Estimating vertebrate biodiversity using the tempo of taxonomy - a view from Hubbert's peak
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Biological Journal of the Linnean Society, 2021, XX, 1–21. With 13 figures.
Estimating vertebrate biodiversity using the tempo of
taxonomy – a view from Hubbert’s peak
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BRUCE H. WILKINSON1,2,*, LINDA C. IVANY2 and CARL N. DRUMMOND3
1
Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109-1005,
USA
2
Department of Earth and Environmental Sciences, Syracuse University, Syracuse, NY 13244, USA
3
Department of Physics, Purdue University Fort Wayne, Fort Wayne, IN 46805, USA
Received 28 April 2021; revised 30 April 2021; accepted for publication 5 May 2021
Reservoirs of natural resources are finite and, with increasing exploitation, production typically increases, reaches
a maximum (Hubbert’s peak) and then declines. Similarly, species are the currency of biodiversity, and recognized
numbers are dependent upon successful discovery. Since 1758, taxonomists have exploited a shrinking reservoir of
as-yet-unnamed vertebrate taxa such that rates of species description at first rose, reached a peak and then declined.
Since about 1950, increases in research funding and technological advances have fostered a renewed increase in
rates of discovery that continues today. Many attempts to estimate global biodiversity are forecasts from data on past
rates of description. Here we show that rates of discovery of new vertebrate taxa have been dependent upon the size
(richness) of the taxonomic pool under consideration and the intensity of ‘sampling’ effected by taxonomists in their
efforts to discover new forms. Because neither the current number of as-yet-to-be-described taxa nor future amounts
of taxonomic efforts can be known a priori, attempts to produce an accurate estimate of total global biodiversity
based on past rates of discovery are largely unconstrained.
ADDITIONAL KEYWORDS: biodiversity – Hubbert – Linnaeus – taxonomy – vertebrates.
‘We will only get a good answer to the age-old numbers of described taxa, the translation of these
question of “how many species are there?” when metrics to total or as-yet-undiscovered richness is
we understand the population biology and social fraught with assumptions. Coming from our perspective
behavior of taxonomists’ (Pimm & Joppa, 2015). as geoscientists, we posit that the realization of a more
complete taxonomy, and thus a better appreciation of
Earth’s total biodiversity, is similar to attempts to infer
the sizes of global reserves of many natural resources
INTRODUCTION
currently under development. Species of vertebrates,
Taxonomy is one of the oldest areas of biological barrels of oil and tons of copper, for example, can be
investigation. The finding, naming and grouping of thought of as the units that comprise reservoirs to be
taxonomic entities are generally understood to be produced (discovered). They are distributed within
critical pursuits in the quest for a fuller understanding local reservoirs (higher taxa, oil fields, ore deposits)
of the current state of Earth’s biodiversity and its that exhibit fractal-like (many small – few large)
ongoing loss. As recently discussed by Moura & Jetz size frequency distributions, and the probability of
(2021), an assortment of biological, environmental their discovery depends on the sizes of the units in
and sociological circumstances serve to influence the question and on the intensity of efforts devoted to
probability that a new species will be discovered and their development. This comparison offers insight into
described. Although past approaches to estimating our ability to project the total biodiversity of a group
group richness have often relied on knowledge of from the history of taxonomic discovery of the fraction
currently known.
In the following, we first examine the numbers of
*Corresponding author. E-mail: eustasy@umich.edu taxonomic units comprising the biological reservoirs
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21 1
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.
org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is
properly cited.2 B. H. WILKINSON ET AL.
that have been ‘exploited’ during the history of Database, 2020 (www.mammaldiversity.org). Details
vertebrate taxonomy, and then discuss several about dates of access and numbers of taxonomic units,
metrics that might serve to quantify the scientific authors and publications are listed as the Supporting
effort expended to produce said taxonomies. For the Information (Table S1).
former, we describe the numbers and size frequencies Current names, taxonomic classification and age of
of taxonomic units at different levels in the Linnaean discovery were tabulated for all valid species; many are
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hierarchy and how they have changed over the past now considered to have a different classification than
~260 years of discovery; in the latter, we consider originally described, and we used the most current.
change in the numbers of papers and authors and their Dates of establishment for all higher taxonomic
association with the pace of description of new taxa over units are taken as those of the earliest identified
that same window of time. Based on observed patterns species within that group. We use parameters of best-
of change at different taxonomic levels, we then develop fit skewed normal and exponential distributions in
models that reproduce observed tempos of description. order to derive semi-quantitative descriptors of the
These confirm the supposition that observed rates of general trends apparent in these somewhat noisy
resource extraction (rates of taxonomic description) data on taxonomic histories. Parameters of these best-
are a function of both reservoir size (total biological fit functions are appended in the Supporting Tables.
diversity) and intensity of exploitation (taxonomic Many aspects of taxonomic histories are similar among
effort). While past rates of description are known different major groups. For brevity, we have elected to
from observation, past and future expenditures of show and/or discuss various relationships with respect
taxonomic effort reflect a complex concatenation of to one particular group as an example, and to illustrate
factors that cannot be forecast a priori. As a result, that same relationship among other vertebrate classes
we are left with one known – the success rate of past in the Supporting Figures.
efforts at description – and two unknowns – the actual
amount of biological diversity that exists on the Earth’s
surface and the total effort that must be expended to
THE OBSERVED PACE OF TAXONOMY
effect a complete census of that diversity. We therefore
suggest that, as has been maintained for reserves of The tempo of description of vertebrate taxa with time
natural resources (e.g. Lynch, 2010), estimates of total shows clear patterns related to hierarchical level (Fig. 1).
biodiversity are largely unconstrained and cannot be Higher taxonomic levels (e.g. orders and families) were
calculated with confidence from information on the differentiated by and soon after Linnaeus in 1758,
history of taxonomic description to date. As much as while numbers at lower taxonomic levels (e.g. genera
one might like to have ‘the number’, species richness of and species) gradually increased, reached a peak and
the planet will remain an elusive target. then decreased. Around 1950, numbers of species
then underwent an abrupt and generally exponential
increase in description that continues today. Of
the 27 orders of modern mammals, 16 (59.3%) were
AVAILABILITY, SOURCES AND TREATMENT
recognized by Linnaeus (1758), and all were defined by
OF DATA
1894, a span of 137 years. In contrast, only 157 (2.0%)
A variety of sources of taxonomic information are of the 6485 currently recognized mammal species
generally available for vertebrate organisms (data were known to Linnaeus in 1758; about 40 new species
for mammals, for example, are accessible from The are currently documented each year, and this rate of
Mammal Diversity Database, the Mammal Species of discovery has increased by about 2% per year since
the World, and the Integrated Taxonomic Information 1950. This ‘ontogeny of taxonomy’ embodied in the
System). We have examined several databases for each history of classification of mammals (Fig. 1) is typical
of the groups considered here and find no important of other vertebrate classes (Supporting Information,
differences with respect to results of analyses Fig. S1; Tables S1 and S2).
