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Can morphotaxa be assessed with photographs? Estimating the accuracy of 2D cranial geometric morphometrics for the study of threatened populations of African monkeys

  • Eastern Africa Primate Diversity and Conservation Program, Kenya
  • Lolldaiga Hills Research Programme, Sustainability Centre Eastern Africa


The classification of most mammalian orders and families is under debate and the number of species is likely greater than currently recognized. Improving taxonomic knowledge is crucial, as biodiversity is in rapid decline. Morphology is a source of taxonomic knowledge, and geometric morphometrics applied to two dimensional (2D) photographs of anatomical structures is commonly employed for quantifying differences within and among lineages. Photographs are informative, easy to obtain, and low cost. 2D analyses, however, introduce a large source of measurement error when applied to crania and other highly three dimensional (3D) structures. To explore the potential of 2D analyses for assessing taxonomic diversity, we use patas monkeys (Erythrocebus), a genus of large, semi‐terrestrial, African guenons, as a case study. By applying a range of tests to compare ventral views of adult crania measured both in 2D and 3D, we show that, despite inaccuracies accounting for up to ¼th of individual shape differences, results in 2D almost perfectly mirror those in 3D. This apparent paradox might be explained by the small strength of covariation in the component of shape variance related to measurement error. A rigorous standardization of photographic settings and the choice of almost coplanar landmarks are likely to further improve the correspondence of 2D to 3D shapes. 2D geometric morphometrics is, thus, appropriate for taxonomic comparisons of patas ventral crania. Although it is early to generalize, our results corroborate similar findings from previous research in mammals, and suggest that 2D shape analyses are an effective heuristic tool for morphological investigation of small differences. This article is protected by copyright. All rights reserved.
Can morphotaxa be assessed with photographs? Estimating
the accuracy of two-dimensional cranial geometric
morphometrics for the study of threatened populations of
African monkeys
Andrea Cardini
| Yvonne A. de Jong
| Thomas M. Butynski
Dipartimento di Scienze Chimiche e
Geologiche, Università di Modena e
Reggio Emilia, Modena, Italy
School of Anatomy, Physiology and
Human Biology, The University of
Western Australia, Crawley, Western
Australia, Australia
Eastern Africa Primate Diversity and
Conservation Program and Lolldaiga Hills
Research Programme, Nanyuki, Kenya
Andrea Cardini, Dipartimento di Scienze
Chimiche e Geologiche, Università di
Modena e Reggio Emilia, Via Campi,
103, 41125 Modena, Italy.
Email:; andrea.
Funding information
SYNTHESYS; Leverhulme Trust
The classification of most mammalian orders and families is under debate
and the number of species is likely greater than currently recognized.
Improving taxonomic knowledge is crucial, as biodiversity is in rapid
decline. Morphology is a source of taxonomic knowledge, and geometric
morphometrics applied to two dimensional (2D) photographs of anatomi-
calstructuresiscommonlyemployedfor quantifying differences within
and among lineages. Photographs are informative, easy to obtain, and low
cost. 2D analyses, however, introduce a large source of measurement error
when applied to crania and other highly three dimensional (3D) structures.
To explore the potential of 2D analyses for assessing taxonomic diversity,
we use patas monkeys (Erythrocebus), a genus of large, semi-terrestrial,
African guenons, as a case study. By applying a range of tests to compare
ventral views of adult crania measured both in 2D and 3D, we show that,
despite inaccuracies accounting for up to one-fourth of individual shape
differences, results in 2D almost perfectly mirror those in 3D. This appar-
ent paradox might be explained by the small strength of covariation in the
component of shape variance related to measurement error. A rigorous
standardization of photographic settings and the choice of almost coplanar
landmarks are likely to further improve the correspondence of 2D to 3D
shapes. 2D geometric morphometrics is, thus, appropriate for taxonomic
comparisons of patas ventral crania. Although it is too early to generalize,
our results corroborate similar findingsfrompreviousresearchinmam-
mals, and suggest that 2D shape analyses are an effective heuristic tool for
morphological investigation of small differences.
anatomical landmarks, crania, measurement error, patas monkey, Procrustes shape,
Received: 19 May 2021 Revised: 23 August 2021 Accepted: 26 August 2021
DOI: 10.1002/ar.24787
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any
medium, provided the original work is properly cited and is not used for commercial purposes.
© 2021 The Authors. The Anatomical Record published by Wiley Periodicals LLC on behalf of American Association for Anatomy.
Anat Rec. 2021;133. 1
Integrative taxonomy is one of the most promising set of
tools to accurately assess variability in relation to classifi-
cation (Dayrat, 2005). Genetics might provide strong evi-
dence of evolutionary distinctiveness, but it offers no
guarantee for either taxonomic accuracy or robustness.
This is especially evident in lineages that occupy a gray
areaof evolutionary divergence. As Zachos (2016, pp.
4-5) states,When speciation is considered a continuous
process through time, the exact point at which it is con-
sidered to be complete (two species) is not key to an
understanding of the whole process any more species
delimitation in practice is the imposing of a binary taxo-
nomic concept (species or no species) on a continuous
process and a continuous organismic world with vague
or fuzzy boundaries.Indeed, the literature abounds with
examples of problematic and unstable taxonomies with
not even genetic data providing conclusive, robust and
stable answers. In our own work on mammals, we have
encountered many cases of this type of unresolved taxo-
nomic conundrum. Examples are the hoary marmot
(Marmota caligata) species complex (Cardini, 2003;
Kerhoulas et al., 2015), nictitans monkeys group
(Cercopithecus [nictitans]) (Butynski & De Jong, 2020;
Kingdon, 2013a), baboons (Papio spp.) (Zinner et al.,
2013; Zinner et al., 2018), and red colobus monkeys
(Piliocolobus spp.) (Oates & Ting, 2015; Ting, 2008), as
well as nanger gazelles (Nanger spp.) (Chiozzi et al.,
2014; Ibrahim et al., 2020; Senn et al., 2014) and dik-diks
(Madoqua spp.) (De Jong & Butynski, 2017; Kingdon,
2013b). Molecular evidence, in fact, reveals only part of
an often complex evolutionary picture and many other
sources of information (e.g., morphology, behavior, ecol-
ogy) should be integrated with DNA data for a deeper
understanding of the history of a lineage.
In this context morphometrics, and especially its
modern, version geometric morphometrics (GMM),
offers a fairly simple and relatively low-cost approach
to further explore group differences. Costs are particu-
larly low when taxonomic analyses using GMM can
take advantage of the extensive collections available in
natural history museums and/or rely on a network of
scientists to provide data, which can be done by shar-
ing standardized photographs and/or measurements,
or even by obtaining new specimens of rare popula-
tions with the help of field biologists who opportunisti-
cally collect skulls of dead animals (e.g., Chiozzi
et al., 2014; Nowak et al., 2008).
Two dimensional (2D) GMM is particularly suitable
to these types of exploratory analyses. This is because it
only requires conventional photographs of crania or other
anatomical structures on which to take measurements.
