The commonness of rarity: Global and future distribution of rarity across land plants

Abstract

A key feature of life’s diversity is that some species are common but many more are rare. Nonetheless, at global scales, we do not know what fraction of biodiversity consists of rare species. Here, we present the largest compilation of global plant diversity to quantify the fraction of Earth’s plant biodiversity that are rare. A large fraction, ~36.5% of Earth’s ~435,000 plant species, are exceedingly rare. Sampling biases and prominent models, such as neutral theory and the k-niche model, cannot account for the observed prevalence of rarity. Our results indicate that (i) climatically more stable regions have harbored rare species and hence a large fraction of Earth’s plant species via reduced extinction risk but that (ii) climate change and human land use are now disproportionately impacting rare species. Estimates of global species abundance distributions have important implications for risk assessments and conservation planning in this era of rapid global change.

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ECOLOGY
The commonness of rarity: Global and future
distribution of rarity across land plants
Brian J. Enquist1,2*, Xiao Feng3, Brad Boyle1, Brian Maitner1, Erica A. Newman1,3,
Peter Møller Jørgensen4, Patrick R. Roehrdanz5, Barbara M. Thiers6, Joseph R. Burger3,
Richard T. Corlett7, Thomas L. P. Couvreur8, Gilles Dauby9, John C. Donoghue10,
Wendy Foden11, Jon C. Lovett12,13, Pablo A. Marquet2,14,15, Cory Merow16, Guy Midgley17,
Naia Morueta-Holme18, Danilo M. Neves19, Ary T. Oliveira-Filho19, Nathan J. B. Kraft20,
Daniel S. Park21, Robert K. Peet22, Michiel Pillet1, Josep M. Serra-Diaz23, Brody Sandel24,
Mark Schildhauer25, Irena Šímová26,27, Cyrille Violle28, Jan J. Wieringa29, Susan K. Wiser30,
Lee Hannah5, Jens-Christian Svenning31, Brian J. McGill32
A key feature of life’s diversity is that some species are common but many more are rare. Nonetheless, at global
scales, we do not know what fraction of biodiversity consists of rare species. Here, we present the largest compi-
lation of global plant diversity to quantify the fraction of Earth’s plant biodiversity that are rare. A large fraction,
~36.5% of Earth’s ~435,000 plant species, are exceedingly rare. Sampling biases and prominent models, such as
neutral theory and the k-niche model, cannot account for the observed prevalence of rarity. Our results indicate
that (i) climatically more stable regions have harbored rare species and hence a large fraction of Earth’s plant
species via reduced extinction risk but that (ii) climate change and human land use are now disproportionately
impacting rare species. Estimates of global species abundance distributions have important implications for risk
assessments and conservation planning in this era of rapid global change.
INTRODUCTION
Why some species are common and others are rare has intrigued
ecologists (1, 2), at least, since Darwin (3). Rare species are orders of
magnitude more likely to go extinct (4, 5), making it puzzling how
so many rare species can be maintained (6). Understanding rarity
and the maintenance of rare species is also central to conservation
biology [e.g., (7)] and to understanding current and future changes
in biodiversity due to global change (8). Despite this importance, we
know unexpectedly little about the causes of commonness and rarity
and their maintenance at a global scale (9, 10).
Most quantifications of species abundance use abundances in local
communities because estimates of global taxon abundance are difficult
to obtain. However, there are two major limitations to focusing solely
on local abundance. First, most species tend to be simultaneously
common in a few parts of their ranges and rare in most of their ranges
(11, 12), making estimates of local abundance a noisy and a poor
measure of how truly rare a species is globally. Second, at a global
scale, a measure of rarity results from a combination of the average local
abundance and the number of sites occupied throughout the species
geographic range. Local species abundance and species occupancy
across the geographic range tend to be correlated (12–14), so locally
rare species tend to also show up in only a few local communities.
This makes it likely that estimates of global abundance will be more
skewed to the rare, but this has rarely been tested (15). A global
estimate of rarity can therefore minimize the potential problems
associated with assessing whether a species is rare. Fortunately, with
the rapid development of biodiversity databases and networks in the
past decade, it is becoming increasingly possible to quantify continental
and global patterns of biodiversity and test competing models for
the origin and maintenance of these patterns at a global scale (16).
Here, we use a global botanical database of unprecedented coverage
to (i) assess global patterns of plant rarity, (ii) test several proposed
hypotheses underlying the generation and persistence of rare species,
(iii) identify regions that harbor hotspots of rare species and explore
1Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721, USA. 2Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA. 3Institute
of the Environment, University of Arizona, Tucson, AZ 85721, USA. 4Missouri Botanical Garden, St. Louis, MO 63110, USA. 5Betty and Gordon Moore Center for Science,
Conservation International, 2011 Crystal Dr., Arlington, VA 22202, USA. 6New York Botanical Garden, 2900 Southern Blvd., Bronx, NY 10348, USA. 7Centre for Integrative
Conservation, Xishuangbanna Tropical Botanical Garden and Center of Conservation Biology, Core Botanical Gardens, Chinese Academy of Sciences, Menglun, Yunnan,
China. 8DIADE, IRD, Université Montpellier, Montpellier, France. 9AMAP, IRD, CIRAD, CNRS, INRA, Université Montpellier, Montpellier, France. 10Rincon Consultants Inc.,
Ventura, CA 93003, USA. 11Cape Research Centre, South African National Parks, Tokai, 7947 Cape Town, South Africa. 12School of Geography, University of Leeds, Leeds, UK.
13Royal Botanic Gardens, Kew, Richmond, Surrey, UK. 14Departamento de Ecología, Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile, CP 8331150
Santiago, Chile. 15Instituto de Ecología y Biodiversidad (IEB), Laboratorio Internacional de Cambio Global and Centro de Cambio Global UC, Chile. 16Department of Ecology
and Evolutionary Biology, University of Connecticut, CT 06269, USA. 17Department of Botany and Zoology, Stellenbosch University, Stellenbosch, South Africa. 18Center
for Macroecology, Evolution and University of Copenhagen, Universitetsparken 15, Building 3, DK-2100 Copenhagen Ø, Denmark. 19Department of Botany, Federal
University of Minas Gerais, Belo Horizonte 31270-901, Minas Gerais, Brazil. 20Department of Ecology and Evolutionary Biology, University of California, Los Angeles,
Los Angeles, CA 90095, USA. 21Department of Organismic and Evolutionary Biology, Harvard University, MA 02138, USA. 22Department of Biology, University of North
Carolina, NC 27599, USA. 23Université de Lorraine, AgroParisTech, INRA, Silva, 54000 Nancy, France. 24Department of Biology, Santa Clara University, Santa Clara, CA 95053,
USA. 25National Center for Ecological Analysis and Synthesis, Santa Barbara, CA 93101, USA. 26Centre for Theoretical Study, Charles University, Prague 1, Czech Republic.
27Department of Ecology, Faculty of Sciences, Charles University, Czech Republic. 28Université Montpellier, CNRS, EPHE, IRD, Université Paul Valéry Montpellier 3, Montpellier,
France. 29Naturalis Biodiversity Center, Darwinweg 2, Leiden, Netherlands. 30Manaaki Whenua—Landcare Research, Lincoln, New Zealand. 31Center for Biodiversity
Dynamics in a Changing World (BIOCHANGE) and Section for Ecoinformatics and Biodiversity, Department of Bioscience, Aarhus University, Ny Munkegade 114, DK-8000
Aarhus C, Denmark. 32School of Biology and Ecology and Senator George J. Mitchell Center of Sustainability Solutions, University of Maine, Orono, ME 04469, USA.
