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Mass extinction in poorly known taxa
Claire Régnier
a,1,2
, Guillaume Achaz
b,c,d,1
, Amaury Lambert
d,e,f
, Robert H. Cowie
g
, Philippe Bouchet
a
,
and Benoît Fontaine
h
a
Institut de Systématique, Evolution, Biodiversité, UMR 7205 CNRS Muséum national d’Histoire naturelle (MNHN), Université Pierre et Marie Curie (UPMC),
Ecole pratique des hautes études (EPHE), Muséum national d’Histoire naturelle, Sorbonne Universités, 75231 Paris Cedex 05, France;
b
UMR 7138, CNRS
Evolution Paris Seine, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France;
c
Atelier de Bioinformatique, Université Pierre et Marie Curie, 75252
Paris Cedex 05, France;
d
UMR 7241, INSERM U1050, Center for Interdisciplinary Research in Biology, Collège de France, 75005 Paris, France;
e
UMR 7599
Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, CNRS, 75252 Paris Cedex 05, France;
f
UMR 7599 Laboratoire de
Probabilités et Modèles Aléatoires, Université Paris Diderot, CNRS, 75252 Paris Cedex 05, France;
g
Pacific Biosciences Research Center, University of Hawaii,
Honolulu, HI 96822; and
h
UMR 7204, Département Ecologie et Gestion de la Biodiversité, Muséum National d’Histoire Naturelle, 75231 Paris Cedex 05, France
Edited by Peter M. Kareiva, The Nature Conservancy, Seattle, WA, and approved May 5, 2015 (received for review February 5, 2015)
Since the 1980s, many have suggested we are in the midst of a
massive extinction crisis, yet only 799 (0.04%) of the 1.9 million
known recent species are recorded as extinct, questioning the
reality of the crisis. This low figure is due to the fact that the status
of very few invertebrates, which represent the bulk of biodiver-
sity, have been evaluated. Here we show, based on extrapolation
from a random sample of land snail species via two independent
approaches, that we may already have lost 7% (130,000 extinc-
tions) of the species on Earth. However, this loss is masked by the
emphasis on terrestrial vertebrates, the target of most conserva-
tion actions. Projections of species extinction rates are controver-
sial because invertebrates are essentially excluded from these
scenarios. Invertebrates can and must be assessed if we are to
obtain a more realistic picture of the sixth extinction crisis.
biodiversity crisis
|
invertebrates
|
IUCN Red List
Status of Invertebrates in the International Union for the
Conservation of Nature Red List
Biodiversity decline has been of concern for several decades (1–
3). However, the International Union for the Conservation of
Nature (IUCN) Red List, the most widely used tool to measure
this decline at a global level (4), lists fewer than 800 modern
extinctions (5), an infinitesimal fraction of the total number of
extant species, commonly estimated at 5–10 million (6, 7). Al-
though the Red List is primarily a tool for identifying those
species that are most threatened and thus most in need of con-
servation action, and not a rigorous catalog of extinctions, re-
actions to this low number of documented extinctions have
ranged from eco-skepticism (8) to eco-satisfaction, the low
number seen by some as a measure of the success of conservation
programs (9). However, there is a bias in estimates of bio-
diversity decline, because most of them focus on mammals and
birds (10). Assessment of a species’conservation status accord-
ing to the IUCN criteria requires robust data on geographic
range, population trends, threats, habitat, and ecology, such that
the evaluation is rigorous and unassailable. This quality of data is
available essentially for only a handful of remarkable species,
almost exclusively vertebrates. By 2013, all 15,528 known bird
and mammal species had been evaluated against the IUCN Red
List criteria (5), with only 5.8% ranked as data deficient (not
allocable to one of the other IUCN categories: extinct, extinct in
the wild, critically endangered, endangered, vulnerable, near
threatened, and least concern). We thus have a fairly good pic-
ture of how the biodiversity crisis is impacting mammals and
birds, especially large charismatic ones (e.g., rhinos, large ceta-
ceans, tigers, and condors), but we are still in the mist for most
invertebrate taxa, a consequence of their poorly documented
conservation status (11, 12). Only 15,911 invertebrate species of
∼1.4 million described (13) are listed by IUCN. Of these, only
28% are categorized as data deficient, a proportion that may
seem low (i.e., the conservation status of almost three-quarters
of the invertebrate species evaluated could indeed be assessed).
