampling strategy allowed us to generate means
and SEs, which are often lacking from large-scale predictions of S.
Resampling and Dependence on Sample Size and Sequence Simil arity. We ex-
amined relationships of rarity, evenness, dominance, and richness to the number
of individual organisms or gene reads (N) using 10,000 bootstrapped multiple
regressions based on stratified random sampling of microbial and macrobial
datasets. We examined the sensitivity of our results to sampling strategy,
sample size, particular datasets, and the microbe/macrobe dummy variable,
results of which can be found in SI Appendix,Figs.S5–S13. To use equal num-
bers of sites for macrobes and microbes in each multiple regression analysis, we
used 100 sites from each macrobial dataset for a total of 500 randomly chosen
sites. To obtain 500 sites from our microbial data, we used 50 randomly chosen
sites from each microbial dataset having more than 100 sites and 20 randomly
chosen sites from smaller datasets. We used the mean values of coefficients and
5974
|
www.pnas.org/cgi/doi/10.1073/pnas.1521291113 Locey and Lennon
Downloaded by guest on February 17, 2021
intercepts (accounting for whether differences between microbes and macro-
bes were significant at P < 0.05; α = 0.05) from multiple regressions to estimate
the relationships of rarity, evenness, dominance, and richness to N.Weexam-
ined whether scaling relationships for microbial data were sensitive to the
percentage cutoff in rRNA sequence similarity, which is used for binning se-
quences into OTUs. These analyses were restricted to datasets obtained from
the MG-RAST but reveal no statistical differences caused by whether sequences
were binned based on 95%, 97%, and 99% similarity.
Power Law Behavior vs. Other Functional Forms. We tested whether relation-
ships of richness, evenness, rarity, and dominance were better fit by a power law
(log–log) than by linear, exponential, and semilog relationships (SI Appendix,
Table S1). The power law model explained substantially greater variance or in
the one case where it was nearly tied in explanatory power, had substantially
lower Akaike information criterion (AIC) and Bayesian information criterion
(BIC) values than other models.
Available Code and Data. We used freely available open-source computing and
version control tools. Analyses and figures can be automatically regenerated
using Python scripts and data files in the public GitHub repository https://github.
com/LennonLab/ScalingMicroBiodiversity. Analyses can be recreated step by step
using the directions given in the repository.
ACKNOWLEDGMENTS. We thank M. Muscarella, W. Shoemaker, N.
Wisnoski, X. Xiao, S. Gibbons, E. Hall, and E. P. White for critical reviews.
We thank the individuals involved in collecting and providing the data used
in this paper, including the essential citizen scientists who collect the
Breeding Bird Survey and Christmas Bird Count data; the researchers who
collected, sequenced, and provided metagenomic data on the MG-RAST as
well as the individuals who maintain and provide the MG-RAST service; the
Audubon Society; the US F orest Service; the Missouri Botanical Garden;
and Alwyn H. Gentry. This work was supported by National Science
Foundation Dimensions of Biodiversity Grant 1442246 and US Army Research
Office Grant W911NF-14-1-0411.
1. Gilbert JA, Jansson JK, Knight R (2014) The Earth Microbiome project: Successes and
aspirations. BMC Biol 12:69.
2. Brown CT, et al. (2015) Unusual biology across a group comprising more than 15% of
domain Bacteria. Nature 523(7559):208–211.
3. Hug LA, et al. (2016) A new view of the tree of life. Nat Microbiol, 10.103 8/
nmicrobiol.2016 .48.
4. Venter JC, et al. (2004) Environmental genome shotgun sequencing of the Sargasso
Sea. Science 304(5667):66–74.
5. Gill SR, et al. (2006) Metagenomic analysis of the human distal gut microbiome.
Science 312(5778):1355–1359.
6. Kallmeyer J, Pockalny R, Adhikari RR, Smith DC, D’Hondt S (2012) Global distribution
of microbial abundance and biomass in subseafloor sediment. Proc Natl Acad Sci USA
109(40):16213–16216.
7. Whitman WB, Coleman DC, Wiebe WJ (1998) Prokaryotes: The unseen majority. Proc
Natl Acad Sci USA 95(12):6578–6583.
8. Hubbell SP (2001) The Unified Neutral Theory of Biodiversity and Biogeography
(Princeton Univ Press, Princeton).
9. McGill BJ (2010) Towards a unification of unified theories of biodiversity. Ecol Lett
13(5):627–642.
10. Harte J (2011) Maximum Entropy and Ecology (Oxford Univ Press, New York).
11. McGill BJ, et al. (2007) Species abundance distributions: Moving beyond single pre-
diction theories to integration within an ecological framework. Ecol Lett 10(10):
995–1015.
12. Reid A, Buckley M (2011) The Rare Biosphere: A Report from the American Academy
of Microbiology (American Academy of Microbiology, Washington, DC).
13. Brown JH, Gillooly JF, Allen AP, Savage VM, West GB (2004) Toward a metabolic
theory of ecology. Ecology 85(7):1771–1789.