*Corresponding author. Email: benquist@email.arizona.edu
Copyright © 2019
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the drivers of these spatial patterns, and (iv) assess how current patterns
of human impact and future climate change scenarios may affect plant
diversity via impacts on rare species. In the past, quantification of
global patterns of abundance and rarity has been hampered by the
many limitations of global biodiversity data. These issues have made
the use of these data in comprehensive biodiversity analyses difficult
(17, 18). Here, we take a novel approach that overcomes many of
these limitations. For all known land plants (Embryophyta), we have
compiled a global database of standardized botanical observation
records—the integrated Botanical Information and Ecology Network
(BIEN) [Fig. 1, BIEN v4.1; http://bien.nceas.ucsb.edu/bien/; see the
Supplementary Materials; (19)]. The BIEN data are mainly composed
of herbarium collections, ecological plots and surveys, and trait ob-
servations. Together, these data constitute more than 200 million
observations of plant species occurrences. Assembling these data
involves overcoming numerous challenges of taxonomy, data quality,
data exchange, provenance, interoperability, and scaling (Fig. 1) (20).
After correcting misspelled or synonymous taxon names and removing
records with invalid or suspect geocoordinates, incomplete or unre-
solvable taxon names, and observations of non-native species and
cultivated plants, the final dataset consists of 34,902,348 observation
records of 434,934 land plant species from herbarium and ecological
plot data (see Fig. 1 and the Supplementary Materials for details of
data cleaning and validation).
We quantified the distribution of global abundance for all land
plant species (hereafter, plant species) on Earth using a metric of
global relative abundance, the total number of unique observations
of a species ever recorded in global databases. The distribution of
the total number of global observations per species [the global species
abundance distribution (gSAD)] is an estimate of global abundance
and is still a sample, as a count of all individuals on the planet is
impossible. Nonetheless, quantifying the functional form of gSADs
has a substantial practical advantage over other estimates of abun-
dance. First, we can combine data from different datasets including
plots and surveys, and herbarium specimens to increase sampling
coverage. These datasets all share the common attribute of observing
an individual of a given species in a given location and time. Second,
comparing and integrating estimates of gSADs from different datasets
(e.g., plots versus herbarium specimens) provide a way to assess po-
tential biases in estimating species global abundance. For example,
gSADs can be estimated by compiling only plot or ecological survey
data. In plot data, a global estimate of species abundance is quanti-
fied directly, as each individual of that species is summed within
and across plots. As we discuss, our approach is less biased than
local plot-based abundance data that samples only a tiny fraction of
Earth’s surface.
Traditionally, measures of rarity have been based on a multi-
dimensional concept. For example, Rabinowitz (21) identified three
major axes on which a species can be common or rare: local abun-
dance, extent of the geographic range, and habitat specificity. Al-
though conceptually these three dimensions are independent, they
are often strongly positively correlated (22). Four of the five criteria
the International Union for Conservation of Nature uses to evaluate
extinction risk for their Red List (23) directly involve measurement
of rarity via absolute levels of or declines in abundance and geo-
graphic distribution, while the fifth involves computer simulations,
which are likely to incorporate population size and range size as well.
These criteria all point to the importance of measuring rarity at
Fig. 1. Computational workflow for creating gSADs. TNRS, Taxonomic Name Resolution Service; GNRS, Geographic Name Resolution Service.
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global scale (in contrast to local rarity). A species may be globally
rare because it has few individuals at many sites or many individuals
at few sites.
RESULTS
We generated three gSAD distributions based on summing individual
observations of species across all ecological plots, by summing
all observations across all other botanical observation records, and
by summing the non-plot observation records found within 100 km
distance from each ecological plot. Our analyses reveal that a large
fraction of the plant species on Earth are rare (Figs. 2 and 3). Ana-
lyzing the distribution of the number of observations per species
reveals that the global-scale distribution is highly skewed and lacking
a central tendency (i.e., the mode of the gSAD is at N = 1; Fig. 2).
The total number of land plant species is ~435,000 (the number
of species before geovalidation based on 66,334,188 observation
records), a large fraction of these species, 36.5% or 158,535, are
rare, with just five observations or fewer, while 28.3% or 123,149
have just three observations or fewer. The large number of rare
species is consistent with past claims that when biodiversity obser-
vations are compiled at increasingly larger spatial (15) and temporal
scales (24), rare species should comprise an increasing majority
of species.
Global species abundance distribution
We tested several long-standing hypotheses concerning the pro-
cesses creating and maintaining large-scale patterns of commonness
and rarity. Specifically, we assessed whether the number of ob-
served rare species follows predictions from biodiversity theory
by comparing several proposed statistical distributions for the
gSAD. First, we assessed two contrasting sets of predictions for
the distribution of commonness and rarity of species (Fig. 2). Spe-
cifically, at increasingly larger geographic scales, both the unified
neutral theory of biogeography (UNTB) (25) and the k-niche model
(26) predict that the gSAD will converge on Fisher’s log-series
distribution (27)
ˆ
f =
 x n
─
n (1)
where
ˆ
f is the expected number of species, n is the total number of
observations per species,  is the diversity parameter, and x is a nui-
sance parameter that is defined by  and the total number of indi-
viduals sampled, N, x = N/(N − ). The UNTB further makes two
predictions: (i) At increasingly large spatial scales (such as continental
and global scales), the Fisher’s log-series distribution will also in-
creasingly converge to approximate a “power law” (or a Pareto dis-
tribution) over most of the range of the distribution (see Fig. 2A)
(28), where
ˆ
f =
 − 1
─
n 0
(
n
─
n 0
)
− (2)
where (ii) the value of , the scaling exponent or slope on a log-log
plot, will equal −1.0. For the continuous Pareto or power law dis-
tribution, n0 is the minimum scale of the distribution, and  is the
scaling exponent (29). For the BIEN data, the minimum number of
observations for a species is 1, so it was set at 1.
The UNTB predicts that the gSAD (called the regional pool in
neutral theory) will follow a log-series distribution. Pueyo (28) notes
that the log-series distribution consists of two parts multiplied
together: a Pareto distribution with exponent  = −1 that is the
result of neutral dynamics and an exponential “bend” that takes
effect at very high abundances due to the finite size assumption.
Pueyo (28) also suggests a generalization of the Pareto and log series
that incorporates a Pareto where the exponent  is allowed to vary
AB
gSAD distribution predictions: Observation:
Observation:
gSAD slope predictions:
(i)
(i)
(ii)
(iii)
(ii)
Neutral theory and niche theory: gSAD will be best fit by log-series distribution;
gSAD best fit by lognormal distribution
slope, < −1.0;
Central limit theorem: gSAD will be best fit by lognormal distribution
Neutral theory slope,
Non-neutral processes generating more rare species; slope,
Non-neutral processes generating more common species; slope,
Finite community
Slope,
21
Log10 (number of species)
Log10 (number of species)
Log10 (number of observations) Log
10
(number of observations)
size
< −1.0
> −1.0
= −1.0;
Fig. 2. The gSAD for all plant species. (A) Schematic illustration of the predicted gSAD based on expectations from theory (see main text) (28). In the inset, we list
several differing predictions for the shape of the gSAD. (B) Two estimates of the gSAD for all land plant species. The first distribution (green) is the observed number
of observations per species for all species found in ecological plots. Each data point represents the total number of individuals observed for a given species. The second
distribution (red) is all botanical specimens collected within 100 km of each plot. The third distribution (light purple) is all botanical specimens per species. Each distribution
is strongly modal at the lowest abundance, showing that most species have only been observed a very small number of times and only a few species are common. The
distributions are shown on log10-transformed axes. Comparing the shape of the distributions of the competing fits of differing proposed gSAD distributions allows us to
test differing hypotheses for the origin of the gSAD.