performed; those selected for analysis herein afforded The history of exploration of oil fields and ore
the most complete and/or current tabulations. Data deposits reflects the fact that the largest reservoirs
for fishes, amphibians, reptiles, birds and mammals are more likely to be discovered early on. So too is the
come, respectively, from FishBase (Froese and Pauly, case with higher taxa: vertebrate groups described
2019; www.fishbase.se), the Integrated Taxonomic chronologically earlier are also those with the highest
Information System online database (www.itis. memberships. As above, more than half the current
gov), the Reptile Database (Uetz et al., 2020; www. orders of mammals (16 of 27) were established by
reptile-database.org) the International Community of Linnaeus in 1758 based on his initial description of only
Ornithologists (IOC) World Bird List (Gill et al., 2020; 157 mammal species. Those original 16 mammal orders
www.worldbirdnames.org) and the Mammal Diversity currently contain 95% of the 6485 now-recognized
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21TEMPO OF VERTEBRATE TAXONOMY 3
100 100
A B
Orders Families
Number Described
Number Described
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Mode = 1750
10 10
n = 67, r2 = 0.269
Mode = 1751
n = 9, r2 = 0.917
Laonastidae
1 1
C D
Genera Species Mode = 1886
Number Described
Number Described
n = 187, r2 = 0.379
100 100
Mode = 1928
n = 226, r2 = 0.350
10 10
S = 5.61 x 10-17 e-0.0203D
n = 187, r2 = 0.595
1800 1850 1900 1950 2000 1800 1850 1900 1950 2000
Figure 1. Rates (number/year) of named groups of living mammals. Data as filled circles; general trends as best-fit skewed
normal distributions except post-1950 species (D, yellow) which is a best-fit exponential. With decreasing taxonomic rank,
rates change from decreasing (orders and families) to modal (genera) to presently increasing (species). Note logarithmic
y-axes. Similar plots for fish, amphibians, reptiles and birds as Figure S1A–M.
species (Fig. 2). Similarly, the 68 mammal families genus) taxonomic–ontogenetic age are apparent among
recognized by Linnaeus (1758) represent 41% of data for other classes of vertebrates (Supporting
(the 167) currently recognized families and 74% of Information, Fig. S2).
currently recognized species. Conversely, the ‘youngest These observations – of early recognition of
family’ of living mammals (Laonastidae) was erected higher taxa, continuing increases in description
with the description of Laonastes aenigmamus by at the species level, and earlier recognition of the
Jenkins et al. (2005) (though this family might most speciose groups at any level – are requisite
actually represent a ‘Lazarus’ group that was thought features of any effort to model the history of
to have become extinct in the Miocene; Dawson et al., taxonomy. Embedded in these metrics are the need
2006). As currently defined, the family contains one to understand the rules of taxonomic membership
genus and one species (Fig. 2B). Likewise, among (the numbers of subtaxa within supertaxa) as well
finfishes, the 47 orders erected by Linnaeus (1758) as the pace of description of the taxa themselves.
(60% of the 78 modern orders) contain 33 913 (94%) We investigate both of these in subsequent sections
of now-recognized species. The most recently defined before constructing numerical models to reproduce
order, Stylephoriformes (Miya et al., 2007), contains the major features of the histories of taxonomic
one living species (Stylephorus chordates, the deep-sea endeavour, and ultimately to evaluate the potential
tube-eye or thread-tail). Similar relationships between for using such a model to predict future discoveries
numbers of species and higher group (order, family, of new species.
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–214 B. H. WILKINSON ET AL.
A
200
Species per Genus
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150
B Genera
800 100
Species per Family
50
C 600
2500
400
1800 1850 1900 1950 2000
Species per Order
2000 Families Year of Species Description
200
1500 Laonastidae
1000
1800 1850 1900 1950 2000
Orders Year of Species Description
500
1800 1850 1900 1950 2000
Year of Species Description
Figure 2. Relationships between the first year of description of some currently-recognized mammal species (x-axes) and
the numbers of species in that group (y-axes). Number of members (species) largely predicates probability (the date) of
group (order, family, genus) recognition. Similar plots for fish, amphibians, reptiles and birds as Figure S2A–L.
SIZES AND MEMBERSHIPS OF (e.g. Fig. 1) and is requisite for the construction of
TAXONOMIC GROUPS model taxonomies, which provide insight into the
utility of observed taxonomic data for estimating the
Understanding the numbers of subtaxa within any
numbers of remaining taxa to be described.
higher level of taxonomic consideration has been a focus
A higher taxonomic unit, such as an order, can
of scholarship since Willis (1922) described the ‘hollow-
be visualized as encompassing some amount of
curve’ nature of membership frequencies. Within any
n-dimensional morphospace whose volume is occupied
supertaxon, relatively few groups (taxa) contain most
(and defined) by some number of non-contiguous
of the subtaxa, while many are monotypic (Supporting
subspaces, each representing a group (e.g. a family)
Information, Table S1). Different authors have variably
that is a member of that order. The amount of
interpreted these distributions as representing
morphospace occupied by that order is proportional to
hyperbolic, logarithmic, log-normal, exponential,
the number of families it contains, and we know from
geometric and/or power law functions; Anderson (1974)
the frequency distribution of family sizes that a few are
provides an excellent review. Moreover, such ‘hollow
large (comprising a significant fraction of the genera
curves’ have been ascribed to both deterministic and
or species within that order) and many are small.
stochastic processes of biological diversification, and/
A two-dimensional (2-D) plane through this visualized
or historical artefacts of taxonomic classification (e.g.