14. Lynch M, Conery JS (2003) The origins of genome complexity. Science 302(5649):
1401–1404.
15. Ritchie ME, Olff H (1999) Spatial scaling laws yield a synthetic theory of biodiversity.
Nature 400(6744):557–560.
16. Lomolino MV (2000) Ecology’s most general, yet protean pattern: The species‐area
relationship. J Biogeogr 27(1):17–26.
17. DeLong JP, Okie JG, Moses ME, Sibly RM, Brown JH (2010) Shifts in metabolic scaling,
production, and efficiency across major evolutionary transitions of life. Proc Natl Acad
Sci USA 107(29):12941–12945.
18. Horner-Devine MC, Lage M, Hughes JB, Bohannan BJM (2004) A taxa-area relation-
ship for bacteria. Nature 432(7018):750–753.
19. Green JL, et al. (2004) Spatial scaling of microbial eukaryote diversity. Nature
432(7018):747–750.
20. May RM (1975) Patterns of species abundance and diversity. Ecology and Evolution of
Communities, eds Cody ML, Diamond JM (Harvard Univ Press, Cambridge, MA), pp
81–120.
21. May RM (1978) The dynamics and diversity of insect faunas. Diversity of Insect Faunas,
eds Mount LA, Waloff N (Blackwell, Oxford), pp 188–204.
22. Siemann E, Tilman D, Haarstad J (1996) Insect species diversity, abundance and body
size relationships. Nature 380:704–706.
23. Locey KJ, White EP (2013) How species richness and total abundance constrain the
distribution of abundance. Ecol Lett 16(9):1177–1185.
24. Xiao X, Locey KJ, White EP (2015) A process-independent explanation for the general
form of Taylor’s Law. Am Nat 186(2):E51–E60.
25. Sogin ML, et al. (2006) Microbial diversity in the deep sea and the underexplored
“rare biosphere.” Proc Natl Acad Sci USA 103(32):12115–12120.
26. Magurran AE, McGill BJ, eds (2011) Biological Diversity: Frontiers in Measurement and
Assessment (Oxford Univ Press, Oxford), Vol 12.
27. Berg RD (1996) The indigenous gastrointestinal microflora. Trends Microbiol 4(11):
430–435.
28. Dethlefsen L, Huse S, Sogin ML, Relman DA (2008) The pervasive effects of an anti-
biotic on the human gut microbiota, as revealed by deep 16S rRNA sequencing. PLoS
Biol 6(11):e280.
29. Jami E, Mizrahi I (2012) Composition and similarity of bovine rumen microbiota across
individual animals. PLoS One 7(3):e33306.
30. Stevenson DM, Weimer PJ (2007) Dominance of Prevotella and low abundance of
classical ruminal bacterial species in the bovine rumen revealed by relative quantifi-
cation real-time PCR. Appl Microbiol Biotechnol 75(1):165–174.
31. Morris RM, et al. (2002) SAR11 clade dominates ocean surface bacterioplankton
communities. Nature 420(6917):806–810.
32. Flombaum P, et al. (2013) Present and future global distributions of the marine Cy-
anobacteria Prochlorococcus and Synechococcus. Proc Natl Acad Sci USA 110(24):
9824–9829.
33. West GB, Woodruff WH, Brown JH (2002) Allometric scalin g of metabolic rate
from molecules and mitochondria to cells and mammals. Proc Natl Acad Sci USA
99(Suppl 1):2473– 2478.
34. May RM (1988) How many species are there on Earth? Science 241(4872):1441–1449.
35. Curtis TP, Sloan WT, Scannell JW (2002) Estimating prokaryotic diversity and its limits.
Proc Natl Acad Sci USA 99(16):10494–10499.
36. Mora C, Tittensor DP, Adl S, Simpson AGB, Worm B (2011) How many species are there
on Earth and in the ocean? PLoS Biol 9(8):e1001127.
37. Stork NE, McBroom J, Gely C, Hamilton AJ (2015) New approaches narrow global
species estimates for beetles, insects, and terrestrial arthropods. Proc Natl Acad Sci
USA 112(24):7519–7523.
38. Schloss PD, Handelsman J (2004) Status of the microbial census. Microbiol Mol Biol Rev
68(4):686–691.
39. Preston FW (1948) The commonness, and rarity, of species. Ecology 29(3):254–283.
40. White EP, Thibault KM, Xiao X (2012) Characterizing species abundance distributions
across taxa and ecosystems using a simple maximum entropy model. Ecology 93(8):
1772–1778.
41. Sauer JR, et al. (2011) The North American Breeding Bird Survey 1966–2009, Version
3.23.2011 (USGS Patuxent Wildlife Research Center, Laurel, MD).
42. National Audubon Society (2002) The Christmas Bird Count Historical Results. Avail-
able at netapp.audubon.org/cbcobservation/. Accessed April 14, 2016.