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combined with an exponential finite size term, which we call here
“Pareto with exponential finite adjustment.” Thus, testing whether
the gSAD is best fit by a log series (where  = −1), a Pareto dis-
tribution (where  is allowed to vary), or a Pareto with exponential
finite adjustment (where  is also allowed to vary) provides a test
of neutral dynamics. In sum, both the UNTB and k-niche model
predict that the log-series distribution will best fit gSADs, but at
large geographic scales, this distribution will also converge to a
Pareto distribution. Thus, fitting the Pareto or the Pareto with ex-
ponential finite adjustment provides a simultaneous test of whether
neutral or niche dynamics are consistent with the data (28). A poor
fit or a value of  ≠ 1.0 rejects neutral theory. A poor fit of the
Pareto regardless of the value of  further rejects the k-niche model
(28). In addition, the value of  is then a useful ecological and evo-
lutionary indicator of whether Earth has more rare species ( < −1;
the slope of the function is steeper) or fewer ( > −1; the slope of the
function is flatter) rare species than expected under zero-sum neutral
evolutionary dynamics (28, 30).
In contrast to the predictions from the UNTB and k-niche model,
the central limit theorem (CLT) predicts that gSADs will be charac-
terized by a lognormal distribution. If the abundance of a species
is the result of several multiplicative processes acting together (31),
then lognormal distributions are expected. Because of the CLT, a
lognormal distribution is expected any time many variables interact
multiplicatively to influence abundance, such as many differing
biotic and abiotic factors [see references in (32)]. Common processes
in ecology and evolution are known to interact multiplicatively to
influence species abundance (see Supplementary Document) (32).
One context in which random variables are multiplied (yielding a
lognormal) is consecutive annual population growth rates, although
the applicability of this across species (i.e., to generate SADs) is
controversial (33), relying on subtle philosophical interpretations
of exchangeability. Some authors such as May (34) and MacArthur
(35) say it can, while others such as Pielou (36) (see page 48) say it
cannot produce a lognormal. This debate, however, is a red herring
because many other biological processes in ecology and evolution
also interact multiplicatively and can influence variation in inter-
specific abundance. For example processes that lead to niche parti-
tioning, stochastic density-dependent differential equation models
(37), models of rates of fixation of favorable alleles (35), or hurdle
models (15) can generate lognormal SADs. Note that in the case of
discrete abundances sampled from a continuous lognormal, we have
a Poisson lognormal (38).
Next, we fit several additional models and statistical distributions
that have been proposed to describe the distribution of commonness
and rarity [see (39, 40) and the Supplementary Materials]. Using
maximum likelihood estimations (MLEs), we fit each distribution
to three ways to assess empirical gSAD: (i) for all of the species
observation records within the BIEN database, (ii) for all species
recorded only from ecological plots, and (iii) for all specimens found
within 100 km around each ecological plot. Comparing the goodness
of fit of various models for each of these gSADs allows us to compare
potential sampling biases in botanical data.
The best model varied with which measure of goodness of fit was
used, as well as with the dataset used (Tables 1 and 2 and tables S1
and S2). However, in general, the truncated Pareto (i.e., a modified
Pareto distribution that adds an additional parameter to allow the
right tail to drop down because of finite sample size (28)] and the
Poisson lognormal (41) both fit well. These models have strong
skew on a log scale, indicative of many rare species. All three models
(at the estimated parameter values) show the mode at species with
one individual. The log series, while also showing a mode at one
individual in a log plot, markedly underestimates the number of
extremely rare species, and the remaining models fit the distribution
even more poorly and have an interior mode, incorrectly predicting
that the most common abundances will be intermediate.
The UNTB predicts that log-series distribution will be approxi-
mated by the fit of the Pareto power distribution, with an exponent,
 = −1.0 (28). However, our fit of the log-series distribution shows
that it was not the best fit and the fitted scaling exponent is steeper
than −1.0 ( MLE = −1.41 for all of the BIEN observations and  MLE =
−1.43 for the observations from ecological plot data; Fig. 2). Thus, a
Pareto power distribution needs an exponent less than −1 to generate
the number of rare species actually observed.
Together, these results underscore that, at continental to global
scales, only a few species abundance distribution models are capable
of producing sufficient numbers of rare species to match the observed
data and that neutral dynamics under the UNTB is not one of them.
The observed value of  for embryophytes is similar to what has been
reported for an extensive dataset for other taxa including animals
and marine phytoplankton (28), suggesting that the shape of the SAD
at increasingly larger spatial scales may converge to a similar distri-
bution across disparate taxa. In sum, the Poisson lognormal is best
fit, the Pareto exponent is markedly steeper than −1.0, and the Pareto
distribution is the second best fit on two of the three metrics.
Assessment of sampling or taxonomic bias
Next, an obvious question is whether the observed number of rare
species is the result of sampling or taxonomic bias. Data from herbar-
ium records are known to exhibit biases in collection and sampling
Fig. 3. Does using the number of observations in botanical datasets provide
a reliable measure of rarity? Assessments of rarity by taxonomic specialists at the
Missouri Botanical Garden and the New York Botanical Garden for a random sample
of 300 species with three observations or fewer in the BIEN database. Most species
(72.7%) identified as “rare” based on the number of unique occurrences within the
BIEN database are also recognized as rare by experts. Approximately 7.3% of these
species appear to be incorrectly characterized as rare, as they are recognized by
experts as abundant or having large ranges. The apparent scarcity of approximately
7.5% of these taxa may reflect recent taxonomic splits or old names no longer
used. Moreover, 10.3% are non-native species (which may or may not be rare). In
sum, we estimate that between 72 and 90% of plant taxa (recognized as rare + recent
name + unresolved + old name) identified by BIEN as being rare would be recog-
nized as rare by other measures.
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(17, 18). However, do these biases influence our identification of
whether a species is rare or not?
We conducted two tests: First, in Fig. 2, we compared the distri-
butions of global abundance in (i) the total BIEN database (including
plot surveys and herbarium records), (ii) only the plot datasets, and
(iii) the subset of herbarium records that reflect the same geographic
distribution as the survey data (e.g., all records within 100 km of any
plot location) (Fig. 2). Ecological plots and surveys, in contrast to
herbarium data, contain less sampling bias, as a robust effort is made
to ensure all individuals within the sampling design are surveyed
within a given area. In many cases, repeated visits ensure accurate
identification to species. Thus, assessing whether the gSAD from
plot data is different from the gSAD from all botanical observations
based on sampling herbarium data at the globe or around plots
enables us to assess potential bias and sampling effectiveness. As
discussed below, both empirical gSADs are described by similar sta-
tistical distributions (e.g., the shape of gSADs in Fig. 2B are similar
to each other and to Fig. 2A; Tables 1 and 2 and tables S1 and S2),
indicating that sampling issues do not greatly influence conclusions
regarding gSADs.
Next, to further assess whether rare species are truly rare or
artifactual, we randomly sampled 300 rare species with three ob-
servations or fewer from the Americas. The Americas were chosen
because our taxonomic expertise was focused on these two conti-
nents. For each species selected, we consulted taxonomic experts at
the Missouri Botanical Garden and the New York Botanical Garden
to sort each species into several classifications (Fig. 3 and see the
Supplementary Materials). Taxonomic experts largely confirm that
the majority of rare species identified by BIEN are rare, with only
7.3% that were clearly erroneous and recognized as abundant or
large-ranged species. We conclude that our results are not driven by
taxonomic and sampling biases.