morphospace transects the volumes of the contained
Walters, 1961; Reddingius, 1971; Chu & Adami 1999;
families such that each is represented by an area on
Scotland & Sanderson, 2004). An understanding of
that plane. The diameters of those areas describe an
membership frequencies of subtaxa within supertaxa
exponential density function that is the same as that
is critical to understanding differences in taxonomic
which describes the variation in the sizes of taxonomic
histories at different levels of Linnean classification
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21TEMPO OF VERTEBRATE TAXONOMY 5
subgroups (like the families comprising an order) through reptile morphospace. The diameters of those
(Wilkinson, 2011). Because here we presuppose that areas exhibit an exponential distribution (many small,
taxonomic ‘size’ equates to numbers of subgroups, ‘size few large) (Fig. 3B).
diameter’ approximately corresponds to the square Given this relationship, we can define a membership
root of the numbers of members comprising that group inclusion parameter p, the probability that the addition
(e.g. genera or species included in a family). of 1 unit of ‘size’ (in this case a species) will result
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Consider the 11242 species partitioned among the 92 in its inclusion in a different family. This inclusion
families that comprise the class Reptilia. The frequency parameter is dependent only upon the number of
distribution of memberships (species) within families families (F) and species (S) in this class:
defines a curvilinear trend in log membership vs. log
exceedance space (Fig. 3A) that reflects the variation πF
p=
in areas of families intersected by any 2-D transect 2S
Families (12)
with 1 species
10 100 1000
100 100
Number of
Families (F) = 92
Families (92)
A Species (S) = 11,242
Inclusion p = 0.113 /species
p= πF/2S
- p2 ES/F
Exceedance
ES/F = O e
r2 = 0.983
Number of 100 10
Families (92) B
Total Diameters (D) = 788
Families (F) = 92
Average Diameter = D/F = 16
Inclusion p = F/D = 0.116
Exceedance
10
Sl
op
1 1
e=
100 1000
-p
Species/Family
-p ES/F
ES/F D = O p e
2
r = 0.989 Family with
Colubridae
1 Most Species (1,972)
10 20 30 40 50 Colubrid snakes
(Colubridae)
~ Species/Family
(2 x 1,972/π)
= 50.1
Figure 3. Sizes of families of reptiles as measured by numbers of species per family. A, number of species per family
among the 92 families of reptiles. B, frequencies of distances across 2-D transects of ‘shape-space’ represented by each of the
families. Functions describing numbers of species (A) and ‘diameters’ of numbers of (B) both suggest that lateral boundaries
of taxonomic units occur independently (randomly). In both cases, the inclusion parameter, p (~0.113), is the likelihood of
incrementing the number of families with the addition of one species.
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–216 B. H. WILKINSON ET AL.
The cumulative percentage of families with ASSESSING EFFORT – WHAT CONTROLS
memberships equal to or greater than some number RATES OF TAXONOMIC DESCRIPTION?
of species (s) is the exceedance (EFs), and is given as:
√ Forecasts of biodiversity also depend on attaining some
2
EFs = Fe− p Fs aggregate measure of the intensity of efforts exerted
by taxonomists in order to reveal said diversity. The
This function yields good agreement with the
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issue of ‘taxonomic effort’ is important (e.g. Cribb &
distribution of species memberships within families of
Bray, 2011). If the collective sampling efforts needed to
reptiles (Fig. 3A), and suggests that the distribution of
discover one new taxon were invariant, then the rate
taxon sizes (measured as the square root of numbers
of description of new taxa should decrease with time
of subtaxa within that group) is the same as that of
because the pool of remaining (undescribed) taxa will
the diameters across morphospaces whose areas are
decrease as well; a classic case of rarefaction. The fact
exponentially distributed. Agreement between this
that rates of new descriptions at lower taxonomic levels
theoretical distribution and observed data on taxon
(genera and species) have increased during of much
sizes suggests that taxonomic memberships largely
of the last 200 years (Fig. 1; Supporting Information,
represent the random subdivision of the n-dimensional
Fig. S1) requires that the intensity of sampling – the
morphospace occupied by some larger taxon (e.g. a
amount of effort devoted to measuring biodiversity –
class) where intermediate taxon sizes (e.g. families) are
has increased as well.
represented by the numbers of contained subtaxa (e.g.
How does one measure aggregate taxonomic
species). Memberships of taxa within a larger group
effort? Rates of discovery must directly or indirectly
are therefore dependent only on their number and the
correspond to the number of opportunities that arise to
total number of subtaxa of which they are comprised.
recognize a new taxon each year, where ‘opportunity’
Observed taxonomic memberships of vertebrate
is the observed occurrence of a species in some place
groups at all levels of Linnaean classification are
by some individual; some subset of these observations
closely approximated when assuming such a stochastic
will be that of a new taxon. Data of this nature, on
pattern of division. When considering the six possible
occurrences regardless of novelty, are recorded
taxonomic subgroupings (species per genus, per family,
in some datasets (e.g. the Paleobiology Database,
per order; genera per family, per order; and families
paleobio.org), but not consistently for modern taxa of
per order) within the class Mammalia, for example, all
vertebrates. A more tractable measure of taxonomic
model memberships are in good agreement with the
effort is perhaps the numbers of biologists engaging in
data (Fig. 4). Data on group memberships for finfishes,
descriptive research, and the number of publications
amphibians, reptiles and birds exhibit similar
in which new taxa are described per year. A number
correspondence (Supporting Information, Fig. S3,
of studies suggest a relationship between rates of
Table S3). Agreement between a stochastic function
taxonomic description and the aggregate scientific
representing the chance division of morphospace and
exertions of systematists, who together examine
taxonomic membership data observed in the real
many individuals from many populations spanning
world, for these and other animal groups, suggests
many biogeographical regions in search of something
that current taxonomic classification largely serves
different enough to be considered a new taxon. Of
to randomly subdivide a morphospace continuum
particular interest has been the nature of relationships
(Wilkinson, 2011).
between rates of species description, and numbers of
The relationship describing the distribution of
taxonomists and papers describing new species (e.g.
subtaxa among taxa in a larger group is consistent
Joppa et al., 2011a, b; Mora et al., 2011; Bebber et al,
across taxonomic levels; that is, p is similar between
2014; Costello et al., 2014; Gómez-Daglio & Dawson,
levels with similar amounts of taxonomic separation
2019). We explore these below with respect to data on
(TS; Table S3), and generally decreases with increasing
the major classes of vertebrates.