Compared to three dimensional (3D) data, 2D GMM is
faster but inevitably less accurate whenever applied to a
structure which is not flat (
Alvarez & Perez, 2013;
Cardini, 2014; Roth, 1993). Thus, especially in mam-
mals, 2D GMM virtually always introduces an impor-
tant source of measurement error (ME) by flattening
the third dimension (reviewed by Cardini & Chiapelli,
2020). There are, however, expedients which may help
mitigate this bias. It is generally best to demonstrate, in
a subsample representative of the variation in the taxo-
nomic group one intends to study, that the 2D to 3D
(TTD) approximation is good.Thisiscrucialwhenthe
differences being investigated are likely to be small,
as typical of microevolutionary studies or those at
the boundary between micro- (i.e., intraspecific) and
macro- (i.e., supraspecific) evolution (Cardini, 2014;
Cardini & Chiapelli, 2020).
1.1 |The case of the patas monkey
Well resolved and widely accepted taxonomies are impor-
tant to our understanding of evolution, ecology, and behav-
ior, and to the management and conservation of species
and subspecies (Cotterill et al., 2014; Grubb et al., 2003;
Zachos, 2016). This taxonomic idealhas, however, seldom
been attained. For most taxonomic groups, a start has been
made, but much work remains to be undertaken. One
example of the magnitude of this problem is the current
taxonomy for Africa's primates with its many on-going
debates and the endless list of unanswered questions
(Butynski et al., 2013; Groves, 2001; Grubb et al., 2003). A
more specific example is provided by the patas monkeys
(genus Erythrocebus), a group of large, slender, long-limbed,
semi-terrestrial guenons, endemic to tropical Africa
(Isbell, 2013). The geographic distribution of patas monkeys
(hereafter referred to as patas) is large, extending from
Senegal across the Sahel to Tanzania (Figure 1 and De
Jong & Butynski, 2020a; De Jong et al., 2020). About
19 patas taxa have been described since 1775 (Elliot, 1913;
Groves, 2001; Hill, 1966; Napier, 1981).
The current taxonomy for patas, as recognized by
IUCN (2020), comprises three species and three subspecies:
western patas (E. patas patas), Aïr Massif patas (E. patas
villiersi), eastern patas (E. patas pyrrhonotus), Blue Nile
patas (E. poliophaeus), and southern patas (E. baumstarki).
This taxonomy is based largely on the study of the
colouration and pattern of the pelage. There are only mea-
ger morphological data to support this taxonomic arrange-
ment and no molecular data. For all six taxa, the historic
geographic limits are poorly known. In terms of the survival
of these taxa, the IUCN Red List of Threatened Species
(IUCN, 2020) indicates that western patas is Near
Threatened(Wallis, 2020), eastern patas is Vulnerable
(De Jong & Butynski, 2020b), Blue Nile patas is Data Defi-
cient(Gippoliti & Rylands, 2020), and southern patas is
Critically Endangered(De Jong & Butynski, 2020a). The
degree of threat status for Aïr Massif patas has yet to be
assessed for the Red List.
Patas taxonomy is contentious and in need of support
or revision, an exercise to which the three authors of this
article are contributing. Since some phenotypic charac-
ters have already been examined, at least preliminarily,
progress toward this end is largely dependent upon
detailed morphological, ethological, biogeographical,
and molecular studies. Through the research presented
in this article, we hope to move one step closer toward
this goal as we prepare to undertake a geometric mor-
phometric study of the crania of patas obtained from
across its geographic distribution. In the longer term,
however, we hope to complement the quantitative study
of morphological differences with multiple lines of evi-
dence using an integrative approach.
1.2 |Objectives
In this paper, we examine TTD by taking advantage of
an available dataset of 3D landmarks collected on
crania obtained for a previous project on the morpho-
logical variability of African monkeys (Cardini &
Elton, 2017, and references therein). This dataset
includes a sample of patas. The sample is small
(Figure 1; Table 1) because this genus, which occurs
naturally at low densities over most of its range, is
poorly represented in museum collections. Neverthe-
less, this sample is precious, as it includes most of the
complete adult specimens found in some of the largest
museums of North America and Europe, and because
we have 2D photographs for the same individuals for
which we have 3D data. To explore whether 2D GMM
provides a promising tool for studying the problematic
taxonomy of patas and to obtain important information
for conservation, we applied 2D and 3D cranial land-
marks to the same adult individuals in order to:
1. estimate digitizing error in the 2D photographs
and use this estimate as a benchmarkto better
understand the impact on size and shape of a typi-
cally much larger source of ME such as the TTD
2. assess the magnitude of TTD ME relative to the bio-
logical variability in size and shape;
3. investigate the nature of the TTD error by exploring
the variancecovariance structure of shape data;
FIGURE 1 Geographic distribution of the patas monkeys (Erythrocebus spp.) with 29 locations depicted for those crania used in this
study for which provenance is known. Provenance not accurately known for seven crania: Three from zoos, two E. baumstarki, and two
E. p. pyrrhonotus. Map based on De Jong et al. (2020) and De Jong and Butynski (2020a, b; 2021)
4. perform parallel tests in 2D and 3D using biological
questions, including taxonomic questionsin rela-
tion to group differences in shape and allometry, to
test whether 2D data provide the same answers as the
more accurate 3D landmarks.
2.1 |Data: Samples and measurements
2.1.1 | Sample and landmarks
Collection localities are shown in Figure 1 and sample
composition is detailed in Table 1. All 36 specimens are
adult and all but three are wild animals. The three indi-
viduals from zoos do not show unusual cranial morphol-
ogies compared to wild specimen and are included in this
methodological study to increase sample size (N) and sta-
tistical power. As mentioned, obtaining large samples of
patas is challenging as they are uncommon in museum
collections. This implies that many specimens can be
measured only by visiting a large number of museums,
which inevitably requires much time and money. Indi-
viduals used in this study belong to the collections of the
American Museum of Natural History (New York),
United States National Museum (Washington, DC),
Harvard Museum of Comparative Zoology (Cambridge),
British Museum of Natural History (London), Powell Cot-
ton Museum (Birchington, UK), Museum für Naturkunde
(Berlin), and Royal Museum for Central Africa (Tervuren,
Belgium). A more detailed description of the sample and
a list with catalog numbers is available at: www. Most of the 3D data
used in this study are part of a larger set of data on guenons
(Tribe Cercopithecini) analyzed by (Cardini et al., 2007;
Cardini & Elton, 2008a, 2008b, 2017), described in
(Cardini & Elton, 2017), and available for download at:
The configuration of landmarks on the ventral side of
the cranium is shown in Figure 2 and described in
Table 2. These also detail which 3D landmarks of the
original configuration used in previous studies they
correspond to. The ventral cranium was chosen as it has
a fairly large number of almost coplanar landmarks,
which aids in reducing the error due to the flattening of
the third dimension. The ventral view of the cranium is
also relatively easy to position in a standardized orienta-
tion, so that it lays approximately parallel to the lens of
the camera (Panasonic Lumix DMC-TZ6 with Leica lens,
held ca. 3545 cm from the specimen, with either no
zoom or a maximum 2zoom factor and resolution of
1,984 by 1,488 pixels). We selected those anatomical land-
marks that are both available in this region in the 3D
dataset and easy to see in the photographs. A few of the
landmarks on the alveolar margin of the premolar-molar
toothrow were, however, excluded to reduce redundancy
and to have a more evenly spread set of landmarks. From
the total configuration of 25 landmarks, we also selected
three smaller (reduced) configurations that might help
to improve the TTD approximation and compared results
from these subsets to those of the full configuration. To
decide which landmarks to include in the reduced config-
urations, we considered both the putative importance of
the information they convey and estimates of ME (see
below for more details). Once we found which of the
reduced configuration datasets had a smaller TTD error
(see point 2 of the section on statistics), we performed all
further analyses (34) on this reduced set of landmarks,
as well as on the full configuration.