Our results from Fig. 3 allow us to estimate the total number
of native land plant species currently observed across the globe with
estimates for taxonomic uncertainty. After correcting and standardizing
data, we estimate that the total number of extant embryophyte
(land plant) species on Earth is between ~358,000 and ~435,000.
The lower limit stems from subtracting 17.8% from the total [10.3%
from the remaining presence of naturalized non-native species +7.5%
Table 1. Three different measures of goodness of fit (r2 or percentage of variance explained in the cumulative distribution function, 2 on log2 bins,
and Akaike’s information criterion) are shown for six different species abundance models [see (40)]. All distributions shown have two parameters except
the log-series and power distributions, which have one. Distributions were fitted for the number of observations per species across all species found
(i) within ecological plots only and (ii) across all datasets within the BIEN database. Sampling species found only in plots standardizes for sampling
influences, as all individuals within ecological plots are sampled and identified to species. Thus, the species abundance distribution from ecological
plots is expected to more accurately describe the species abundance distribution. As predicted by the CLT, the Poisson lognormal distribution provides
the best fit to both gSADs. Nonetheless, Pareto and truncated Pareto also all fit well. The log-series distribution, predicted by the k-niche model and
neutral theory, falls behind these distributions across the different goodness-of-fit measures. AIC, Akaike’s information criterion; CDF, cumulative
distribution function.
Model Plot data only All data
CDF r22 log2AIC ∆AIC CDF r22 log2AIC ∆AIC
Zipf-Mandelbrot 0.929 54,188 139,822 25,848 0.447 73,884,947 7,402,206 330,9517
Weibull 0.999 1.6 × 1010 127,111 13,137 0.999 3.01 × 1010 4,269,287 176,598
Log series 0.991 1.57 × 1013 120,082 6109 0.999 5.08 × 1013 4,119,057 26,368
Pareto 0.999 5.69 × 1013 115,244 1270 0.999 1.46 × 1013 4,110,900 18,211
Poisson lognormal 0.999 490 113,974 0 0.999 2966 4,092,689 0
Pareto with finite
sample
exponential
adjustment
0.999 563 114,096 122 0.998 100,558 4,203,550 110,861
Table 2. Parameter fits for each of the fitted statistical distributions.
The estimated slope values, , of the gSAD are given in bold by fits of the
Pareto and Truncated Pareto distributions. Note that the estimated slope
values differ from −1.0 expected from the unified neutral theory of
biodiversity. Instead, the observed fitted slope, , is steeper than expected
from neutral theory (with fitted exponents more negative than −1.0). The
steeper exponents indicate that of all of the observed plant species on
Earth, proportionally more of them are rare and that there are more rare
species than expected by demographic and evolutionary neutral
processes. Thus, the processes creating and maintaining rare species on
Earth generate proportionally more rare species.
Model Plot data All data
Zipf-Mandelbrot, b13.3 1186.7
Zipf-Mandelbrot, c1.4 1.2
Log series, c0.9 0.9
Pareto fitted exponent, −1.4 −1.3
Weibull scale 18.1 40.6
Weibull shape 0.4 0.5
Poisson lognormal, m4.07 × 10−8 1.7
Poisson lognormal, s2.9 2.6
Pareto with finite sample
exponential adjustment (28)
fitted Pareto exponent, 
−1.3 −1.1
Pareto with finite sample
exponential adjustment:
Exponential parameter, 
0.1 0.1
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caused by the inflation of names due to “old names” (basionyms)
not yet corrected for by taxonomic data cleaning; see Fig. 3]. Our
estimates are consistent with previous estimates of the total number
of embryophytes in the world of approximately 391,000 [see (42)]
or 403,911 (43) (see the Supplementary Materials). However, now,
we can quantify that ~36% of these species are highly rare with very
little distributional information for each species. In sum, our results
from Fig. 2 show that rarity is commonplace across the land plants.
Little botanical information exists across the world’s herbaria and
ecological collections for between 11.2 and 13.6% (species with one
observation) or between 30.0 and 36.5% (species with fewer than or
equal to five total observations) of all vascular plant species.
“Hotspots” of rare species
To identify the regions that harbor hotspots of rare species, in
Fig. 4, we mapped the locations of rare species across the world. We
controlled for variation in sampling effort by calculating both the
Menhinick and Margalef indices (see Materials and Methods). Plotting
the sampling-corrected number of rare species reveals several pat-
terns. Rare species cluster in the Americas in (i) mountainous regions
(particularly along the thin strip along the western flank of the
Andean Mountains, Central America, and the southern Sierra Madre
of Mexico), (ii) the Guiana shield in northern South America, and
(iii) relatively small climatic regions that are strongly distinct from
surrounding areas (the Atlantic Forest or Mata Atlântica in Brazil,
the southern region of the California Floristic Province, and the
Caribbean); in Africa in (iv) the Cape Floristic Region of South
Africa, (v) mountainous regions of Madagascar, (vi) the coastal
mountains of Cameroon, and (vii) the Ethiopian highlands and the
Somali peninsula; and in Asia in (viii) southwestern China and the
border regions of Myanmar, Laos, and Thailand, (ix) Malaysia, (x)
New Guinea, and (xi) the mountainous strip from Iran through
Turkey. In Europe, there are several regions of notably high diversity
of rarity in and around (xii) the Mediterranean, including the Pyrenees
and Caucasus.
There is a relative dearth of rare species throughout the Amazon
basin, confirming past claims that the Amazon flora consists largely
of widespread and relatively abundant species (44). The areas iden-
tified by our methods show some overlap with areas independently
identified as biodiversity hotspots (45) (e.g., Mesoamerican high-
lands, the Andes, Southeast Asia, and New Guinea) but differ in
other areas.
Drivers of the spatial distribution of rarity
To assess the drivers of the spatial distribution of rarity, we con-
ducted ordinary least squares (OLS) linear regression and simulta-
neously autoregressive (SAR) models to analyze the relationship
between rarity index and environmental variables, including pres-
ent climate, glacial-interglacial climatic velocity or instability of
climate, and topography. Our OLS models showed that all the
variables (annual mean temperature, annual precipitation, tempera-
ture seasonality, precipitation seasonality, temperature velocity,
precipitation velocity, elevation, and heterogeneity of elevation)
have significant relationships with both the Menhinick rarity index
(tables S3 to S5 and fig. S2) and the Margalef rarity index (tables S6
to S8 and fig. S3), with the largest effects from temperature velocity
and heterogeneity of elevation. In comparing the group models
[present climate (annual mean temperature, annual precipitation,
temperature seasonality, and precipitation seasonality), stability
of climate (temperature and precipitation velocity), and topography
(elevation and heterogeneity of elevation)], the model with instability
of climate tended to outperform models with current climate and
topography, while the full model showed the lowest Akaike’s infor-
mation criterion (AIC). The exhaustively selected model did not
include elevation as a predictor, although it had minor differences
in model performance compared with the full model.
A Moran’s I test showed high spatial autocorrelation in the
residuals of the OLS models, while we found no significant spatial
autocorrelation in the residuals of the SAR models (tables S3 to S8).
The coefficients of the SAR models were generally similar to those
from OLS models, with the exceptions that signs of annual mean
temperature, precipitation seasonality, and precipitation velocity
switched from positive to negative in the SAR model. Temperature
velocity remains the largest negative effect, and heterogeneity of
elevation remains the largest positive effect in the SAR models (see
figs. S2 and S3 and tables S3 to S8). Models incorporating climate
stability and topography outperformed the model with current
climate, while the full model remains the best-performing SAR
model. The modeling results based on Menhinick and Margalef rarity
index showed comparable results (tables S3 to S8 and figs. S2 and S3).