degrees of TS (Fig. 5) as:
Rates of new species described and rates of taxonomic
papers published (in which a new species is described)
p = e−1.12 TS
exhibit similar patterns of temporal variation. For
The exponent of this decrease averaged across example, beginning with the description of 330
vertebrate classes, −1.12, is the natural logarithm species of finfish by Linnaeus in 1758, 33 913 species
of 32.5%, which represents the average decrease (Supporting Information, Table S1) have been described
in p with increasing separation among Linnaean to the end of 2019 (254 years) in 6055 publications (3.0
levels (i.e., p = 0.325TS). Taxonomic memberships – species per paper). Over this time interval, rates of
the partitioning of subtaxa among higher taxa – are species description and rates of publication have both
largely the same, regardless of taxonomic levels of increased more or less exponentially. Since 1950, the
consideration. rate of naming of new finfish species has increased
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21TEMPO OF VERTEBRATE TAXONOMY 7
100
A Species = 6,485
Orders = 27
p = 0.081
r2 = 0.930
Exceedance
10
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100
Exceedance B
1
10 100 1000
10 Species per Order
100
C Genera = 1,331
Orders = 27
p = 0.179 D Species = 6,485
r2 = 0.914
Exceedance
Families = 167
1 p = 0.201
10 10 100 100
r2 = 0.966
Exceedance
Genera per Order
Families = 167
Orders = 27 E 10
p = 0.504
r2 = 0.885
1
1 10 100 100
Families per Order
Exceedance
10 100 1000
Species per Family
10 Genera = 1,331
Families = 167 F Species = 6,485
p = 0.444
Genera = 1,331
r2 = 0.906 1000
p = 0.568
10 100 Exceedance r2 = 0.896
Genera per Family
100
10
10 100
Species per Genus
Figure 4. Random division functions fit to taxonomic data on mammals plotted as number of subtaxa among each
hierarchically higher level of supertaxa (x-axes) relative to numbers of subtaxa that are equal to or are greater than
some x-axis membership number (y-axes). Metrics for each membership curve are listed in Table S2. Similar plots for fish,
amphibians, reptiles and birds as Figure S3.
by ~2.1% per year to a current pace of ~400 species define a trend of exponentially decreasing importance
per year (Fig. 6A). Similarly, since 1950, the number of monographs toward the present (Fig. 7B for
of publications containing species descriptions has amphibians; see Supporting Information, Fig. S5,
increased by ~2.6% per year (Table S4) to a current Table S5 for other classes). These changes are just one
rate of ~250 papers per year (Fig. 6B). Data on rates of ramification of the increasing specialization of modern
description and numbers of papers related to species scientific inquiry.
of amphibians, reptiles, birds and mammals exhibit Trends in numbers of described species and
nearly identical relationships (Fig. S4). numbers of papers designating new taxa exhibit a
A decrease in the variance of the rate of species rather obvious change around the early 1950s (Fig.
description is also apparent over time in all vertebrate 6; Supporting Information, Fig. S4), when rates of
taxonomies (Fig. 7), and most probably reflects the description and publication began renewed and
decreasing importance of monographs as an outlet exponential increases that continue to the present.
for the formal recognition of new groups (e.g. Joppa Rate metrics for all vertebrate classes are similar
et al., 2011a). Residuals of best-fit trends through data except for birds (an order of magnitude lower; Fig.
on the numbers of species described per publication S4), and equate to the naming of about 500, 160,
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–218 B. H. WILKINSON ET AL.
1
A species per class
Inclusion p
Mammals genera per class
species per order
families per class
0.1
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genera per order
1 species per family
B
p = 1.25 exp-1.07TS orders per class
Inclusion p
n = 9; r2 = 0.942 families per order
0.0 1 genera per family
1 2 3 4 species per genus
0.1 Taxonomic Separation
1
1 Birds D
C
Inclusion parameter (p)
Inclusion p
p = 1.25 exp-1.14TS
n = 9; r2 = 0.926
0.0 1 Amphibians
1 2 3 4 0.1
0.1 Taxonomic Separation
Reptiles 1
E
Inclusion parameter (p)
p = 1.25 exp-1.21TS p = 1.25exp-1.16TS
n = 9; r2 = 0.978 n = 9; r2 = 0.944
0.0 1 1 2 3 4
1 2 3 4 Taxonomic Separation
Fishes
0.1
Taxonomic Separation
p = 1.25 exp-1.04TS
n = 10; r2 = 0.996
0.0 1
1 2 3 4
Taxonomic Separation
Figure 5. Values of the inclusion parameter p as a function of degree of taxonomic separation among classes of vertebrates.
Here, the slope (on average, −1.12) is the natural logarithm of 0.325, and represents the rate of decrease in p for each
increase in level of separation (0 = 100%; 1 = 32.5%, 2 = 10.6%, 3 = 3.4%, 4 = 1.1%). This rate of change corresponds to about
a three-fold increase in membership with each increase in Linnaean level of taxonomy.
150, five and 40 new species of fishes, amphibians, papers began to increase (by ~10% per year) around
reptiles, birds and mammals, respectively, in the year 1950 (Supporting Information, Fig. S6). Papers with
2020. Interestingly, current rates of discovery and three or more authors account for ~65% of species
description are some several hundred times higher descriptions since 2000. With more authors overall, the
than estimated coeval rates of extinction of vertebrate number of papers published has grown (Fig. 8A), and
species (Ceballos et al., 2017, 2020). papers published since 1950 are also more likely to
Such a profound change – one of both sign (negative describe fewer (or one) new species per paper (Fig. 8B).
to positive) and acceleration – in species identification The shift to multi-authored and monospecific papers
and publication rates seen across all vertebrate classes alone, however, cannot account for the increase in both
since c. 1950 argues for a common cause (e.g. Joppa papers and species descriptions per year. An increase
et al., 2011b). Publication norms have changed since in the latter must be associated with increasing rates
1950 (Ioannidis et al., 2018; Gómez-Daglio & Dawson, of discovery of new taxa.