However, the invertebrate species that have gone through the
Red List process belong to relatively charismatic and well-stud-
ied groups, such as butterflies, dragonflies, reef-building corals,
and certain snails. Because of the lack of information on threats
to invertebrates, the vast majority of species are not addressed by
the Red List process (14). If, instead, IUCN evaluated randomly
chosen invertebrates, the proportion of species that could not be
assessed would be much higher. The fact is that after more than
four decades of IUCN Red Lists, invertebrates are still essen-
tially unevaluated overall, because for many of these species, the
only useful data are, at best, collection dates and localities,
sometimes only type localities (13, 15).
Gathering All Available Information on Poorly Known
Species
Here, we suggest two alternative methods to assess the conser-
vation status of poorly known species. We test these methods on
a sample of land snail species from around the world. Mollusks
are particularly suitable for this evaluation, being the group the
most impacted by extinction according to the IUCN Red List
(16, 17). Moreover, a large community of both professional and
amateur scientists has long been involved in recording locality
data and vouchering specimens in reference collections. A ran-
dom worldwide sample of 200 pulmonate land snail species
was drawn from the literature and data relevant for evaluating
their conservation status were compiled from (i) the literature
Significance
Since the 1980s, many biologists have concluded that the earth is
in the midst of a massive biodiversity extinction crisis caused by
human activities. Yet fewer than 1,000 of the planet’s 1.9 million
known species are officially recorded as extinct. Skeptics have
therefore asked “Is there really a crisis?”Mammals and birds
provide the most robust data, because the status of almost all
has been assessed. Invertebrates constitute over 99% of species
diversity, but the status of only a tiny fractionhas been assessed,
thereby dramatically underestimating overall levels of extinc-
tion. Using data on terrestrial invertebrates, this study estimates
that we may already have lost 7% of the species on Earth and
that the biodiversity crisis is real.
Author contributions: C.R., G.A., A.L., P.B., and B.F. designed research; C.R. performed
research; G.A. and A.L. contributed new reagents/analytic tools; C.R. and G.A. analyzed
data; and C.R., R.H.C., and B.F. 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
C.R. and G.A. contributed equally to this work.
2
To whom correspondence should be addressed. Email: cregnier@mnhn.fr.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1502350112/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1502350112 PNAS Early Edition
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(SI Discussion), including gray literature, (ii) museum collec-
tions, and (iii) consultation with experts (SI Discussion). The
literature search resulted in 932 references, of which 80% fo-
cused primarily on taxonomy, 32% provided localities, 26%
provided dates of collection, and 11% gave information on
habitat, range, abundance, and ecology. The collections of five
major natural history museums were searched, either via their
online databases or directly, to gather additional unpublished
data on collection dates and localities. Experts with local
knowledge of regional faunas or with global knowledge on par-
ticular groups of species were consulted if available. Of the 200
species, nine (4.5%) were already on the Red List (three as ex-
tinct, two as threatened, two as near threatened, one as least
concern, and one as data deficient). Sixty-one (30.5%) had not
been recorded in the field since their original description, and 79
(39.5%) had not been recorded in the previous 50 y (Fig. 1).
Sixty-seven species (33.5%) are known from one locality only,
and for 37 species (18.5%) we did not find a precise locality
(geographic coordinates or named locality that could be pin-
pointed on a map to within a few kilometers).
Results
Experts Assess 10% of the Sampled Species As Extinct. Data on
ecology and distribution, of the robustness required for standard
IUCN assessments (SI Discussion), were found for only 31 spe-
cies; thus, according to the IUCN criteria, 84.5% of our sample
wouldbelistedasdatadeficientintheRedList(Fig. S1).