To summarize, areas that contain a higher number of rare spe-
cies have had a more stable climate. The best predictor of plant
rarity is the historical temperature velocity. Climate velocity de-
scribes climate instability with ecologically relevant units (distance/
time; see discussion in Supplementary Document). In addition,
mountainous area, as measured by the SD of elevation, is also a
predictor with positive effect (tables S3 to S8 and figs. S2 and S3).
Adding short-term annual variation (annual seasonality) in tem-
perature and precipitation and mountainous conditions in addition
to climate velocity does improve the explanation of the current
spatial distribution of rarity (e.g., the proportion of variation ex-
plained, R2, increased to 0.193 for the OLS model and to 0.518 for
the SAR model of Menhinick rarity index but less so for Margalef
rarity index, 0.176 for the OLS model and 0.263 for the SAR model;
tables S3 to S8). Together, these results are consistent with previous
results [see (46, 47) and references therein], indicating that increased
rates of climate change velocity negatively affect the retention of
rare species, presumably because of increased rates of extinction
during times of rapid climate change.
The overlaps between future climate velocity and human
footprint and rarity indices
Our environment is facing rapid human changes at the global scale,
so we quantified the intensity of human impact on the area with rare
species (48). Regions with rare species are currently characterized
by higher human impact and will experience faster rates of future
climate change under representative concentration pathway 8.5
(RCP8.5) (Fig. 5). Areas with rare species have human footprint
values of 8.5 ± 5.8, which is ~1.6 times higher (P < 0.001, Wilcoxon
test) than that of the globe on average (5.2 ± 5.8). Furthermore, on
average, areas with rare species are predicted to experience ~200
(±58) times greater rates of temperature velocity than those same areas
experienced historically in terms of the overall glacial-interglacial
climate shift across the past 21,000 years [from the last glacial max-
imum (LGM) to the present]. The ratio between future temperature
velocity and this long-term overall historical temperature velocity
is ~1.2 times greater (P < 0.001, Wilcoxon test) for areas with rare
species than the globe will experience on average (170 ± 77) (Fig. 5).
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This is because areas with concentrations of rare species have pre-
viously been characterized by relatively more stable climates, but
under the predicted climate change under RCP8.5, they will now
experience velocities as high as the rest of the globe (see fig. S5).
Predicted changes of rarity indices
With the previously calibrated OLS and SAR full models, we made
predictions of rarity indices under future projected climate. These
showed worldwide decreases in rarity indices (Fig. 6), with the southern
Andes and Southeast Asia predicted to experience the largest decreases.
These decreases were likely due to the accelerated future climate
velocities under RCP8.5, which are two orders of magnitude higher
than those experienced from LGM [~21 thousand years (ka) ago]
to the present day (see fig. S5). Note, however, that future velocities
are estimated over a shorter time frame, which will tend to produce
higher estimates.
DISCUSSION
Our dataset represents the most comprehensive assembly of global
plant diversity data to date, comprising both plots and herbarium
specimens, from far more sources than previously available. Large
quantities of primary biodiversity data have still not been mobilized,
and those data that are available are subject to various forms of
Fig. 4. Where are rare species distributed geographically? Plotting the geographic coordinates for all the observations for species with three observations or fewer at
a coarse, 1° resolution reveals several patterns. The sampling background is shown (grey cells are areas with no georeferenced botanical sampling records, while yellow
cells indicate re gions with observation records but no rare species). Colored cells correspond to areas with rare species (species with three observations or fewer) rarified
to the sampling intensity using the Margalef index (see the Supplementary Materials). Areas with a proportionally high number of rare species are dark brown (“hotspots of
rarity”), while areas with relatively low numbers of rare species are yellow to orange. Areas with a high number of rare species tend to be clustered in a small number of
locations including mountainous tropical and subtropical regions including New Guinea, Indonesia, southwestern China, Madagascar, the Andes (in Ecuador, Columbia,
and Peru), Central America (Costa Rica and Panama), and southern Mexico. In addition, several notable temperate zone locations including the Fynbos in South Africa and
southwest Australia, Northern Iran/Georgia/Turkey, and the Iberian Peninsula.
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collection bias (17, 18). Thus, it is possible that the patterns we ob-
serve may change with additional data. However, comparison be-
tween plot and all observation gSADs (Fig. 2 and Table 1) indicates
that both sampling methods yield similar results. Furthermore, the
notable efforts we made in data cleaning and curation assure that our
analyses represent, by far, the best window yet into global common-
ness and rarity in plants.
Our results indicate that hotspots of plant biodiversity largely
reflect the accumulation of very rare species. Assessing the predic-
tions of the Unified Theory of Neutral Biogeography [UTNB; (25)]
for the distribution of commonness and rarity across species enables
us to reveal likely drivers of rarity. The UTNB assumes that species
overlap in their niches and are equivalent in their rates of speciation,
extinction, and dispersal (25). It implies that biodiversity arises at
random, as the abundance of each species follows a random walk
so that the distribution of abundances across species is given by a
dynamic equilibrium of speciation and extinction. Our results show
that  ≈ −1.4, indicating that the proportion of plant species that are
rare is higher than expected from neutral processes. Given that rare
species are orders of magnitude more likely to go extinct (4, 5) than
more abundant species, this begs the question: Why do we observe
a larger proportion of observed rare species than expected from
neutral theory?
Our analyses (tables S1 to S8 and figs. S1 to S5) suggest two pri-
mary reasons. First, current hotspots of rare species (Fig. 4) likely
reflect areas with lowered risk of historical extinction. Rare species are
often found in geographic localities that have had more stable climates
that have likely lowered the probability of extinction [see (4, 5)]. Models
that include relative climate stability better explain both the locations
of hotspots of rarity and the shape of rarity distributions. The find-
ing that climate (in)stability is important in non- neutral models has
important real-world implications for ecology and conservation.
Second, rare species are spatially clumped in ways that support
mechanisms for generating and maintaining rare species articulated
Fig. 5. Regions that currently have high numbers of rare species are also characterized by higher human impact and will experience faster rates of future
climate change. (A) Density plot of human footprint index in areas with rare species (light gray) and the global map (dark gray). Areas with rare species have, on
average, human footprint values of 8.5 ± 5.8, which is ~1.6 times higher (P < 0.001, Wilcoxon test) human impact than on the globe on average (5.2 ± 5.8). (B) Densi-
ty plot of the ratio of future climate (temperature) velocity versus historical climate velocity. On average, areas with rare species will experience ~200 (±58) times greater
rates of temperature velocity than those same areas experienced historically and will experience ~1.2 times greater (P < 0.001, Wilcoxon test) rates of temperature
velocity change than the globe will experience on average (170 ± 77). (C) Global variation in the human footprint index. Areas with high human footprint are in
brown. Areas with low human footprint are dark green. (D) Global map of the ratio between future (baseline climate to late century, 1960–1990 to 2060–2080, under
RCP8.5) and historical rates of temperature change [LGM to baseline climate (~21 ka ago to 1960–1990)]. Future temperatures will increase across the globe. However, in
comparison with historical rates of climate change, some areas will experience relatively faster (ratio values greater than 1; yellow to red values) or slower (ratio values less
than 1; green to blue values) rates of change. Note that many of the regions of rarity hotspots are found in regions that will be experiencing relatively faster rates of climate
change compared to historical rates of change.
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by early theorists, who proposed roles for mountains and climate
stability in influencing both rates of speciation and dispersal. In
1964, Simpson (49) hypothesized that “Small population ranges
and numerous barriers against the spread and sympatry of related
populations would therefore tend to increase density of species.”