2D landmarks were digitized in TPSDig 2.31
(Rohlf, 2015), only on the left side of the cranium.
Although it is generally better to landmark and measure
both sides of a symmetric structure (Cardini, 2017), we
opted for a one-side only approach for consistency with
the 3D dataset. For the 3D data (collected using a three-
dimensional digitizer (MicroScribe 3DX; Immersion
Corporation, San Jose, CA), this also reduced costs and
maximized sample size. The left-side only 2D-measuring
of landmarks was repeated after 1 week to have replicates
to estimate digitization error. Both sets of measurements
were taken by AC. Paired landmarks were then mirrored
and the very small asymmetries on the midplane
removed following (Cardini, 2017). Because the photo-
graphs of the ventral crania were originally taken as
snapshots with no specific research purpose, the scale
factor in those images is approximate and may show
small inconsistencies among individuals. Thus, as in
TABLE 1 Sample composition for
western patas monkey (Erythrocebus
patas patas), eastern patas monkey (E.
patas pyrrhonotus), and southern patas
monkey (E. baumstarki)
Sex Eastern Southern Western Zoo Total
Females 4 1 5 2 12
Males 15 3 5 1 24
Sex-corrected19 4 10 3 36
Cardini and Chiapelli (2020), the 2D data were rescaled
using a measure of condylobasal length obtained from
the 3D coordinates between landmarks 1 and 19. This is
akin to using a simple but accurate caliper measurement
taken directly on the crania instead of a distance mea-
sured using a scale factor in the photograph, as custom-
ary in 2D GMM analyses.
2.1.2 | Geometric morphometrics and
Landmark-based GMM extracts the features of interest
from a study structure by computing the centroid size of
a set of anatomical landmarks and, having set centroid
size to unit in all individuals, by standardizing positional
differences in the sample using a Procrustes superimposi-
tion (Rohlf & Slice, 1990). The superimposition produces
a new set of variables, the Procrustes shape coordinates.
This allows the measurement of multivariate differences
in terms of Procrustes distances, which are generally
equivalent to Euclidean distances in a multidimensional
Euclidean space tangent to the curved Procrustes space
(Rohlf, 2000). It is, however, important to bear in mind,
as stressed in Cardini (2020a), that Procrustes is a least
square approach, which has statistically desirable proper-
ties but is not based on a biological model. The biologi-
cal arbitrarinessof this choice, thus, prevents univariate
analyses of the shape variables, as well as analyses and
interpretations of variance one landmark at a time. In
contrast, this method performs well, and results can be
accurate, when shape coordinates are analyzed all
together using multivariate methods (Rohlf, 1998) and
the findings are carefully interpreted using diagrams that
integrate patterns of covariation over the entire set of
landmarks (Klingenberg, 2013).
Another consequence of the Procrustes superimposi-
tion is that shape spaces are specific to each landmark
configuration. This is also true when the landmarks are
the same but one set is 2D and the other is 3D. The
dimensionality of the data is also necessarily different in
this case, because 2D data have only two coordinates
(Xand Y) for each landmark, whereas 3D data have a
third (Z) coordinate. For these reasons, 2D and 3D results
are usually compared with correlational analyses in sepa-
rate data spaces (as we do specifically to answer our
fourth study question). The two types of data can, how-
ever, be broughtinto the same space using an
FIGURE 2 Landmark configuration (FULL). Red landmarks are those of the reduced configuration with the smallest TTD ME
(i.e., RED-4)
expedient (Cardini, 2014; Cardini & Chiapelli, 2020). This
simply involves adding a zero Z coordinate to the X and
Y coordinates of the 2D data, superimposing these data
with the 3D data (Figure 3a), and mean-centering the
two sets of shapes to remove the bias due to the missing
information in the third dimension (Figure 3b). This
allows for exploratory analyses in the same data space,
such as ordinations and phenograms (Viscosi &
Cardini, 2011), as well as analysis of variance (ANOVA;
Klingenberg et al., 2002), which is conventionally used to
assess whether individual variation in a sample is larger
than ME.
mostly visualized in MorphoJ 1.07a (Klingenberg, 2011),
although we did most of the statistical analyses in R
(R Core Team, 2020) using scripts written by AC. Specifi-
cally, we used the following main R packages: vegan
(Oksanen et al., 2011) for permutational analyses of
TABLE 2 Landmark definitions: Gray background shows potentially problematic landmarks (underscored for those with largest
digitizing error in 2D; bold for those with largest difference between 2D and 3D shapes in the common shape space)
Midplane Paired Definition Cardini et al. (2007)
1 Prosthion: antero-inferior point on projection of
premaxilla between central incisors
2 Posterior-most point of lateral incisor alveolus 3
3 Anterior-most point of canine alveolus 4
4 Mesial P3: most mesial point on P3 alveolus,
projected onto alveolar margin
56 Contact points between adjacent premolar/molar
projected onto alveolar margin
7Posterior midpoint onto alveolar margin of M3 10
8 Posterior-most point of incisive foramen 15
9 Meeting point of maxilla and palatine along
10 Point of maximum curvature on the posterior
edge of the palatine
11 Tip of posterior nasal spine 19
12 Meeting point between the basisphenoid and
basioccipital along midline
13 Meeting point between the basisphenoid,
basioccipital and petrous part of temporal bone
14 Most medial point on the petrous part of temporal
1516 Anterior and posterior tip of the external auditory
1718 Distal and medial extremities of jugular foramen 28, 30
19 Basion: anterior-most point of foramen magnum 31
2021 Anterior and posterior extremities of occipital
condyle along margin of foramen magnum
32, 35
22 Opisthion: posterior-most point of foramen
23 Inion: most posterior point of the cranium 37
24 Zygo-temp inferior: infero-lateral point of
zygomaticotemporal suture on lateral face of
zygomatic arch
25 Posterior-most point on curvature of anterior
margin of zygomatic process of temporal bone
Note: The last column shows the corresponding landmarks in previous studies.
variance and covariance, and for matrix correlations; car
(Fox & Weisberg, 2011) and adegraphics (Siberchicot
et al., 2017) for ordinations and scatterplots; MASS
(Venables & Ripley, 2002) for simulating random normally
distributed multivariate data; and shapes (Dryden, 2019)
and Morpho (Schlager, 2017) for analyses which required
that the superimposition be redone for visualizing 3D sup-
erimposed shapes in a common space, and for testing classi-
fication accuracy according to taxonomic groups.