However, based on expert knowledge of species and threat levels,
we suggest an alternative assessment method (SI Discussion), and
provide the following two examples of the approach. Amastra
baldwiniana, endemic to the Hawaiian island of Maui (and
member of the endemic Hawaiian family Amastridae), would not
be listed as extinct under the IUCN criteria because no targeted
surveys have been conducted to search for the species and be-
cause no confirmed date of extinction is known. However, it is
well understood (16, 18, 19) that amastrids have declined dras-
tically in the Hawaiian Islands through loss of habitat and in-
troduction of invasive species; and, given the taskforce of both
professional land snail researchers and amateur shell collectors in
Hawaii, and the manageable size of the area to be searched, it is
very unlikely that this species would not have been found in the
last few decades if it still survived. Consequently, the experts are
reasonably sure that this species is extinct, and we would classify it
as such. Conversely, Eucalodium moussonianum (Urocoptidae),
from Mexico, has not been recorded since its original description
in 1872 from the State of Vera Cruz, and there are no data on its
distribution or habitat preferences. Given the paucity of field
surveys in Mexico, the possibility that the species still survives
cannot be excluded, and we would classify it as impossible to
assess. Based on this approach, 91 species (45.5%) would be
assessed as not threatened, seven (3.5%) as threatened, 20 (10%)
as extinct, and 82 (41%) as impossible to assess. Note that these
categories are parallel but not identical to the IUCN categories
(Materials and Methods).
Stochastic Modeling Approach Is Congruent with Expert Approach.
Because the method outlined above relies mostly on supposition
derived from interpretation of data and expert opinion and
therefore is somewhat subjective, we compared the results with
those from a mathematical modeling approach that uses collec-
tion records. Similar approaches have been implemented to as-
sess extinction dates of well-known extinct mammal and bird
species (20, 21). We inferred an extinction probability for each of
our 200 species by comparing dates of collection of a species with
overall land snail sampling effort. Dates of sampling of land
mollusks were compiled from the entire collections of four major
museums (SI Discussion), and the number of collection dates was
used as a proxy for sampling effort. The dataset was split into 14
geographic areas (Fig. S2) according to their similarities in terms
of biogeography, history of sampling, and factors driving species
to extinction. A discrete probabilistic model was built (Materials
and Methods and SI Discussion) to estimate three parameters for
each species: a global date of extinction rate shift (S), after which
extinctions become possible, and, for each geographic area, a
probability of extinction per year (μ) and a probability of col-
lecting the species when field work took place (λ) (Fig. 2).
The date Sof the extinction rate shift was estimated by pooling
all species and finding the mean of its a posteriori distribution.
0
50
100
150
200
1800 1850 1900 1950 2000
Species
Field Surveys
Successfull Collections
Years
Fig. 1. Collection dates for 200 randomly selected land snail species. Collection dates, recorded from the literature, museum collections, and consultation
with experts for 200 randomly selected land snail species, ordered by date of last collection. Each horizontal line represents all of the collection dates for a
single species from 1786 until 2012. Open circles (○; top line) represent all collection dates of mollusks (i.e., proxy for sampling effort). Note the large
proportion of species known only from the original collection (e.g., most species between lines 150 and 200).
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The estimate of Sfound by this method is 1894 (Fig. S3). The
historical context can be invoked to explain this result. The end
of the 19th century was the time of the second industrial revo-
lution, that mostly happened in the Western world, but was
concomitant with extensive human colonization of preserved
natural habitat all over the world, such as in North America or in
the midelevation areas of oceanic islands. Because of the pre-
ponderant role of recent extinctions in Polynesia in our data, at
least the second explanation should be considered seriously.
The μand λparameters were estimated independently for
each of the 14 geographic areas. Then, for each species of each
geographic area, using the three estimated parameters, we
computed the ratio of “the probability of being currently ex-
tant but not collected”to “the probability of being extinct”to
assess its status.
The expert and model approaches lead to the same general
result (Fig. 3; Fig. S1), that the number of extinct species is closer
to 7% of biodiversity (130,000 known nonmarine animal species
extinctions out of 1.9 million described species) than to the
0.04% currently suggested by the IUCN Red List [if we accept
the current figure of 799 extinct species in the Red List (5) and
1.9 million named species (13)].
Fig. 3 shows clear heterogeneity in extinction numbers among
geographic areas. In Polynesia, ∼75% of the sampled species are
considered extinct by both approaches. In North America, where
species have on average much larger ranges than in oceanic is-
lands and are thus less prone to extinction, more than 90% of the
sampled species are extant. Large-range species also occur in
Africa and in South America, but North America is compara-
tively more surveyed, hence the lower number of impossible-to-
assess species.