Janzen’s 1967 (50) “Why mountain passes are higher in the tropics”
extended Simpson’s hypothesis to predict that mountainous regions
in the tropics will harbor proportionally more rare species than
temperate mountains or even topographically uniform tropical
regions due to less variability in climate. Our findings of dispro-
portionate numbers of rare species in mainly tropical mountains
and more isolated regions support these ideas. More recent studies
have also documented the importance of tropical mountains as
harbors of biodiversity (51, 52), which supports our findings.
Our results have important implications for conservation in the
face of climate change and other human impacts. If ~36% of species
are rare and threatened (Figs. 5 and 6), then ~158,000 plant species
are at risk of extinction. Although not all primary biodiversity data
have been digitized, it is still remarkable that ~36% of all plant
species known are only documented a very small number of times. In
addition, our analyses show that rapid rates of current human impact
and projected future climate change appear to disproportionately
affect regions that harbor most of these rare species (Fig. 5), whereas
the rare species likely have been in relatively more stable climates
through their evolutionary history.
Ultimately, rare species, by definition, are more prone to reductions
in population size and extinction and should be high priorities for
conservation (4, 5) . Our results suggest that redoubling global efforts
to conserve rare species is needed and that we have a closing window
to do so. The tools to ensure that these rare species are maintained
are area-based conservation and solutions to climate change (53).
The Convention on Biological Diversity should recognize these areas
as critical to conserving all life on Earth and important focal areas
for expansion of conserved areas after 2020 (54). The climate con-
vention seeks to avoid extinctions due to the exceedance of species’
natural ability to adapt to climate change, making these areas with
high numbers of rare species and very high future-to-historic velocities
of climate change yet another reason the world should move quickly
to curb greenhouse gas emissions (55). Joint climate and biodi-
versity efforts should be made to ensure that these numerous but
little-known species, living in unusual climatic circumstances, persist
into the future.
Fig. 6. What will happen to rare species diversity with climate change? (A) The predicted change in Margalef SAR rarity index under climate change from the au-
toregressive models (SAR). The rarity indices are log-transformed. Large decreases in climate suitability for rare species are in red to orange, whereas smaller reductions
in climate suitability are given in green to blue colors. Note the large decreases in climate suitability for rare species in the Andes and Mesoamerica, African highlands,
New Guinea, southwestern China, Indonesia, Nepal, and New Zealand. (B) The diagonal 1:1 line (red) represents situations of no difference between the predicted current
and future rarity index from SAR and OLS models. All points in the scatter plot are below the diagonal line, indicating a reduction of rare species diversity across all the
areas where they currently occur.
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MATERIALS AND METHODS
Competing different hypothesized gSADs
As we described in the Supplementary Materials, we fit several
additional hypothesized univariate distributions to the gSAD using
the following proposed biological and statistical distributions. Most
theories produced SADs that were so similar to each other that it
was difficult to distinguish them given the noisy data and the fact
that the differences were most pronounced in the tails, which were,
by definition, infrequently observed (40). In Table 1, we provided
several different goodness- of-fit measures. Each emphasizes different
aspects of fit (chi-square on log-binned data emphasizes the fit of
each statistical distribution to rare species, calculating an r2 on the pre-
dicted versus empirical cumulative distribution function); cumulative
distribution function [describes the probability that a random variable,
X, drawn from f(x) is ≤x] emphasizes the abundances with the most
species (usually intermediate abundances), while likelihood em-
phasizes avoidance of extreme outliers. As previously noted, it is
common for different measures of fit to select different SAD theories
as providing the best fit to a single dataset (32). As a result, any
claim of a superior fit must be robust by being superior on multi-
ple measures.
Rarity indices
Because the sampling intensity for plants across the globe is not uni-
form, we assessed the rarified species diversity. For each 1° grid cell,
we calculated the total number of observations or samples, N, as well
as the total number of observed rare species, S; for mapping rarity
across the globe, we focused on the rarist species - those species having
three observation records or fewer. We calculated two separate rarified
diversity measures for each 1° grid cell:
1) Margalef diversity (SMargalef), which assumes that species rich-
ness increases with sampling intensity N and, in particular, increases
nonlinearly and approximately logarithmically with N.
S Margalef = (S − 1 ) / ln N (3)
2) Menhinick diversity (SMenhinick). In a similar vein, the Menhinick
diversity measure assumes that species richness also increases non-
linearly with sampling intensity, N, but according to a square root
function
S Menhinick = S /
√
_
N (4)
As the Menhenick index assumes a square root rarefaction func-
tion and the Margalef assumes a logarithmic rarefaction function,
they represent both a more liberal and more conservative estimate of
higher estimates of richness, respectively. Comparing both measures
of SMargalef and SMenhinick revealed similar spatial maps, indicating that
both measures result in identical conclusions.
Methods for regression models
As described in the Supplementary Materials, we conducted OLS
linear regression models to analyze the relationship between envi-
ronmental variables and rarity index. We included three groups of
environmental variables that portray present climate (annual mean
temperature, annual precipitation, temperature seasonality, and
precipitation seasonality), stability of climate (temperature velocity
and precipitation velocity), and topology (elevation and hetero-
geneity of elevation). We also calculated the SD of elevations within
each one by 1° window and considered this as the heterogeneity
of elevation. We performed log transformation of rarity index, tem-
perature and precipitation velocity, elevation, and heterogeneity of
elevation to get normally distributed residuals in the regression
models. We standardized all variables to zero mean and 1 SD to
make the regression coefficients comparable. With 4571 records (for
Menhinick index, or 2940 for Margalef index) we conducted OLS
linear regression models to explore the bivariate relationship between
rarity index and each environmental variable.
We also constructed multiple regression models using each
group of variables (present climate, stability of climate, and topology)
and using all variables (full model). We conducted multiple re-
gression models through exhaustive model selection based on AIC
values using all environmental predictors. Last, to account for spa-
tial autocorrelation in climate data, we performed Moran’s I test
and SAR models for all the OLS models mentioned above.
Climate change and future predicted
changes in rarity indices
With the previously calibrated full models (OLS and SAR models),
we made predictions of rarity indices under future projected climate.
We used the full models, as they outperformed individual models
or subgroup models and had comparable performances with the
exhaustively selected model. We obtained future climatic variables
from WorldClim (http://www.worldclim.com/CMIP5v1) (56). We used
the future climate in 2070 constructed by the Community Climate
System Model (CCSM4) under RCP8.5 scenario, which has com-
paratively high greenhouse gas emissions (57). To match the reso-
lution of the rarity map, we sampled the environmental variables
(annual temperature, annual precipitation, temperature seasonality,
and precipitation seasonality) to 1° cells. We further calculated the
temperature and precipitation velocity between present and future
following (46). The two topological variables (elevation and hetero-
geneity of elevation) were kept the same as the present. After making
the predictions, we compared the differences between predicted rarity
indices under present and future climate.
Rarity and climate velocity
Using data sources and methods described above in regression model
methods, we derived velocity of temperature change and velocity of
precipitation change over the following periods: LGM to baseline
climate (~21 ka ago to 1960–1990) and baseline climate to late century
(1960–1990 to 2060–2080) (www.worldclim.org/paleo-climate1) under
RCP8.5 (see Supplementary Document). Velocity was calculated
using the neighborhood statistic approach originally described by
Sandel et al. (46); see also (58).We note that our calculation of velocity
of historical climate change and future climate change must be inter-
preted with caution, as they were calculated over different time in-
tervals (46). We compared velocity values at locations where (i) there
are rare species observations and (ii) there are no rare species obser-
vations and to (iii) background sampled locations. This comparison
was conducted for both historical change since LGM and projected
future change.