2.1.3 | Dataset abbreviations and criteria for
selecting reduced configurations
A summary of all the main abbreviations used in this
study is presented in Appendix A. Here, we describe, in
more detail, the abbreviations for the different sets of data:
FULLis the total configuration of 25 left side land-
marks (Figure 2), which became 43 after mirror reflection
of the paired landmarks. FULL-0refers to the data
using the full configuration in the two 2D replicates
(i.e., the same photographs digitized twice). FULL-1is
the same configuration both with 2D (using for each indi-
vidual the mean of the two digitizations) and 3D data.
REDrefers to the reduced configurations where land-
marks potentially affected by a relatively larger ME were
removed. To decide these potentially problematicland-
marks we used three criteria:
RED-2: in this configuration, we excluded land-
marks with the largest 2D median digitization error in
FULL-0. These were selected by summing the variance
of Xand Ycoordinates of, for instance, the two repli-
cates of landmark 1. For this, we used the raw coordi-
nates (before doing any superimposition) because they
are separate digitizations of the same photograph and,
therefore, any difference in Xand Yis purely due to
digitizing error. As an estimate of the average digitiz-
ing error of this landmark, we took the median of the
variances of landmark 1 across all 36 individuals. We
did the same for all landmarks. Finally, we excluded
FIGURE 3 Procrustes superimposed 3D and 2D shapes (FULL-1) before (a) and after (b) removing their mean difference (side view in
the right half of the figure). The arrows indicate inion (landmark 23), which is off the main plane of the other landmarks even after mean-
the anatomical landmarks whose median 2D digitizing
error is larger than the 90th percentile of the medians
of all 25 landmarks. Specifically, we removed land-
marks 11, 15, 16 and 18 (and the corresponding
mirror-reflected paired landmarks). In fact, landmark
16 had a variance (12.5 mm
), which is slightly lower
than the 90th percentile (12.8 mm
), but we decided
not to include it because we were already aware that
15 and 16 (anterior tip and posterior tip of the external
auditory meatus) are difficult to locate precisely both
in 2D and 3D.
RED-3: in this configuration, landmarks with the largest
median 2D-3D shape variance in FULL-1 were removed.
They were selected using the same procedure as in RED-2
ond replicate was 2D (means of the two digitizations on
the photographs) brought into the same shape space, sup-
erimposed (Figure 3a) and mean-centered (Figure 3b)
(Cardini, 2014). RED-3 tentatively explores whether a spe-
cific landmark might have a very poor TTD approxima-
tion. The hints provided by this analysis, however, should
be taken with great caution and are potentially misleading
because, as mentioned, after a Procrustes superimposition,
landmarks cannot be analyzed or interpreted one at a time
(Rohlf, 1998; Viscosi & Cardini, 2011, and references
therein). Using this approach we excluded landmarks
7, 11 and 23. As this information is preliminary to the
main analyses, we need to mention that we did not expect
the posterior extremity of the premolar-molar toothrow
(landmark 7) to have a particularly large error. This might
be a case where we were misled by the superimposition
spreading the shape variance across the whole set of land-
marks (thus, potentially inflating or deflating variance
locally). In contrast, for the other two landmarks (11 and
pated that they might have a very large ME. The posterior
tip of the nasal spine (11) is difficult to locate precisely,
which is why it also has a large 2D digitization error and
was excluded from RED-2. The inion (23), however, is rel-
atively easy to digitize with a good replicability but, as
suggested by Figure 3a (showing the superimposed 2D
and 3D data before mean-centering), it tends to lie well off
the plane of most other landmarks and is, therefore,
strongly affected by TTD distortions.
RED-4(marked in red in Figure 2): in this last con-
figuration, we selected landmarks by complementing
clues obtained in the selection of RED-2 and RED-3
with our knowledge of anatomy to decide which land-
marks might be particularly problematic or informa-
tive. We, therefore, excluded all those of RED-2 and
RED-3 which we most expected to have large errors,
but made an exception for landmark 7 (the posterior
midpoint onto the alveolar margin of the third molar).
We decided to keep this landmark since we are skepti-
cal about its apparently large TTD error (as explained
above), and also because measuring the length of the
masticatory toothrow potentially provides information
on a taxonomically and functionally important trait.
2.2 |Statistics
Before detailing the statistical analyses, which we subdi-
vide into four main subsections corresponding to the
four sets of research questions, we here clarify more pre-
cisely what components of ME we have assessed, as well
as why we believe that flattening the third dimension is
(i.e., in FULL-1 and the three RED configurations). For
additional information on different sources of ME in
GMM, please refer to the reviews of Arnqvist and
Martensson (1998) and Fruciano (2016), as well as a
recent case study by Fox et al. (2020).
Because all data were collected by a single operator, there
is no interoperator bias, which can be a large contributor to
ME in GMM shape data (Daboul et al., 2018; Fox et al., 2020;
Fruciano et al., 2017). In the newly collected 2D data, how-
ever, besides digitizing error (i.e., the precision or repeatabil-
ityinlocatingthelandmarks in the same photograph of a
specimen), which we assessed, there could be a further
source of error in relation to how well (or poorly) the orienta-
tion of a specimen in a photograph can be standardized. In
fact, orientation errors, together with digitizing error, may
affect both 2D and 3D data, with the additional difficulty, in
2D, of landmarking a photograph instead of doing it directly
on the 3D structure. Both of these components of ME are,
however, part of the differences between 2D and 3D and,
therefore, indirectly included in the assessment of the TTD
approximation. Nonetheless, it is likely that 2D flattening is a
major source of ME in our TTD analysis. This is why we
largely interpret the estimates of ME in this main part of the
study as principally due to the distortion of the third dimen-
sion in the photographs. This interpretation is consistent
with the finding (see Section 3) that individual shape vari-
ance is 14 times larger than 2D digitizing error (and on aver-
age more than 10 times larger using 3D skulls of guenons;
Cardini & Elton, 2008a), whereas in the TTD comparison it
was only four to five times bigger. Thus, if the digitizing
error in the TTD comparison is only slightly larger than in
2D, with the orientation error typically about as large as
digitization error (smaller sometimes: Evin et al., 2020; Fox
et al., 2020; Joji
comm.; Cardini, unpublished; although larger in a few
cases: Fruciano, 2016; Klenovšek & Joji
c, 2016; Murta-
Fonseca et al., 2019), the flattening of the third dimension
becomes the most likely main source of TTD error.