There are some discrepancies between the results of the two
approaches, but their explanation is straightforward (SI Discus-
sion). Generally, however, the model approach is more pessi-
mistic than the expert one: 25 species should be declared extinct
as opposed to 20, because for some species that were assessed as
extinct by the model, experts suggested that even with recent
surveys in the geographic area considered, lack of data on these
species could be due to lack of surveying effort. For instance, E.
moussonianum (see above) was evaluated as extinct by the model
because there have been unsuccessful surveys in Central Amer-
ica as recently as 2011. However, experts classify it as impossible
to assess because, despite these surveys, so much of Mexico and
Central America, generally, remains insufficiently explored for
mollusks, and recent data are limited regarding species status,
range, and availability of suitable habitat, knowledge that is not
incorporated by the model.
Discussion
Conservation Status Must Be Assessed for Poorly Known Species.
Both approaches, using available data that cannot be in-
tegrated into the current IUCN evaluation methodology, suggest
that the status of most land snails (and probably nonmarine in-
vertebrates) can indeed be evaluated; if it exists, the expertise of
taxonomists should be used, and natural history museums offer a
wealth of data suitable for the evaluation of conservation status.
With appropriate models, it is possible to allocate a conservation
status to a major proportion of the invertebrate species that
currently languish in the shadows out of the conservation spot-
lights, provided that their biological and ecological characteris-
tics make them suitable for this kind of evaluations. Nonmarine
arthropods in general, and most specifically insects, share such
characteristics with land snails: size, restricted range, rarity, and
specific habitat requirements (22, 23). Moreover, most recorded
extinctions involve island endemic species, and range size and
level of endemism in marine species are poorly documented (24,
25): for these reasons, our approaches should only be extrapo-
lated to nonmarine fauna.
Some may argue that past and current extinction rate pre-
dictions have failed to forecast changes in biodiversity because
current figures do not reflect the dramatic losses that conserva-
tionists had expected to occur 30 y ago (9). Recently, several
studies have attempted to refine such predictions by developing a
better understanding of the major drivers of biodiversity changes
(26, 27), using process-based models and applying them to
groups for which sufficient data exist, i.e., mammals and birds.
The current Red List underestimates the actual number of ex-
tinct and threatened invertebrate species: there are almost seven
times as many extinctions in our sample as would have been
listed following the IUCN criteria, and we suggest that discrep-
ancies of this order of magnitude, or greater, given that mollusks
are one of the better known invertebrate groups, should be
expected for other invertebrate groups. We contend that pro-
jections of species extinction rates are controversial not because
of methodological challenges but because the “other 99%”of
biodiversity, i.e., invertebrates (11), are continually excluded
from these scenarios. With an “extant until proven extinct”(28)
approach, any poorly studied taxonomic group or geographic
region is bound to escape the conservation spotlight. However, a
number of studies (17, 29, 30) and our own work suggest that
invertebrate extinctions are mostly overlooked: we suggest that
we have probably already lost 7% of described living species of
the world. On oceanic islands, there is evidence that this per-
centage is much higher (17, 19, 31).
The Red List is primarily a tool for identifying those species
that are most threatened and thus most in need of conservation
action, and it works well for charismatic species (mainly terres-
trial vertebrates) for which it measures levels of threats and
time (in years)
Extinction rate shift (unkown)
S
Extinction year (unkown)
E
t*
Last collect (observed)
T
Last eld survey (observed)
Unsuccessfull Collections (extant species)
Successfull Collections Unsuccessfull Collections (extinct species)
Years without eld survey
Fig. 2. Schematic representation of data used in the probabilistic model for a single hypothetical species. Black circles (●), years in which the species was
found; open circles (○), years when searches were undertaken but the species was not found; dashes, years in which there were no searches. The year in which
the species was last seen is designated t*, and the year of the last survey is T. Extinction can happen only after year S(year of extinction rate shift), and after
the last successful search. The extinction year (E) is unknown. Given the sampling effort before and after the last collection (number of searches, successful or
not), the model assesses whether not finding a species is due to extinction or to insufficient sampling.