2019), particularly with respect to the proportion of Several factors in particular probably account
multi-authored papers per year; might this contribute for the 1950s’ inflection in the rate at which new
to the inflection? Single and dual authored papers species are described. The establishment of national
account for ~85% of all new species descriptions over agencies dedicated to the public support of university-
the past 250 years, but the number of multi-authored based research, including taxonomic studies, surely
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21TEMPO OF VERTEBRATE TAXONOMY 9
A
500 S = 8.42 x 10-17 e-0.0214D
n = 68, r2 = 0.802
Species per year
400
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Mode = 1900
300
n = 185, r2 = 0.605
B
250
200
S = 3.80 x 10-21 e-0.0261D
n = 68, r2 = 0.907
Papers per year
200
100 200
150
1800 1850 1900 1950 2000
100
Mode = 1950
n = 185, r2 = 0.810 50
1800 1850 1900 1950 2000
Figure 6. Relationships between naming of 33 913 new species of finfishes (A) and rates of their publication as papers per
year by unique authors of sets of authors (B). Brown curves are best-fit skewed normal distributions to data before 1950;
yellow curves are best-fit exponentials. Low numbers for 2018 and 2019 in both plots (lighter points) represent incomplete
tabulations. Since 1950, rates of newly named species and associated papers have increased at about the same rate: by ~2.14
and 2.62% per year, respectively. Similar plots for amphibians, reptiles, birds and mammals as Figure S4A–H.
contributes to the renewed increase in description with which scholars in the developing world can share
rate. In the United States, for example, the National their work with the broader international community
Science Foundation was created in 1950. In Canada, (e.g. Grieneisen et al., 2012).
while the National Research Council was created Finally, the advent of molecular techniques with
in 1916, war-related and medical research were which to recognize and distinguish among genetically
handed off to newly formed organizations around distinct populations must contribute to the renewed
1950, and research funding in the natural sciences increase in the rate of description of new species.
has been handled through the Natural Sciences and Data in Bouchet et al. (2016), for example, suggest
Engineering Research Council since 1978. Federal that the description of marine molluscs based on
funding for scientific endeavour promoted growth in molecular criteria has increased by ~35% per year
the number of taxonomic researchers and hence in the over the past decade. In addition, the recognition
number of papers and new species described per year. of cryptic species has resulted in a subdivision of
Access to new habitats afforded by technological existing taxa into multiple new taxa based on genetic
innovation has also allowed researchers to explore information (e.g. Bickford et al., 2007; Pfenninger &
biodiversity in places that had been difficult or Schwenk, 2007; Ladner & Palumbi, 2012); molecular
impossible to reach before (Donoghue & Alverson, methods may add tens of thousands of cryptic marine
2000). As an example, the ratio of marine to terrestrial species (Appeltans et al., 2012). Genetically distinct
species described each year began to increase at about populations recognized using molecular data, however,
this time (Costello et al., 2012), reflecting a progressive are not always the same as the species that would
expansion in the exploration of marine habitats, have originally been defined morphologically, so the
including deep-sea settings. Similarly, the increasing inclusion of both types of ‘species’ in the same dataset
globalization of science has allowed more attention to largely equates to the development of new reservoirs
formerly difficult-to-access or otherwise understudied that were not considered during earlier research.
biogeographical regions through the growing number An intriguing correlate to the naming of vertebrate
of international collaborations and the increasing ease species can be found in the nearly identical changes
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–2110 B. H. WILKINSON ET AL.
100 100
A
Species per paper
Mode = 1892
Species per paper
n = 221, r2 = 0.210
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10 10
B
Residual species per paper
10 1
1900 1950 2000
1
0.1
0.01 Res = 4.81 x 108 exp-0.0109Date
n = 221; r2 = 0.254
1800 1850 1900 1950 2000
Figure 7. A, historical (x-axis) change in rate of description of new species of amphibians (y-axis, log scale). Best-fit skewed
normal distribution (brown line) to log rates (brown dots) suggests a maximum taxonomic ‘per paper productivity’ c. 1890.
Note decreasing scatter of rates with decreasing age. B, exponential decrease in the ‘monograph effect’ among amphibians
manifested as decreasing differences between observed rates of description of new species and that described by a longer-
term average. ‘Spikiness’ in the description of new species has decreased by ~1.1% per year since the end of the 17th century.
Similar data for fishes, reptiles, bids and mammals as Figure S5.
in the rate of discovery of new minerals and the proxies for ‘taxonomic effort’? Probably not. Linnaean
proportion of multi-authored papers describing new species are the coin of the biodiversity realm; the first
mineral discoveries that occurred at the same time. description of any vertebrate species necessitates the
Barton (2019) reports that the rate of discovery of new identification of some genus, some family, and some
minerals was relatively constant (~15 per year) from order within the class to which it belongs. Numbers
1917 to about 1950, but then increased exponentially of species descriptions, published papers and/or
(by ~1.9% per year) to a current (2020) rate of ~100 per contributing authors are all measures of the success
year. Over the same time interval, the average number of taxonomic efforts, rather than a direct measure
of authors on mineral discovery papers also underwent of the aggregate scientific exertion expended by the
an exponential (~2% per year) increase from abour two community in deriving this classification. The difficulty
in 1950 to over six in 2020. She ascribes these changes in assessing taxonomic effort is that there is no easily
to a variety of interrelated factors, including the greater accessible record of ‘unsuccessful’ research; there is no
availability of instrumentation and an exponential adequate metric for measuring the cost and/or effort
growth in the funding and focus of mineralogical research expended during those expeditions that failed to locate
at universities and museums. The striking coherence and/or identify new forms.
in pattern between such disparate fields argues for Even if a satisfactory metric were available with
similar drivers, and the combination of federal research which to track the history of taxonomic effort, several
funding, globalization and technological advance would factors would complicate a straightforward forecast
affect both in the same way. of future industry and its impact on probabilities
All this being said, do numbers of authors or of discovering new forms. First, there are a number
publications or described taxa per year serve as valid of factors intrinsic to specific taxa that predicate
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21TEMPO OF VERTEBRATE TAXONOMY 11
Number of Papers
A
100
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2018 B P = 0.288 S1.11
2019 r2 = 0.935
10
P = 1.19 A0.877
Number of Papers
n = 254, r2 = 0.991 100
10 100
Number of Authors
2000-2025
1975-2000
1950-1975
1925-1950 10 10
1900-1925
1875-1900
1850-1875
1825-1850 P = 0.671 S0.655
1800-1825 n = 185, r2 = 0.684
1775-1800
1750-1775
10 100
Number of Species
Figure 8. Relationships between numbers of papers and participating authors describing new vertebrate species (A), and
numbers of species described (B) since 1758. A, number of authors and resulting papers are well correlated, an increasing
proportion of multi-authorship giving rise to a slight decrease in slope. The two youngest points (2018 and 2019) are thought
to represent incomplete database tabulations. B, correlations between numbers of papers and described species are also
increasingly well correlated, with greater noise during earlier years reflecting a greater impact of monographs.