2.2.1-2.2.2 | Analyses comparing the
magnitude of ME to biological differences in
size and shape using ANOVAs (1) and
correlational/graphical approaches (2)
We assessed whether the magnitude of variation among
averaged replicates of the individuals in the sample
(which for brevity we refer to as biologicalvariation) is
larger than differences between replicates using hierar-
chical ANOVAs (analysis of variance) with sex as the
main factor and individuals as a random factor
(Fruciano, 2016; Klingenberg et al., 2002; Viscosi &
Cardini, 2011). This design controls for sex differences
before comparing individual variation to the residual var-
iance, which represents differences between replicates
(i.e., our estimate of ME). Thus, by statistically control-
ling for sexual dimorphism, we avoid underestimating
the importance of ME relative to individual variation.
Taxonomic comparisons of appreciably dimorphic taxa
using separate analyses for females and males are gener-
ally more desirable (Cardini, 2020a) than sex-correc-
tions(such as the one we used here). However, we
adopted the strategy of statistically controlling for sex dif-
ferences in order to increase N in a study where N is low
and which is mostly methodological. Thus, as our main
aim is the assessment of ME, we preferred to tolerate the
cost of a small reduction in biological accuracy in order
to gain a higher statistical power.
In relation to sex-correction, we concisely report here
an issue that has no consequences on the robustness of our
results. In the specific case of an ANOVA on 2D and 3D
shapes, brought into the same shape space using Car-
dini's (2014) approach, the effect of sex is not completely
removed if some of the analyses are later performed sepa-
rately on the two types of data. For instance, by retesting
sex within sex-corrected 2D (or 3D) shape alone, one finds
that, on average, about 3% of variance is still explained by
sex. This small effect (about 10 times smaller than the total
observed sex differences in shapesee Section 3) is a conse-
quence of the interaction between sex and type of data
(2D vs. 3D). This interaction term was not included in the
ANOVA model because it is small and not significant. If
included, however, the sex-correction completely removes
within 2D (or 3D). The effect of the interaction in our
dataset is, therefore, real but negligible. Indeed, sex-
corrected shape distances, without or with the interaction
in the model, have an almost perfect matrix correlation
(r=0.981.00, depending on the configuration). This indi-
cates that the shape similarity relationships are almost the
same despite the small amount of sexual dimorphism left in
the residuals of the ANOVA with no interaction term. In
this study, therefore, the interaction was ignored in all
analyses except the parallel tests of taxonomic differences
(i.e., the fourth set of tests, described below), which are run
separately in 2D and 3D. Yet, even in this last set of ana-
lyses, as in all others, the two slightly different ways of sex-
correcting shapes produced virtually identical results. Even
repeating the parallel tests using only the larger male sam-
ple (thus, using no sex-correction) did not appreciably
change our findings (as we concisely summarize here).
Using male-only data in FULL-1 and RED-4, the main dif-
ferences were the typically larger percentages of variance
explained in the tests of group differences (712%, and con-
sistently slightly larger in 2D, although significant only in
FULL-1 2D) and the marginally better prediction of taxo-
nomic affiliation using shape in FULL-1 (7585% cross-
validated accuracy in, respectively, 3D and 2D). This first
observation is expected, because R
tends to be over-
estimated in small samples (Cramer, 1987; Nakagawa &
Cuthill, 2007), while the second observation may be a con-
sequence of a smaller within-taxon heterogeneity (and thus
better separation) in same-sex data compared to sex-
corrected data. However, as mentioned, none of these small
differences changed the conclusions of the main analyses
and are briefly discussed here so as to not further distract
the reader from the main findings.
We performed ANOVA tests both on size and shape
with the same design using the vegan adonis() function
and permutations of Euclidean distances (Oksanen
et al., 2011). In this and all other tests of significance (see
next sections) we used 10,000 permutations for the spe-
cific test statistics. For digitizing error in 2D data (FULL-
0), the first and second replicates correspond to the first
and second digitization of landmarks. In contrast, for the
analysis of the TTD approximation (FULL-1 and all the
RED configurations), the first replicate used the 3D data
and the second replicate the 2D data (averaged between
the two digitizations of FULL-0). When analyses required
a common shape space, as in the case of the ANOVA,
phenograms, and some of the ordinations (see below),
the 2D and 3D sets of data were the mean-centered
shapes superimposed together, as explained in the
section on GMM (Cardini, 2014).
Using sex-correcteddata (i.e., after removing the
mean differences due to sex), we computed the correla-
tion between estimates of centroid size and shape dis-
tances in the first and second replicate. For shape, we
did this by computing the matrix correlation of Pro-
crustes shape distances in 2D and 3D. Also, for shape,
we calculated the proportion of specimens with the
two replicates of an individual clustering together as
sistersin phenograms (unweighted pair group
method with arithmetic mean UPGMA using the
matrix of Procrustes sex-corrected shape distances in
the common shape space). If differences between
replicates are small relative to those among specimens
in a sample, the expectation is that they will cluster in
pairs as nearest neighbors.
2.2.3-2.2.4 | Exploring the structure of ME
(3) and the congruence of results (4) in 2D with
those in 3D
In the sections dedicated to the third (2.2.3) and fourth
(2.2.4) set of our research questions, we restricted the ana-
lyses to shape in the two configurations which are poten-
tially more interesting, either becausetheyincludethemost
complete information (FULL) or are the most promising in
terms of smaller TTD error (RED-4, see Section 3). We did
not analyze size because, as in previous studies
(Cardini, 2014; Cardini & Chiapelli, 2020), analyses (12)
demonstrated that centroid size in 2D corresponds accu-
rately to its estimates in 3D, except for a very small bias,
which likely leads to a slight underestimate of 2D size. Also,
unless we specify otherwise, we analyzed only sex-corrected
shape in order to control for the otherwise dominant effect
of sex differences.
As before, we employed the FULL configuration in the
two sets of 2D digitizations (i.e., the FULL-0 dataset) as a
sort of benchmarkto compare the impact of a strong
source of ME, such as the TTD approximation, to a much
smaller one, such as digitizingerror.Thus,sectionthree
explores covariance in relation to ME (2D digitizing error in
FULL-0 or TTD error in FULL-1 and RED-4). Section 4, in
contrast, explores the congruence of findings from analyses
of group differences by comparing them either between the
first and second replicate of the 2D landmarks (FULL-0) or
between the 2D averaged (between replicates) shapes and
the 3D data (FULL-1, RED-4).