Régnier et al. PNAS Early Edition
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success of conservation measures, especially for conservation-
dependent large vertebrates such as the California condor,
mountain gorilla, or white rhino. For mammals and birds, the
IUCN Red List also documents extinction correctly, and the
figure it gives of 1.3% of mammal and bird species being extinct
is probably quite accurate, all these taxa having been thoroughly
evaluated. But the Red List does a poor job of estimating ex-
tinction on a global scale across all taxa and should not be used for
this purpose: there are many documented invertebrate extinctions
that are not in the Red List (17, 32). Our suggestion that 7% of
modern species are extinct is closer to the truth than the 1.3% that
is based only on the species evaluated in the Red List.
Data acquisition for invertebrates is far behind that for ter-
restrial vertebrates, yet the IUCN procedure for categorization
requires that the data processing should be based on the same
categories and criteria as for terrestrial vertebrates. For the bulk
of invertebrates, most of the data are locality and date of col-
lection information currently residing in museum collections and
the personal collections of professional and amateur taxono-
mists. Such data are not readily evaluated against the IUCN
criteria, unlike the ecological and demographic data that are
widely available for terrestrial vertebrates, which are often the
result of studies by numerous scientists on just one or a few species.
However, our aim is not to improve the IUCN Red List ap-
proach or to adapt its criteria for invertebrates. Instead, we
suggest an alternative approach, aimed at measuring levels of
extinction globally (and not at evaluating threats and conserva-
tion actions). Our approach accepts some level of uncertainty for
individual species, but at a large scale, it aims to provide an es-
timate of the true level of extinction, something which is neither
a priority of the Red List nor something that it is designed to
accomplish. The Red List and our approach are not mutually
TROPICAL ASIA
SOUT
H
H AMERICA W
ES
ES
T
T INDIES
NORTH A
ME
MERICA
EASTERN ASIA
W
ES
ESTERN ASIA
MACARONESIA
POLYNESIA
SUB-S
AHA
AHARA
N
N AFRICA
INDIAN OCEAN
WESTERN PACIFIC
CENTRAL AMERICA
NORTH AFRICA
EUROPE
Fig. 3. Number of mollusk species in our sample assigned to the different extinction risk categories. Assessments are given according to the model pre-
diction, the expert assessment, and the IUCN criteria. The IUCN categories are simplified in this figure such that endangered includes the categories critically
endangered, endangered, and vulnerable, and extant includes the categories least concern and near threatened. Color coding of the model assessments are
graded to reflect the probabilistic nature of the assessments.
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exclusive but represent complementary mechanisms for doc-
umenting the biodiversity crisis.
Because the expert and model approaches, which we developed
independently, are remarkably consistent in this study, our estimated
fraction of extinct species appears to be genuinely robust, and this
suggests that the current Red List approach grossly underestimates
the extinction crisis for invertebrates. Either we essentially only as-
sess vertebrates, butterflies, and a few snails using the strict IUCN
criteria, and accept that we have almost no idea for the rest of
biodiversity, or we accept some educated guesses by experts, often
based on museum collection data, and/or inferences made from
proxy data processed through suitable models, to get closer to the
real picture. Model-based analyses are reproducible, quantitative,
and can be rigorously evaluated. Because there has been a steady
effort to render IUCN criteria stricter, quantified, and objective (4),
we believe that adding the model approach to our study constitutes a
step forward in the evaluation of the extinction crisis.
Materials and Methods
Species Sampling. In the absence of a global checklist of the terrestrial
mollusks of the world, we used Schileyko’sTreatise on Recent Terrestrial
Pulmonate Molluscs (33). We first ordered the genera according to Schileyko’s
treatment, in which the number of species in every genus is given, allowing us
to generate a list of species numbers from 1 to 17,102. Species and subspecies
were treated similarly, because they both represent distinct, recognizable taxa,
and because subspecies rank is subject to change depending on authors and
species concepts. In the rest of the article, we use the term “species”for ter-
minal taxa. We then generated 200 random numbers between 1 and 17,102.
For each genus in which one or more of these numbers fell, we generated a list
of all known species (from multiple sources, because Schileyko does not treat
all species individually) and ordered them alphabetically, each named species
in these genera thereby being given a number. We then selected those 200
species corresponding to the original set of 200 random numbers.
Data Compilation.