Rarity and the human footprint
We downloaded global human footprint data (48) and resampled to
the resolution of the rarity map. We extracted the values of human
footprint where rare species exist (i.e., 1° by 1° spatial windows
where one or more rare species are observed) and compared the
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mean of those values with that of the global human footprint map
using the Wilcoxon test.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/
content/full/5/11/eaaz0414/DC1
Supplementary Document
Table S1. As in Table 1 but for specimen data found within 1° proximity to each plot.
Table S2. As with Table 2 but for specimens near plots.
Table S3. Summary statics of OLS linear regression models and SAR models for predicting the
Menhinick rarity index.
Table S4. Summary statics of OLS linear regression models for predicting the Menhinick rarity
index.
Table S5. Summary statics of SAR models for predicting the Menhinick rarity index.
Table S6. Summary statics of OLS linear regression models and SAR models for predicting the
Margalef rarity index.
Table S7. Summary statics of OLS linear regression models for predicting the Margalef rarity
index.
Table S8. Summary statics of SAR models for predicting the Margalef rarity index.
Fig. S1. Sampling density for different data types in BIEN.
Fig. S2. Scatter plots showing the relationships between bivariate relationship between
Menhinick rarity index and environmental variables.
Fig. S3. Scatter plots showing the relationships between bivariate relationship between
Margalef rarity index and environmental variables.
Fig. S4. Predicted changes of Margalef rarity index using either the OLS or the SAR models.
Fig. S5. Historical and future global temperature velocities.
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Acknowledgments: This work was conducted as a part of the BIEN Working Group,
2008–2012. We thank all the data contributors and numerous herbaria who have contributed
their data to various data compiling organizations (see the Supplementary Materials) for the
invaluable data and support provided to BIEN. We thank the New York Botanical Garden;
Missouri Botanical Garden; Utrecht Herbarium; the UNC Herbarium; and GBIF, REMIB, and
SpeciesLink. The staff at CyVerse provided critical computational assistance. We thank the
more than 50 scientists who participated in our various BIEN working group and subgroup
meetings since 2008 including B. Blonder, K. Engemann, E. Fegraus, J. Cavender-Bares,
B. Dobrin, K. Gendler, R. Jorgensen, G. Lopez-Gonzalez, L. Zhenyuan, S. McKay, O. Phillips,
J. Pickering, N. Swenson, C. Vriesendorp, and K. Woods, who participated in a working group
meeting, and D. Ackerly, E. Garnier, R. Guralnick, W. Jetz, J. Macklin, N. Matasci, S. Ramteke, and
A. Zanne who participated in subgroup meetings. We also acknowledge the critical support
of the University of Arizona high-performance computing resources via the Research Data
Center as well as iPlant and CyVerse support from R. Jorgensen, S. Goff, N. Matasci,
N. Merchant, M. Narrow, and R. Walls. Furthermore, the long-term vision, encouragement, and
computational support of F. Davis, S. Hampton, M. Jones, N. Outin, and the ever-helpful staff at
NCEAS were critical for the completion of this first stage of the BIEN working group. Special
thanks to K. Koenig for cartographic support. We acknowledge the herbaria that contributed
data to this work: A, AAH, AAS, AAU, ABH, ACAD, ACOR, AD, AFS, AK, AKPM, ALCB, ALTA, ALU,
AMD, AMES, AMNH, AMO, ANGU, ANSM, ANSP, AQP, ARAN, ARIZ, AS, ASDM, ASU, AUT, AV,
AWH, B, BA, BAA, BAB, BABY, BACP, BAF, BAFC, BAI, BAJ, BAL, BARC, BAS, BBB, BBS, BC, BCMEX,
BCN, BCRU, BEREA, BESA, BG, BH, BHCB, BIO, BISH, BLA, BM, BOCH, BOL, BOLV, BONN, BOON,
BOTU, BOUM, BPI, BR, BREM, BRI, BRIT, BRLU, BRM, BSB, BUT, C, CALI, CAN, CANB, CANU, CAS,
CATA, CATIE, CAY, CBM, CDA, CDBI, CEN, CEPEC, CESJ, CGE, CGMS, CHAM, CHAPA, CHAS, CHR,
CHSC, CIB, CICY, CIIDIR, CIMI, CINC, CLEMS, CLF, CMM, CMMEX, CNPO, CNS, COA, COAH, COCA,
CODAGEM, COFC, COL, COLO, CONC, CORD, CP, CPAP, CPUN, CR, CRAI, CRP, CS, CSU, CSUSB,
CTES, CTESN, CU, CUVC, CUZ, CVRD, DAO, DAV, DBG, DBN, DES, DLF, DNA, DPU, DR, DS, DSM,
DUKE, DUSS, E, EA, EAC, EAN, EBUM, ECON, EIF, EIU, EMMA, ENCB, ER, ERA, ESA, ETH, F, FAA,
FAU, FAUC, FB, FCME, FCO, FCQ, FEN, FHO, FI, FLAS, FLOR, FM, FR, FRU, FSU, FTG, FUEL, FULD,
FURB, G, GAT, GB, GDA, GENT, GES, GH, GI, GLM, GMDRC, GMNHJ, GOET, GRA, GUA, GZU, H, HA,
HAC, HAL, HAM, HAMAB, HAO, HAS, HASU, HB, HBG, HBR, HCIB, HEID, HGM, HIB, HIP, HNT, HO,
HPL, HRCB, HRP, HSC, HSS, HU, HUA, HUAA, HUAL, HUAZ, HUCP, HUEFS, HUEM, HUFU, HUJ,
HUSA, HUT, HXBH, HYO, IAA, IAC, IAN, IB, IBGE, IBK, IBSC, IBUG, ICEL, ICESI, ICN, IEA, IEB, ILL, ILLS,
IMSSM, INB, INEGI, INIF, INM, INPA, IPA, IPRN, IRVC, ISC, ISKW, ISL, ISTC, ISU, IZAC, IZTA, JACA,
JBAG, JBGP, JCT, JE, JEPS, JOTR, JROH, JUA, JYV, K, KIEL, KMN, KMNH, KOELN, KOR, KPM, KSC,
KSTC, KSU, KTU, KU, KUN, KYO, L, LA, LAGU, LBG, LD, LE, LEB, LIL, LINC, LINN, LISE, LISI, LISU, LL,
LMS, LOJA, LOMA, LP, LPAG, LPB, LPD, LPS, LSU, LSUM, LTB, LTR, LW, LYJB, LZ, M, MA, MACF,
MAF, MAK, MARS, MARY, MASS, MB, MBK, MBM, MBML, MCNS, MEL, MELU, MEN, MERL, MEXU,
MFA, MFU, MG, MGC, MICH, MIL, MIN, MISSA, MJG, MMMN, MNHM, MNHN, MO, MOL, MOR,
MPN, MPU, MPUC, MSB, MSC, MSUN, MT, MTMG, MU, MUB, MUR, MVFA, MVFQ, MVJB, MVM,
MW, MY, N, NA, NAC, NAS, NCU, NE, NH, NHM, NHMC, NHT, NLH, NM, NMB, NMNL, NMR, NMSU,
NSPM, NSW, NT, NU, NUM, NY, NZFRI, O, OBI, ODU, OS, OSA, OSC, OSH, OULU, OWU, OXF, P,
PACA, PAMP, PAR, PASA, PDD, PE, PEL, PERTH, PEUFR, PFC, PGM, PH, PKDC, PLAT, PMA, POM,
PORT, PR, PRC, PRE, PSU, PY, QCA, QCNE, QFA, QM, QRS, QUE, R, RAS, RB, RBR, REG, RELC, RFA,
RIOC, RM, RNG, RSA, RYU, S, SACT, SALA, SAM, SAN, SANT, SAPS, SASK, SAV, SBBG, SBT, SCFS,
SD, SDSU, SEL, SEV, SF, SFV, SGO, SI, SIU, SJRP, SJSU, SLPM, SMDB, SMF, SNM, SOM, SP, SPF,
SPSF, SQF, SRFA, STL, STU, SUU, SVG, TAES, TAI, TAIF, TALL, TAM, TAMU, TAN, TASH, TEF, TENN,
TEPB, TEX, TFC, TI, TKPM, TNS, TO, TOYA, TRA, TRH, TROM, TRT, TRTE, TU, TUB, U, UADY, UAM,
UAMIZ, UB, UBC, UC, UCMM, UCR, UCS, UCSB, UCSC, UEC, UESC, UFG, UFMA, UFMT, UFP, UFRJ,
UFRN, UFS, UGDA, UH, UI, UJAT, ULM, ULS, UME, UMO, UNA, UNB, UNCC, UNEX, UNITEC, UNL,
UNM, UNR, UNSL, UPCB, UPEI, UPNA, UPS, US, USAS, USF, USJ, USM, USNC, USP, USZ, UT, UTC,
UTEP, UU, UVIC, UWO, V, VAL, VALD, VDB, VEN, VIT, VMSL, VT, W, WAG, WAT, WELT, WFU, WII,
WIN, WIS, WMNH, WOLL, WS, WTU, WU, XAL, YAMA, Z, ZMT, ZSS, and ZT. Funding: The BIEN
working group was supported by the National Center for Ecological Analysis and Synthesis, a
center funded by NSF EF-0553768 at the University of California, Santa Barbara and the State of
California. Additional support for the BIEN working group was provided by iPlant/CyVerse via
NSF DBI-0735191. B.J.E., B.J.M., and C.M. were supported by NSF ABI-1565118. B.J.E. and C.M.