2.2.3 | Structure of ME
Variance and covariance in relation to ME: Differences
in variance covariance
First, using matrix correlations, we explored how well
covariance in 2D corresponds, in terms of overall propor-
tionality, to estimates in 3D. We then tested if the magni-
tude of shape variance is the same in 2D and 3D using
paired permutation tests for estimates of total multivariate
variance. The tests for differences in magnitude of shape
variance are the multivariate equivalent of a (paired)
Levene's test for univariate data (Willmore et al., 2006). As
test statistics, we employed the absolute difference of each
of three estimators of overall multivariate variance: VAR1,
the sum of variances of the shape coordinates (whose test
is approximately equivalent to using an Fratiothus,
showed in Section 3 together with the corresponding R
but not tested); VAR2, the mean of pairwise Procrustes
shape distances among all individuals in a sample; VAR3,
the 90th percentile of the same set of pairwise Procrustes
distances used in VAR2. VAR1 is intuitive, as it is a
straightforward extension of univariate variance. VAR2
and VAR3 can be interpreted, respectively, as the average
difference in shape among all individuals in a sample and
the equivalent, based on multivariate distances, of a
trimmed range (from minimum to maximum) for univari-
ate data. These types of variance metrics are commonly
employed in disparity analyses (Foote, 1997).
Although we did these analyses on sex-corrected
shapes, as anticipated, data without sex-correction pro-
duced very similar results (not shown).
Variance and covariance in relation to ME: Exploring
the strength of covariance in the ME component of
shape variation
Cardini and Chiapelli (2020) found that, despite a large TTD
error in ventral cranial shapes of equids, tests of biological
questions (such as the relevance and patterns of allometry
and species or sex differences) produced results in almost
perfect agreement when performed in parallel on 2D and 3D
data. They speculated that, despite inaccuracies in the precise
relative positions of the specimens in the 2D shape space
compared to the 3D shape space, and the relatively large ME
(accounting for ca. 919% of variance within, respectively,
genus Equus and plains zebra [E. quagga]), the biological
covariance of the data was much stronger than that of
ME. Thus, they argued that the genuine signal(behind the
test results and patterns) could overcome the noiseintro-
duced by the TTD approximation.
To explore Cardini and Chiapelli's (2020) hypothesis on
why 2D may produce accurate results despite an apparently
fairly poor TTD approximation, we first checked the magni-
tude of the correlation between covariance matrices of the
first and second replicate. We then compared the mean
covariance of the individuals with that of ME (be it the 2D
digitizing error, again used as a benchmark,or the TTD
inaccuracy). Thus, we separated the individual from the
error component of shape using the same ANOVA design
as in the tests of ME (12). On these variables, we com-
puted the covariances of the shape data for the individuals
and the ME, and summarized them using histograms and
the median of the absolute covariances. The use of the abso-
lute value is justified, as we were not interested in the sign
of covariances but only in their average magnitude.
Since we found that covariance is on average much
smaller in ME (see Section 3), we wondered if the
observed small ME covariances might be simply random
noise. This would mean that the error due to the TTD
approximation, or the one related to the imprecision of
2D landmarks, is not structured. We used the mvrnorm()
function in R (Venables & Ripley, 2002) to simulate ran-
dom normally distributed data with variance and no
covariance. In the simulation, variances were those
observed in the ME component of shape, but covariances
were set to zero. Any covariance found in the simulated
data is, therefore, the product of sampling error. How-
ever, because the Procrustes superimposition introduces
a degree of covariation when nonshape parameters are
standardized (Cardini, 2019; Rohlf, 1998; Rohlf &
Slice, 1990), we added the simulated random numbers to
the mean shape of the dataset and performed a Procrus-
tes superimposition. With these randomshape data we
computed the covariance matrix to be compared with the
observed ME covariances. This extra step does not seem
to make an appreciable difference as before and after the
superimposition the simulated covariance matrices had a
correlation of 0.95 or larger. We preferred, however, to
include the superimposition of random data to increase
comparability with observed shape data. This simulation
was run 100 times for each dataset (i.e., FULL-0, FULL-1,
and RED-4) and in each simulation we computed the
median absolute covariance. The resulting 100 medians
were summarized using a histogram, in which we also
plotted the medians of the absolute covariances both of
the observed ME and individual shape data.
2.2.4 | Parallel tests of taxonomic differences
In this final part of the study we performed a series of
tests related to taxonomic differences between the two
largest taxonomic samples, the western patas and eastern
patas (thus, excluding the four southern patas crania and
three zoo specimens crania). Two analyses were under-
taken in parallel, one to compare the first and second dig-
itizations of 2D data (assessing the impact of 2D
digitizing error on results), and one to compare the 2D
and 3D shape variables (the most interesting comparison
to investigate if conclusions from 2D shapes are accu-
rate). As anticipated, we did not analyze centroid size
because its ME is, as determined in previous studies
(Cardini, 2014; Cardini & Chiapelli, 2020), typically negli-
gible. We did, however, briefly explore centroid size
graphically (using box-plot and violin plots) to determine
if 2D data really suggest the same pattern of size variation
as 3D data in relation to taxonomic groups. On shape, in
contrast, we performed three sets of statistical tests:
Differences in mean shapes between taxa
We tested the significance of mean differences between
western patas and eastern patas in a hierarchical per-
mutational multivariate ANOVA controlling for sex
(adonis() function using Euclidean distances in vegan;
Oksanen et al., 2011). Thus, sex is the first main factor
followed by taxon. We also calculated the mean classifica-
tion accuracy (hit rate) of the sex-corrected shape data
using a cross-validated between group principal compo-
nent analysis (XbgPCA; Cardini & Polly, 2020) in Morpho
(groupPCA() function; Schlager, 2017) and assessed if it
was better than expected by chance using a random
chance baseline based on 100 randomizations (Kovarovic
et al., 2011; Solow, 1990; White & Ruttenberg, 2007).
Finally, we illustrated the patterns of sex-corrected shape
variation in the two taxa using ordinations (principal
component analysis, PCA, and also XbgPCA) and visual-
ized the mean differences in shape with wireframe dia-
grams both for 2D and 3D data (Klingenberg, 2013).
Differences between taxa in magnitude of sex-corrected
shape variance
These were tested using permutations and the same test
statistics (VAR1, VAR2, and VAR3) as explained in the pre-
vious subsection but, because the groups (i.e., western patas
and eastern patas) are now independent, the permutations
simply affiliated randomly the individuals to the groups to
simulate the null hypothesis of no differences.
Static allometric trajectories of sex-corrected shapes in
western patas and eastern patas
We tested the significance and divergence of static allom-
etries (Klingenberg, 1998) using a permutational multi-
variate analysis of covariance (ANCOVA, in vegan using
the adonis() function and Euclidean distances; Oksanen
et al., 2011). In this analysis, the taxon by centroid size
interaction tests the significance of the differences in the
allometric trajectories, for which we also computed the
angles in the multivariate space.
As with the methods, we present the results by sub-
dividing them into four sections which correspond to the
four sets of research questions.
3.1-3.2 |Analyses comparing the
magnitude of ME to biological differences
in size and shape
ANOVAs of size (Table 3) are dominated by sex differ-
ences that in all datasets account for about 75% of total
variance. Individual variation, sex-corrected by control-
ling for differences between females and males, accounts
for almost all the remaining variance (25%), with ME
explaining only 0.04% (2D digitizing error in FULL-0) to
0.3% (TTD error in FULL-1) of centroid size differences.