Bibliographic search. The following online databases were queried to accumu-
late as much published information as possible on the 200 species: Thomson
Reuters (formerly ISI) Web of Knowledge (including Zoological Record), Bio-
diversity Heritage Library, Google Books, Google Scholar supplemented by a
search on Google and manual search in the extensive malacological library at
the Museum National d’Histoire Naturelle (MNHN) in Paris.
Museum collections. We augmented the bibliographic data with collection date
and locality information from the online collection databases of four US
natural history museums: Museum of Comparative Zoology, Harvard Uni-
versity; Field Museum, Chicago; National Museum of Natural History,
Washington, DC; Academy of Natural Sciences, Philadelphia. In addition, we
manually searched the collections of the MNHN on site.
For the model approach, we also compiled all of the known collection
dates globally for all terrestrial mollusks from the four museum collection
databases (above).
Consultation with experts. Experts (taxonomists specialized in a given molluscan
family or geographic region; list found in Acknowledgments) were asked
whether (i) they had personally collected the species in the field, (ii ) they
could make an educated guess regarding its conservation status, and (iii)they
were aware of recent indications, published or unpublished, of where and
when this species had been last seen: e.g., published records, museum or
personal collections, or personal field work.
Conservation Status Assessments.
Assessment according to the IUCN categories and criteria. All 200 species were
evaluated according to the IUCN criteria and placed in the appropriate
category (34) (Fig. S1). Even if some relevant information—e.g., indicating a
range reduction—was available for a species, it was considered as data de-
ficient unless we had the minimum set of information required to place it in
one of the other formal IUCN categories. These data included countries of
occurrence, maps showing the geographic distribution, rationale for the
listing (including any numerical data, inferences or uncertainty that relate to
the criteria and their thresholds), current population trends, habitat pref-
erences, major threats, and conservation measures.
Assessment according to the experts. Expert opinion was available for 54 species.
Based on expert field work experience, the species were categorized as not
threatened, threatened, extinct, or impossible to assess (if experts estimated
that not finding a species was possibly due to insufficient search effort and
not to the probable extinction of the species). Note that these categories
differ from the IUCN categories.
For species for which no expert opinion was available, our assessment was
based on the number of dated records and information on their habitat, as
follows: (i) species collected alive at least five times between 1962 and 2012
(i.e., in the previous 50 y) and with no specific habitat threat identified were
evaluated as not threatened; (ii) species not collected in the last 50 y but
with insufficient information on range size and habitat quality were eval-
uated as impossible to assess; and (iii) species not collected in the last 50 y
and occurring in a highly disturbed or vanished habitat shared by other
species already listed by the IUCN as critically endangered or extinct were
evaluated as extinct (Fig. S1).
Assessment according to the probabilistic model.
Data compilation. Collection years were compiled for each species in each
geographic area (Fig. S2). We use the term “Polynesia”for the sake of
simplicity, although our data are from both Polynesia and Micronesia. In
addition, for each geographic area A, all years in which mollusk sampling
occurred were listed. These two lists were taken from the databases of the
four US museums listed previously. For each species, each survey date twas
then tagged by a 1 if the species was collected, or a 0 if otherwise.
Model. The model is diagrammed for one species in one geographic area in Fig.
2. We define Sas the date at which extinction becomes possible. Each species
extant at year y≥Sin geographic area Acan independently become extinct
between year yto year y+1 with a constant probability μ
A
.BeforetimeS,the
probability of extinction is assumed to be 0. Sis therefore the date of the ex-
tinction rate shift. We also assume that, at each survey date t, each extant species
in the geographic area A, independently, is successfully collected with a constant
probability λ
A
. We assume that λ
A
and μ
A
only depend on the geographic area A
and that Sis identical for all species and all geographic areas. A species that has
been observed most recently at date t* is necessarily extant up until t*.In
mathematical terms, we have E>t*,whereEis the unknown date of extinction
of this species. There are two reasons why a species is not observed in a survey
subsequent to t*: the species is extant but was not collected (i.e., the survey
preceded E)orthespeciesisalreadyextinct(i.e.,Epreceded the survey). We
define Tas the date of the last survey (successful or not). We define n
1
as the
number of survey dates on which the species has been collected, and n
0,y
as the
number of survey dates prior or equal to year yon which the species was not
collected; given this, the likelihood of the data for one species is given by
LðS,μA,λAÞ=λn1
Að1−λAÞn0,t*ð1−μAÞðt*−S+1Þ
×
2
6
6
6
6
4
ð1−μAÞðT−S+1Þð1−λAÞ1+n0,T−n0,t*
+X
T
E=maxðt+1, SÞ
μAð1−μAÞðt−S+1Þð1−λAÞðn0,E−n0,tÞ
3
7
7
7
7
5
.