probabilities of discovery. These include things up only about 1.4% of the Earth’s land surface.
related to appearance such as flamboyance of colour, Sociopolitical infrastructures are also frequently
openness of biome and mode of mobility, as well as limited in high-biodiversity regions, and scientists from
abundance of members (e.g. Cribb & Bray, 2011), countries with more robust taxonomic infrastructures
range size (e.g. Collen et al., 2004; Krasnov et al., typically require significant resources to explore in
2005) and body size (e.g. Gaston, 1991). Second, the other areas (e.g. Grieneisen et al., 2012).
spatial distributions of new (undescribed) taxa are The concatenation of all these and other factors, as
geographically heterogeneous, and in order to attain illustrated so dramatically by the 1950s’ inflection,
taxonomic ‘success’ through their description, even collectively makes projections about the success rate of
relatively abundant species will not be found until future taxonomic efforts based on past trajectory highly
exploration expands into their range; the discovery of uncertain and subject to happenstance. If, as noted by
hydrothermal vent communities in the late 1970s is Pimm & Joppa (2015), we can only achieve an accurate
a classic example. Geographical ranges and densities estimate of the size of the global biodiversity reservoir
of taxa are also often variable and uncorrelated. when we can also accurately forecast numbers,
More recently discovered species, for example, have practices and collective efforts of systematists, we are
typically been found in biodiversity hotspots of high left in a precarious position. The equation has one
endemism (e.g. Thompson et al., 2021); Myers et al. known – the success rate of past collective efforts –
(2000) estimated that 35% of all recently described and two unknowns – the actual amount of biological
amphibian, reptile, bird and mammal species are diversity that exists on the Earth’s surface, and the
restricted to some 25 hotspots that collectively make total effort necessary to effect a census of that diversity.
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–2112 B. H. WILKINSON ET AL.
A better understanding of how different scenarios of each of which represents some intermediate level of
future effort might affect estimates of total diversity is Linnaean taxonomy, like families. The population is
afforded from simple numerical models structured such that that most of the marbles (e.g.
species) represent only a few colours (e.g. families),
while many other colours are represented by a few
or only one marble(s). The distribution of marbles
MODELLING TEMPOS OF TAXONOMIES
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(subtaxa) among colours (taxa) is determined by the
Thus far, we have proposed that: (1) the tempo at stochastic function defining memberships for a given
which new Linnaean categories have been established taxon provided by the inclusion parameter p (Section
is similar for equivalent ranks across different IV, Figs 4, 5). The population is randomly sampled
vertebrate classes; (2) rates of definition at the family with replacement over time, with each draw reflecting
level and higher have deceased rapidly since 1758, the taxonomic observation of a (new or previously
when a large number of groups were first erected; recognized) species. Because the same marble (species)
(3) rates of generic description increased until can be drawn more than once, the number of marbles
c. 1870 before falling off; (4) rates of description of drawn per time step reflects some measure of effort,
new species exhibit a similar peak in the mid-to-late as some observations turn out to be taxa already
1800s (1889 ± 20), declined until about 1950, and have described. The time step in which new marbles
exponentially increased since then, now by ~2.5% per (subtaxa) and new colours (taxa) are first sampled is
year; (5) the most speciose orders, families and genera the recorded year of discovery.
are historically the earliest ones defined; (6) Linnaean If sampling intensity – the number of marbles
group memberships measured as numbers of contained drawn in each time step – were constant over time,
subtaxa exhibit frequency distributions similar to the number of new taxa discovered at any level per
those expected from the random division of taxonomic time step (per year) would have to decline from the
morphospace; and (7) numbers of described taxa, inception, as speciose clades are discovered early and
numbers of publications and numbers of contributing then repeatedly resampled, and progressively less
authors are all correlated manifestations of taxonomic speciose groups are eventually encountered by chance
successes. Although their rates of appearance are over greater intervals of time. This simple scenario,
directly related to scientific effort expended, no readily however, is inconsistent with the observation of modes
available data exist by which to adequately quantify in the number of new descriptions per year, which also
increases in total taxonomic effort. occur later in time at progressively lower taxonomic
To better understand the processes underlying these levels (e.g. Fig. 1). These observed trends require
observations, and hence to evaluate the potential for that sampling intensity (taxonomic effort) must be
predicting them in the future, we construct several increasing over time.
numerical models that incorporate parameters To more accurately capture the observed structure
reflecting both the inherent nature of the groups being in taxonomic histories, we specify various changes in
sampled and described (numbers and memberships) as the rate of sampling (the number of marbles drawn,
well as some model estimate of the effort expended in or taxonomic observations made) over time. The first
the process by systematists over time. As demonstrated model assumes a constant rate of increase in sampling
in the prior section, quantifying the effort involved effort and considers how membership histories unfold
in discovering a new taxon is difficult, but one can as a function of taxonomic rank. A second set of models
bring some clarity to the impact of different degrees of explores the impact of each of three different rates of
effort on resulting biodiversity trajectories and tallies increase in sampling effort on the shapes of resulting
through the use of such simple numerical models. To membership histories at a single taxonomic rank.
this end, we combine the understanding of taxonomic Both of these models span 350 years (1758–2108) of
memberships at different Linnaean levels with three taxonomic history.