This means that individual biologicalvariation is,
respectively, almost 600 and 100 times larger than
ME. RED-4 shows the best 2D approximation of 3D cen-
troid size, with an R
of 0.1% (i.e., differences between 2D
and 3D estimates of size are more than 200 times smaller
than those among sex-corrected individuals). The correla-
tion between 2D and 3D centroid size ranges from 0.98
(FULL-1 and RED-3) to 1.00 (FULL-0).
Sexual dimorphism is important also for shape
(Table 4) but accounts for a smaller percentage of total
variance (ca. 25%). Sex-corrected individual variation, in
contrast, explains most of the variance (5866%), whereas
ME is almost two orders of magnitude larger than for
size (R
=515%). 2D digitizing had the smallest error
=5%) with individual variation 14 times larger than
ME. TTD error is larger than 2D digitizing error, but
about the same in all configurations (R
=15%) except
RED-4 (R
=14%). For this reason, as well as for its
slightly larger differences among individuals compared to
other configurations except RED-3, individual variation
in RED-4 is five times larger than TTD ME but only four
times bigger in all other configurations.
Correlations of pairwise Procrustes shape distances
mirror the rankingsuggested by the ANOVAs R
terms of relative importance of ME with FULL-0 having
the highest (r=0.93) and RED-4 the second highest
(r=0.80) correlations. The other three TTD datasets
(FULL-1, RED-2, and RED-3) shows lower correlations
(r=0.710-79) and, thus, confirm the marginally smaller
TTD ME of RED-4. In the phenograms (not shown,
except for FULL-1, used as an example in Figure 4), how-
ever, RED-4 turns out not to be the configuration with
the highest percentage of correctly paired replicates. Both
RED-3 and RED-2 perform slightly better than RED-4
(respectively, 5047% vs. 44%), whereas FULL-1 performs
slightly worse (42%). 2D digitizing error (FULL-0), in
contrast, is again much smaller than TTD error in terms
of individuals with sister replicates in the phenogram, as
TABLE 3 Ventral cranial size: analysis of variances testing if individual variation is significantly larger than measurement error (ME);
in the last column, the correlation between the two replicates, after controlling for sex, is also shown
Configuration Factor df SS MS FpR
ratios r
FULL-0 Sex 1 57,869.5 57,869.5 101.53 .0001 74.9% 3
Individual 34 19,379.5 570.0 614.57 .0001 25.1% 580 1.00
36 33.4 0.9 0.04%
Total 77,282.3 100.0%
FULL-1 Sex 1 59,202.8 59,202.8 101.56 .0001 74.7% 3
Individual 34 19,820.0 582.9 97.01 .0001 25.0% 92 0.98
ME 36 216.3 6.0 0.3%
Total 79,239.1 100.0%
RED-2 Sex 1 49,132.4 49,132.4 99.05 .0001 74.3% 3
Individual 34 16,865.3 496.0 111.40 .0001 25.5% 105 0.99
ME 36 160.3 4.5 0.2%
Total 66,158.0 100.0%
RED-3 Sex 1 56,164.7 56,164.7 104.69 .0001 75.3% 3
Individual 34 18,241.1 536.5 137.37 .0001 24.5% 130 0.98
ME 36 140.6 3.9 0.2%
Total 74,546.4 100.0%
RED-4 Sex 1 46,900.0 46,900.0 101.76 .0001 74.9% 3
Individual 34 15,671.0 460.9 219.40 .0001 25.0% 207 0.99
ME 36 75.6 2.1 0.1%
Total 62,646.6 100.0%
Note: In this and following tables, significant (p< .05). pvalues are emphasized using italics or bold italics if highly significant (p< .01); R
ratios compare the
variance explained by one factor (numerator) to the one explained by the next factor (denominator; i.e., how large sex-related variance is compared to
individual differences or how large the individual differences are compared to ME); a gray background is used for results of FULL-0, which only concern2D
digitizing error.
This is just 2D digitizing error whereas in all other cases ME is mainly TTD error.
this happens almost 100% of the time compared to the
ca. 50% that we report above for TTD data.
Thus, among the configurations used to assess TTD,
differences in the magnitude of ME are small but, both
for size and shape (with the exception of the phe-
nograms), RED-4 seems slightly less impacted by TTD
errors. The next two series of analyses are, therefore, per-
formed using RED-4, as well as the complete set of land-
marks (FULL-1, plus FULL-0 for 2D digitization error).
3.3 |Variance and covariance in relation
to ME
3.3.1 | Differences in variance covariance
The correlation between variance covariance matrices
(Table 5) is close to one (0.95) for FULL-0 (first vs. second
replicate of the 2D digitizations), but smaller (ca. 0.8) when
2D is compared with 3D (FULL-1andRED-4).Thisiscon-
sistent with correlations of Procrustes shape distances and
the ANOVA results (Table 4) which show a small 2D
digitization error (FULL-0) but a larger TTD error (FULL-1
and RED configurations). RED-4, again, does marginally
better than FULL-1 (r=0.81 and 0.75, respectively).
the first and second digitization of the 2D photographs is
significant only for VAR2 (.05 > p> .01) and marginally
significant (.1 > p> .05) for VAR1, with absolute deviations
from the means of the two replicates accounting for less
than 1% of variation (Table 5). Thus, it seems that for
FULL-0, variance is approximately the same in the two rep-
licates and differences are overall minor and negligible. In
contrast, all test statistics are significant (with most highly
FULL-1 and RED-4. R
is approximately 5%, and 3D shapes
consistently show larger variance than 2D.
3.3.2 | Exploring the strength of covariance
in the ME component of shape variation
The correlation between covariance matrices (excluding
the diagonal with variances) of individuals and ME is
TABLE 4 Ventral cranial shape: Multivariate analysis of variances testing if individual variation is significantly larger than
measurement error (ME); in the second to last column, the matrix correlation between the pairwise sex-corrected shape distances (first vs.
second replicate) is shown; the last column reports the percentage of cases with replicates clustering as pairs withinindividuals (sister
Configuration Factor df SS MS FpR
ratios Matrix rSister repl.