Pooling species within the same geographic area A, the likelihood of the
data are the product of the above likelihoods over all species in A(this as-
sumes species are independent replicates).
Statistical inference. Our goal was to infer a single Sfor all data together
and (λ,μ) for each geographic area. We first estimated jointly
^
S,^μ, and
^
λfor
all geographic areas pooled (i.e., using worldwide information). Second, we
fixed Sto
^
S, and estimated for each geographic area ^μAand
^
λA. To compute
^
S, we explored parameter space by Markov chain Monte Carlo (MCMC) with
all geographic areas pooled. We used a uniform prior for Sin [1800, 1950]
and a uniform prior in [0, 1] for both λand μ. We selected as proposal dis-
tributions of the Metropolis–Hastings algorithm the uniform distribution in
[0, 30] for Sand the uniform distribution in the log-scale between 0.1 and
0.0001 for λand μ. We performed an optimization by maximum likelihood
before running the MCMC to focus on the interesting region of parameter
space. We discarded the first 100 steps of the chain as burn-in, and sampled
1,000 values every 20 steps. We checked the convergence of the distributions
visually. The posterior Sdistribution showed a clear mode around 1900 and a
mean of the distribution of 1893.96 (Fig. S3). Consequently, we set Sto 1894
for all further parameter estimation. We were not able to retrieve Sfor each
geographic area independently, presumably because of a lack of signal. For
each area, we then ran an independent MCMC to estimate λ
A
and μ
A
.
To characterize the probability of being extant or extinct, we computed,
for each species, the likelihood ratio (LR) of the chance it went extinct since it
was observed at t* to the chance of being extant but not found since t*.
More precisely, LR is defined as
Régnier et al. PNAS Early Edition
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ECOLOGY
LR =1−ð1−^μAÞT−t*
1−
^
λAn0,T−n0,t*.
LR is a continuous positive variable, and gives an indication of the current
conservation status of the species: the higher it is, the higher is the probability
that the species is extinct. However, to assign conservation status, two thresholds
were arbitrarily chosen for LR: when LR is above 10 (i.e., there is a 10×greater
probability that the species is extinct than that it is extant but not found), we
suggest that the species should be declared extinct; when LR is below 0.1 (i.e.,
there is a 10×greater probability that the species is extant but n ot found than
that it is extinct), we suggest that the species should be declared extant.
Between 0.1 and 10, we declare the species impossible to assess.
To check the MCMC algorithm performance, we built 10 random replicates
of time series, for each species, keeping the survey dates as they are, but
randomlydrawing the extinction dates (using a geometric distribution with the
estimated μ
A
) and subsequently the successful surveys (using Bernoulli trials of
parameter λ
A
before the extinction date). The results show that the MCMC
algorithm performs well, estimating values (λ
A
,μ
A
) that are close to those set
in the simulations (Fig. S4).
ACKNOWLEDGMENTS. We acknowledge contributions and data sharing from
G. M. Barker, A. S. H. Breure, A. C. van Bruggen, C. C. Christensen, D. J. D. Chung,
R. Clements, J. Espinosa, A. Fernández Velázquez, J. Gerber, E. Gittenberger,
J. Grego, O. Griffiths, M. G. Hadfield, D. Herbert, Y. Kano, W. Maassen, B. Marshall,
F. Naggs, E. Neubert, T. A. Pearce, D. Raheem, B. Roth, B. Rowson, R. J. Rundell,
M. Severns, J. Stanisic, F. G. Thompson, R. Ueshima, D. Uit de Weerd, A. J. de
Winter, and M. Wu. R. Cameron and R. Hershler reviewed an earlier draft of the
manuscript. We thank H. Annoni for the design of Fig. 3. We thank C. Fontaine,
S. Languille, and H. Le Guyader for comments that improved the manuscript. This
work was supported by French National Research Agency Losers Project Grant
ANR-09-PEXT-007 (to P.B.).
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