43. US Department of Agriculture (2010) Forest Inventory and Analysis: National Core
Field Guide (Phase 2 and 3), Version 4.0 (US Department of Agriculture Forest Service,
Forest Inventory and Analysis, Washington, DC).
44. Phillips O, Miller JS (2002) Global Patterns of Plant Diversity: Alwyn H. Gentry’s Forest
Transect Data Set (Missouri Botanical Garden Press, St. Louis).
45. Thibault KM, Supp SR, Giffin M, White EP, Ernest SKM (2011) Species composition and
abundance of mammalian communities. Ecology 92(12):2316.
46. Turnbaugh PJ, et al. (2007) The human microbiome project. Nature 449(7164):
804–810.
47. Meyer F, et al. (2008) The metagenomics RAST server - a public resource for the au-
tomatic phylogenetic and functional analysis of metagenomes. BMC Bioinf ormatics
9:386.
48. Flores GE, et al. (2011) Microbial community structure of hydrothermal deposits from
geochemically different vent fields along the Mid-Atlantic Ridge. Environ Microbiol
13(8):2158–2171.
49. Wang J, et al. (2013) Phylogenetic beta diversity in bacterial assemblages across
ecosystems: Deterministic versus stochastic processes. ISME J 7(7):1310–1321.
50. Chu H, et al. (2010) Soil bacterial diversity in the Arctic is not fundamentally different
from that found in other biomes. Environ Microbiol 12(11):2998–3006.
51. Fierer N, et al. (2012) Comparative metagenomic, phylogenetic and physiological analyses
of soil microbial communities across nitrogen gradients. ISME J 6(5):1007–1017 .
52. Yatsunenko T, et al. (2012) Human gut microbiome viewed across age and geogra-
phy. Nature 486(7402):222–227.
53. Amend AS, Seifert KA, Samson R, Bruns TD (2010) Indoor fungal composition is
geographically patterned and more diverse in temperate zones than in the tropics.
Proc Natl Acad Sci USA 107(31):13748–13753.
54. Goris J, et al. (2007) DNA-DNA hybridization values and their relationship to whole-
genome sequence similarities. Int J Syst Evol Microbiol 57(Pt 1):81–91.
55. Sunagawa S, et al.; Tara Oceans coordinators (2015) Ocean plankton. Structure and
function of the global ocean microbiome. Science 348(6237):1261359.
56. Smith B, Wilson JB (1996) A consumer’s guide to evenness indices. Oikos 76(1):70–82.
Locey and Lennon PNAS
|
May 24, 2016
|
vol. 113
|
no. 21
|
5975
ECOLOGY
Downloaded by guest on February 17, 2021
That's a very convincing r-squared for the dominance-abundance scaling law. This scaling law is key to the the earth microbiome calculations.
Species richness (S): "Species richness is the number of different species represented in an ecological community, landscape or region. Species richness is simply a count of species, and it does not take into account the abundances of the species or their relative abundance distributions."
Evenness: "refers to how close in numbers each species in an environment is. Mathematically it is defined as a diversity index, a measure of biodiversity which quantifies how equal the community is numerically"
S source: https://en.wikipedia.org/wiki/Species_richness
Evenness source: https://en.wikipedia.org/wiki/Species_evenness
Stunning conclusion!
"We estimate that Earth is inhabited by 10^11–10
^12 microbial species. This prediction is based on ecological theory reformulated for large-scale predictions, an expansive dominance scaling law, a richness scaling relationship with empirical and theoretical support, and the largest molecular surveys compiled to date. The profound magnitude of our prediction for Earth’s microbial diversity stresses the need for continued investigation. We expect the dominance scaling law that we uncovered to be valuable in predicting richness, commonness, and rarity across all scales of abundance."
Key finding of paper: "The most unifying relationship that we observed was a nearly isometric (i.e., 0.9 < z < 1.0) scaling of dominance (Nmax). When extended to global scales, this dominance scaling law closely predicts the abundance of dominant ocean bacteria. Using the lognormal model of biodiversity, published estimates of global microbial N, and published and predicted values of Nmax, we predict that Earth is occupied by 10^11–10^12 microbial species. This estimate is also supported by the scaling of S with N."
Scaling laws describe functional relationships between quantities (i.e. physical variables) that last over meaningful intervals. Perhaps the most well known scaling law is the power law, where a relative change in one quantity results in a proportional change in the other quantity. Power laws are found across different complex systems, ranging from biology to economics.
These numbers are very difficult to quantify and could be off by an order(s) of magnitude. For example, the number of bacterial cells that inhabit a human was often said to be 10:1 the number of human cells - this ratio was challenged after the publication of this paper, and the new estimate is a 1:1 ratio.
Source: https://www.nature.com/news/scientists-bust-myth-that-our-bodies-have-more-bacteria-than-human-cells-1.19136
This is the basic equation of power laws.
Intriguing! I'd not read that the 10:1 ratio had been so challenged. Thanks.