prescribed scenarios of taxonomic effort in order to: The first scenario (Fig. 9) is parameterized so as to
(1) replicate taxonomic tempos at different Linnaean loosely approximate the taxonomic histories of a clade
levels; (2) assess the impact of differing effort scenarios of vertebrates (e.g. mammals, with 6485 described
on taxonomic history at a single Linnaean level; and species divided among 1331 genera and 176 families;
(3) examine how changes in taxonomic effort affect the Supporting Information, Table S1). A pool of taxonomic
tempo of taxonomic description. observations comprising 6500 species is randomly
Conceptually, we might imagine a very large sampled with replacement each year for 350 years,
population of marbles that represents some high for a total of 30 000 observations. We presuppose that
taxonomic level (like a class) of vertebrates. Marbles sampling effort increases exponentially by ~1% per
each represent some unit at a lower taxonomic level, year, from a rate of six observations made per year
like species, and marbles comprise different colours, in 1758 to 154 per year in 2108 (Fig. 9A). Drawn
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21TEMPO OF VERTEBRATE TAXONOMY 13
A
Samples
Taxonomic Observations
150
Samples in 1759, 2020, 2108 = 6, 63, 154
Sampling increase = 1.0% per year
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100
B Families 50
6
5
Famlies
Mode = 1759
4 1800 1900 2000 2100
n = 73, r2 = 0.514
3
2
C Genera
5
1
10 Mode = 1860
n = 263, r2 = 0.477
1800 1900
Genera
D Species
5
30
Species
20
1800 1900 2000 2100
10
Mode = 2014
n = 350, r2 = 0.848
1800 1900 2000 2100
Figure 9. Modelling differences in taxonomic histories as a function of Linnaean level of classification employing the
same sampling regime. A, a scenario of taxonomic effort modelled as an exponential change in per-year ‘attempts’ at taxon
description, increasing from six per year in 1758 to 154 per year in 2108. B–D, rates of ‘discovery’ of new taxa as a function
of their memberships at different taxonomic levels.
observations constituting new species are apportioned only 76% (4965) of species, are discovered by the year
into genera and families based on the inclusion 2020. By model year 2108, a time span of 350 years,
parameters (p) for modern mammals (Table S3). We 98% (6393) of the prescribed 6500 species have been
plot the first model year in which each species, genus discovered. The lower the Linnaean taxonomic rank,
and family is first ‘discovered’, yielding histories of the later the date of ‘peak taxonomy’.
discovery over 350 years at each of those taxonomic The second model compares the effect of varying
levels (Fig. 9B–D). the rate of increase in sampling on the recovered
Such modelled taxonomic histories are qualitatively taxonomic history at a single taxonomic level, in this
similar to those observed among all vertebrate groups: case genera. A total of 15 000 taxonomic observations
higher levels (e.g. families) are completely censused are drawn with replacement from a pool comprising
within a few decades, while rates of ‘discovery’ at lower 6500 species, and the membership inclusion parameter
levels (e.g. genera and species) initially increase because (p; 0.57 per species) comes from modern mammals.
rates of sampling exceed rates of pool depletion, reach We calculate the number of new genera discovered/
a peak rate of discovery (in model year 1860 for genera, described each year given each of three different rates
year 2014 for species), and then decline as rates of pool of increase of sampling intensity (Fig. 10). The results
depletion overtake rates of sampling. In this example, demonstrate that taxonomic effort has a first-order
100% (170) of families and 99% (1355) of genera, but influence on resultant taxonomic histories for a given
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–2114 B. H. WILKINSON ET AL.
A
400
Samples
Samples Annual
300 1759 2020 2108 increase
22 58 90 0.5%
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200
6 63 153 1.0%
1 31 443 3.5%
B
100
20 Mode = 1759
n = 211, r2 = 0.786
Genera
15
1800 1900 2000 2100
10
C
Mode = 1860
5 n = 263, r2 = 0.477
10
1800 1900 2000
5 D
Genera
15
Genera
10
1800 1900 2000 2100
Mode = 2018
n = 318, r2 = 0.887 5
1800 1900 2000 2100
Figure 10. Differences in simulated taxon discovery histories as a function of sampling intensity of subtaxa. A, three
different scenarios of taxonomic effort modelled as exponential increases in number of subtaxon descriptions/year resulting
from sampling a pool of 6500 subtaxa. B–D, rates of ‘discovery’ of new taxa as a function of the three subtaxon sampling
scenarios in A.
hierarchical level. Low rates of increase in sampling must reflect synchronous and significant changes
intensity (i.e. closer to the initial scenario of constant in the amount of taxonomic effort. We examine
sampling intensity over time) result in progressive, this supposition with a model of taxonomic history
approximately exponential depletion of the pool of similar to that described above but now imposing
as-yet undescribed genera, while higher rates of two changes in sampling effort over the 350 model
increase in taxonomic effort yield progressively more years. Both cases comprise a net taxonomic ‘effort’
bell-shaped ‘discovery’ histories. The model year of of 30 000 observations. In the first instance (Fig.
peak rate of discovery marks the time that the impact 11A, B), the pool contains 6500 species. We make
of increasing sampling intensity is overtaken by the observations at an initial rate of four per year in
influence of depletion of the pool of undiscovered genera. 1758 increasing to 35 per year in 1840, holding
With higher rates of increase in taxonomic effort, ‘peak steady at that rate until 1950, and then increasing
taxonomy’ occurs at progressively later dates. up to ~280 per year in 2108 (Fig. 11A). This scenario
Finally, recall that the rate of description of new results in the ‘discovery’ of ~5000 species (~76%) by
species in nearly all vertebrate groups experienced 2020 and ~6400 (~98%, nearly all) by 2108 (Fig. 11B).
a renewed and exponential rise following c. 1950 In the second instance, we again make 30 000 total
(Fig. 1D; Supporting Information, S1). Because observations, but now drawn from a pool containing
(presumably) finite pools of vertebrate species are 20 000 species. We make observations at an initial
increasingly depleted with each new discovery, rate of ten per year in 1758 increasing to 40 per year
changes in sign of the slope of rates of description in 1840, then decreasing in rate to one per year in
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–21TEMPO OF VERTEBRATE TAXONOMY 15
300
A C
30,000 samples 30,000 samples
r
r
Samples
ea
ea
200
/y
5/y
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15
0.1
0.