were supported by NSF HDR-1934790. B.J.E., L.H., R.T.C., G.M., W.F., and P.R.R. were supported
by the Global Environment Facility SPARC project grant (GEF-5810). N.M.-H. was supported by
the European Union’s Horizon 2020 research and innovation program under the Marie
Sklodowska-Curie grant agreement no. 746334 and acknowledges the Danish National
Research Foundation for support to the Center for Macroecology, Evolution and Climate (grant
no. DNRF96). C.V. was supported by a Marie Curie International Outgoing Fellowship within
the 7th European Community Framework Program (DiversiTraits project no. 221060) and by
the European Research Council (ERC) Starting Grant Project (grant ERC-StG-2014-639706-
CONSTRAINTS). B.J.E., B.M., N.J.B.K., C.V., and B.J.M. acknowledge the FREE group funded by the
synthesis center CESAB of the French Foundation for Research on Biodiversity (FRB) and
EDF. J.-C.S. and B.J.E. acknowledge support from the Center for Informatics Research on
Complexity in Ecology (CIRCE), funded by the Aarhus University Research Foundation under
the AU Ideas program. J.-C.S. also considers this work a contribution to his VILLUM Investigator
project “Biodiversity dynamics in a changing world” funded by VILLUM FONDEN (grant 16549).
X.F., D.S.P., and E.A.N. were supported by the University of Arizona Bridging Biodiversity and
Conservation Science program. C.M. acknowledges funding from NSF Grant DBI-1913673. S.K.W.
acknowledges funding from the Strategic Science Investment Fund to Crown Research
Institutes from the New Zealand Ministry of Business, Innovation and Employment. I.Š. was
supported by the Charles University (UNCE 204069). T.L.P.C., G.D., and J.J.W. acknowledge the
French FRB and the Provence-Alpes-Côte d’Azur région (PACA) through the Centre
for Synthesis and Analysis of Biodiversity (CESAB) data program, as part of the RAINBIO
research project. Author contributions: B.J.E. and B.J.M. designed the study. B.B., X.F., B.M., and
D.S.P. integrated and cleaned data. P.M.J., B.M.T., T.L.P.C., G.D., D.M.N., A.T.O.-F., R.K.P., J.M.S.-D., J.J.W.,
W.F., and S.K.W., contributed data. B.J.E., B.J.M., X.F., B.M., B.B., and P.R.R. performed the analyses.
B.J.E., B.J.M., J.M.S.-D., L.H., P.M.J., B.M.T., X.F., B.B., B.S., E.A.N., P.M.J., P.R.R., B.M.T., J.R.B.,
R.T.C., T.L.P.C., J.C.D., J.C.L., P.A.M., C.M., G.M., N.M.-H., N.J.B.K., D.S.P., R.K.P., M.P., J.M.S.-D., B.S.,
M.S., I.S. C.V., S.K.W., and J.-C.S. helped interpret and analyze results. All authors helped collect
and assemble data. B.J.E. wrote the first draft of the manuscript, and all authors contributed
to revisions. Competing interests: The authors declare that they have no competing
interests. Data and materials availability: All data needed to evaluate the conclusions in
the paper are present in the paper and/or the Supplementary Materials. All data and code
used in this study are available via GitHub, https://github.com/EnquistLab/BIEN_Rarity. The
MATLAB code used for fitting gSADs are available from B.J.M. upon request. The public
version of the BIEN database is accessible via the BIEN R package, https://cran.r-project.org/
web/packages/BIEN/index.html. Additional data related to this paper may be requested
from the authors.
Submitted 8 August 2019
Accepted 4 November 2019
Published 27 November 2019
10.1126/sciadv.aaz0414
Citation: B. J. Enquist, X. Feng, B. Boyle, B. Maitner, E. A. Newman, P. M. Jørgensen, P. R. Roehrdanz,
B. M. Thiers, J. R. Burger, R. T. Corlett, T. L. P. Couvreur, G. Dauby, J. C. Donoghue, W. Foden, J. C. Lovett,
P. A. Marquet, C. Merow, G. Midgley, N. Morueta-Holme, D. M. Neves, A. T. Oliveira-Filho, N. J. B. Kraft,
D. S. Park, R. K. Peet, M. Pillet, J. M. Serra-Diaz, B. Sandel, M. Schildhauer, I. Šímová, C. Violle, J. J. Wieringa,
S. K. Wiser, L. Hannah, J.-C. Svenning, B. J. McGill, The commonness of rarity: Global and future
distribution of rarity across land plants. Sci. Adv. 5, eaaz0414 (2019).
on December 20, 2019http://advances.sciencemag.org/Downloaded from

The commonness of rarity: Global and future distribution of rarity across land plants
McGill
Schildhauer, Irena Símová, Cyrille Violle, Jan J. Wieringa, Susan K. Wiser, Lee Hannah, Jens-Christian Svenning and Brian J.
Oliveira-Filho, Nathan J. B. Kraft, Daniel S. Park, Robert K. Peet, Michiel Pillet, Josep M. Serra-Diaz, Brody Sandel, Mark
Foden, Jon C. Lovett, Pablo A. Marquet, Cory Merow, Guy Midgley, Naia Morueta-Holme, Danilo M. Neves, Ary T.
Barbara M. Thiers, Joseph R. Burger, Richard T. Corlett, Thomas L. P. Couvreur, Gilles Dauby, John C. Donoghue, Wendy
Brian J. Enquist, Xiao Feng, Brad Boyle, Brian Maitner, Erica A. Newman, Peter Møller Jørgensen, Patrick R. Roehrdanz,
DOI: 10.1126/sciadv.aaz0414
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REFERENCES http://advances.sciencemag.org/content/5/11/eaaz0414#BIBL
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