100
ar 0.00/year ar -0.015/y
0.03/ye 0.02/ye e ar
120
B 6,500 species
D 20,000 species
100
Species
Mode = 2022
80
n = 148, r2 = 0.804 Mode = 1834
Mode = 1862
n = 202, r2 = 0.427 n = 202, r2 = 0.764
60
40
Mode = 2051
20 n = 148, r2 = 0.950
1800 1850 1900 1950 2000 2050 2100 1800 1850 1900 1950 2000 2050 2100
Figure 11. Similarities and differences in 350-year taxonomic histories resulting from slight differences in taxonomic
effort. A, hypothetical tempo of effort as two changes in rate of sampling (+0.03/year to 1840; 0.00/year to 1965; +0.15/year
to 2107). B, rates of recognition when drawing samples from a pool of 6500 hypothetical species; 76% are sampled by 2020,
98% by 2107. C, hypothetical effort as two changes in rates of sampling (+0.02/year to 1840; −0.015/year to 1965; +0.15/year
to 2107). D, rates of recognition of when drawing samples from a pool of 20 000 hypothetical species; 35% are sampled by
2020, 77% by 2107. Although the latter scenario (C and D) represents about three times the biodiversity, rates of recognition
before ~2020 (brown circles and lines in B and D) are nearly the same.
1950, and then increasing to ~350 per year in 2108 TAXONOMY AND HUBBERT’S PEAK –
(Fig. 11C). This scenario results in the ‘discovery’ PARALLELS WITH RESOURCE PRODUCTION
of ~7000 species (~35%) by 2020 and ~16 000 (only
The histories of discovery and description of new
~78%) by 2108 (Fig. 11D).
taxa embody philosophic and practical similarities to
The rate of species ‘discovery’ in either case
processes involved in the discovery and exploitation
comprises two cycles in which rates of sampling first
of natural resources such as petroleum or mineral
exceed rates of pool depletion, then are overtaken
deposits. In both instances, rate of recovery is
by it. More importantly, despite the fact that total
dependent on the inherently finite sizes of reservoirs
numbers of species in the latter case is about three
to be exploited and the effort devoted to exploitation.
times that in the former, histories of taxonomic
The production of a barrel of petroleum, extraction
discovery are very similar up to ~2020, and
of a tonne of ore and the description of a new taxon
comparable to those actually observed for classes
are all exercises in the successful discovery/sampling
of vertebrates. That small differences in taxonomic
of some resource reservoir that is being depleted,
effort can yield a high degree of similarity in
and histories of taxonomic description and resource
realized histories of taxonomy, yet might represent
exploitation therefore share a number of similarities.
grossly different numbers of total extant species,
Memberships of taxonomic units, volumes of petroleum
casts doubt on our ability to accurately estimate
reservoirs and tonnages of ore deposits exhibit similar
total standing biodiversity on the basis of currently
‘many small – few large’ size frequency distributions
known tabulations.
© 2021 The Linnean Society of London, Biological Journal of the Linnean Society, 2021, XX, 1–2116 B. H. WILKINSON ET AL.
(e.g. Laherrere, 2000). A greater likelihood of sampling abrupt increase in effort at exploration, the application
from the larger entities results in their earlier dates of of new technologies and the subsequent ‘discovery’ of
discovery in comparison to small/monospecific entities. new large reservoirs that were not available for earlier
Exponential decreases in the rate of description exploitation. In the case of petroleum production,
of higher Linnaean levels over time reflect the early growth since c. 2010 has been almost entirely due to the
depletion of resource pools; any subsequent increase in increasing exploitation of ‘unconventional oil’ from coal,
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discovery or production requires substantial renewed tar sands, biofuels and primarily shale, made possible
effort. In each case, rates of exploitation/discovery by the technological advances of horizontal drilling
have been a manifestation of the ‘successful sampling’ and hydraulic fracturing, as opposed to ‘conventional
of these reservoirs; increases occurred during intervals oil’ produced by drilling a vertical hole in the ground.
when rates of sampling exceeded rates of reservoir The striking similarities in these otherwise unrelated
depletion, while times of decrease represent intervals histories of reservoir exploration suggest that lessons
when rates of reservoir depletion exceed effort at learned from one will apply to the other. In both cases,
exploitation. Following the first oil well drilled near attempted forecasts for when the reservoir would be
Titusville, Pennsylvania, in 1859, ever-increasing fully explored, and hence how big it is in total, based
efforts at exploitation led to a more-or-less exponential on the documented histories of sampling would have
increase in production until the mid-1970s, when been very different prior to the renewed sampling
production peaked, followed by a subsequent drop-off enabled by the – largely unpredictable – respective
(Fig. 12A), much like the history of species descriptions. developments in each field. We consider such efforts in
‘Hubbert’s peaks’ in both records demark the apices of more detail below.
exploitation (Hubbert, 1956).
Because resource exploitation curves can be
described mathematically, one is then tempted to
TAXONOMIC TEMPO AND THE LIMITS OF
extrapolate them out to their presumed time of
MEASURING BIODIVERSITY
depletion in the future, thereby forecasting the
amount remaining in the reservoir at any given time Earth’s biodiversity is currently decreasing at rates
and the total cumulative reservoir size. All else being that many have compared to the mass extinctions
equal, this is not unreasonable. However, following in the geological past (e.g. Pimm et al., 1995). Our
decades of decline, both histories exhibit an abrupt collective understanding of the scope and magnitude
change in slope: oil production has increased rapidly of depletion would therefore be improved by the
since ~2010 and description of vertebrate species has knowledge of how many species actually exist within
increased rapidly since ~1950 (Fig. 12). In both cases, groups (e.g. Brito, 2010; Braje & Erlandson, 2013).
the central reasons for the turnaround include an The phrase ‘how many species’ appears in the titles
A B
New Barrels per year (106)
New species per year (%)
1.0%
4
Mode = 1878
n = 190, r2 = 0.569
N = 2.08 x 10-3 exp-0.0227A
0.8%
n = 69; r2 = 0.896
3 Mode = 1974
n = 150, r2 = 0.992
0.6%
2
0.4%
1 B = 1.63 x 106 exp-0.0823A
n = 12; r2 = 0.959 0.2%
1880 1900 1920 1940 1960 1980 2000 1800 1840 1880 1920 1960 2000
Figure 12. Rates of production of crude oil and naming of vertebrate organisms. A, US field production of crude oil from
1858 to 2019. Skewed normal distribution to interval up to 2007 peaks at c. 1974; exponential distribution between 2007
and 2019 reflects an increase of 8.2% per year. B, proportional naming of all new species of vertebrate organisms between
1760 and 2020. Skewed normal distribution between 1760 and 1950 peaks at c. 1878; exponential distribution between 1950
and 2020 defined by an annual increase of 2.23%. Abrupt changes in slope in both oil and taxonomic curves in part reflect
changes in the nature of resource reservoirs being sampled.
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