FULL-0 Sex 1 0.05605 0.001367 14.97 .0001 29.1% 0.4
Individual 34 0.12732 0.000091 30.23 .0001 66.2% 14 0.93
36 0.00892 0.000003 4.6% 97%
Total 0.19229 100.0%
FULL-1 Sex 1 0.05449 0.000447 16.00 .0001 27.2% 0.5
Individual 34 0.11579 0.000028 4.10 .0001 57.8% 4 0.77
ME 36 0.02989 0.000007 14.9% 42%
Total 0.20017 100.0%
RED-2 Sex 1 0.05581 0.000553 16.28 .0001 27.7% 0.5
Individual 34 0.11655 0.000034 4.24 .0001 57.8% 4 0.79
ME 36 0.02912 0.000008 14.5% 47%
Total 0.20148 100.0%
RED-3 Sex 1 0.03522 0.000320 11.50 .0001 21.6% 0.3
Individual 34 0.10413 0.000028 4.61 .0001 63.8% 4 0.71
ME 36 0.02392 0.000006 14.7% 50%
Total 0.16327 100.0%
RED-4 Sex 1 0.04786 0.000488 13.60 .0001 24.7% 0.4
Individual 34 0.11971 0.000036 4.80 .0001 61.7% 5 0.80
ME 36 0.02638 0.000007 13.6% 44%
Total 0.19395 100.0%
This is just 2D digitizing error whereas in all other cases ME is mainly TTD error.
very modest (ca. 0.20.3; Table 6). This suggests large dif-
ferences in covariance structure between these two com-
ponents of shape. Absolute covariances of individuals are
also typically larger than those of ME (Figure 5). This is
particularly evident when individuals are compared to
2D digitizing error (FULL-0; Figure 5a). Most of the
covariances of this type of ME (in blue) are close to zero,
whereas a large proportion (82%) of covariances among
individuals (in red) are larger than that. The same is true
for TTD errors in FULL-1 and RED-4 (78% of individual
covariances larger than those of ME), but TTD error
seems to show more structure and a larger overlap with
individual absolute covariances.
Indeed, that covariance is largely random for 2D digi-
tizing error but more structured for TTD is confirmed in
the simulation of random data with variance of the same
magnitude as ME but with no covariance. As an example,
Figure 6 illustrates the pattern of covariance of individ-
uals, ME error, and simulated random noise by using a
PCA performed on each of the three types of data. The
example is specific to FULL-0 (with ME due to 2D digitiz-
ing error) and RED-4 (with ME being mainly that of the
TTD approximation), but the reasoning and results (not
shown) are similar in other cases. In general, multivariate
data with a strong covariance should produce a few dom-
inant PCs, as a small number of dimensions captures
most of the variance in highly correlated data. This is
what happens for the individuals in both datasets
(Figures 6a1,b1). In contrast, random noise should pro-
duce PCs which explain about the same amount of vari-
ance, although a certain degree of structuremight be
found even for random noise when sample size is small
compared to the number of variables (Bookstein, 2019;
FIGURE 4 Phenogram using, as an example, the sex-corrected
FULL-1 Procrustes shape distances. Individuals are numbered
progressively from 1 to 36. This number is followed by a label
indicating the type of shape data (2D or 3D). The tree shows 42% of
individuals with 2D and 3D replicates clustering together as
TABLE 5 Correlation between
variance covariance matrices (varcov),
and paired tests (using 10,000
permutations) for differences in
magnitude of sex-corrected shape
variation between replicates: First
versus second digitization for FULL-0
and 2D versus 3D in the other instances
All individuals with sex-corrected shape
Statistic rRatio
Statistic pR
FULL-O varcov 0.95
Fratio 0.302 0.4%
VAR1 1.1 0.00015 .0549
VAR2 1.0 0.00239 .0463
VAR3 1.0 0.00186 .3737
FULL-1 varcov 0.75
Fratio 3.604 4.9%
VAR1 1.2 0.00044 .0007
VAR2 1.1 0.00715 .0004
VAR3 1.1 0.00736 .0244
RED-4 varcov 0.81
Fratio - 4.056 5.5%
VAR1 1.3 0.00053 .0002
VAR2 1.1 0.00838 .0002
VAR3 1.1 0.01046 .0071
Second to first replicate for 2D digitizations and 3D to 2D for TTD data: thus, for instance, if >1 for FULL-1
or RED-4, that means that 3D shape has more variance than 2D.
TABLE 6 Summary statistics for covariances of sex-corrected shapes: Matrix correlation between individual and measurement error
(ME) covariances (signed and excluding variances) and comparison of absolute covariances between individuals, ME and simulated ME with
no covariance
Configuration rindiv. vs. ME Obs. vs. simulated Summary statistics Abs. Covariances Ratios
FULL-0 0.25 Obs.: median Individuals 0.00000314 31.4
Obs.: median 2D digitizing error 0.00000010 1.3
Simulated: median Random error 0.00000008
Simulated: 95th percentile Random error 0.00000008
FULL-1 0.15 Obs.: median Individuals 0.00000108 3.4
Obs.: median TTD error 0.00000032 1.3
Simulated: median Random error 0.00000024
Simulated: 95th percentile Random error 0.00000025
RED-4 0.16 Obs.: median Individuals 0.00000141 3.5
Obs.: median TTD error 0.00000040 1.4
Simulated: median Random error 0.00000028
Simulated: 95th percentile Random error 0.00000030
Note: Ratios of medians (individual vs. ME and ME vs. random ME) are shown in the last column.
FIGURE 5 Distribution of absolute covariances for the sex-corrected individuals (red) and the ME residuals (blue): (a) FULL-0;
(b) FULL-1; and (c) RED-4
Cardini, 2019). Thus, as evident in Figures 6a3,b3, vari-
ance accounted for by simulated random noise decreases
fairly smoothly as one moves from the first to higher
order PCs. In contrast, variances accounted for by either
digitizing (Figure 6a2) or TTD error (Figure 6b2) are
somewhat in between the strong pattern of individual
shapes and the gradual pattern of random data. This is
suggested by PC1 of ME explaining some 50% less variance
than PC1 of individuals but about twice the variance
be noted that the difference between observed ME and ran-
dom noise is particularly pronounced for TTD data.
Table 6 and Figure 7 show the overall results of the
simulations, which confirm the impression from Figures 5
and 6. ME has a median absolute covariance above the
95th percentile of the medians in the 100 simulated
datasets and is, therefore, significantly larger (ca. 30
40%) than expected in random variables with the same
variance but no real covariance (except for that due to
sampling error and the superimposition). The median
absolute covariance of ME is, however, much smaller
than for individuals. More precisely, the median absolute
covariance of individuals is more than 30 times larger
than that of 2D digitizing error (FULL-0) and about 34
times larger than the TTD error (FULL-1 and RED-4).
Overall, these results suggest that ME is not random and
has structure, but weak when compared to covariation in
relation to differences among individuals.
3.4 |Parallel tests of taxonomic
Analyses restricted to western patas and eastern patas
(after controlling for sex) confirm the very high congru-
ence of size data, with 2D and 3D suggesting virtually
identical patterns of differences (Figure 8): eastern patas
have, on average, larger crania, but the range of sizes in
the two taxa overlaps extensively. As anticipated, all fur-
ther analyses were done only on sex-corrrected shape,
whose larger ME makes crucial the question about
whether 2D and 3D shape results are similar.
FIGURE 6 Percentages of sex-corrected shape variance accounted for by PCs in FULL-0 (a) and RED-4 (b): (a1b1) individuals; (a2) 2D
digitizing error; (a3) example of simulated random errorwith the same variance as a2 but no covariance; (b2) TTD error; (b3) simulated
random errorwith the same variance as b2 but no covariance
3.4.1 | Differences in mean shapes
between taxa
Tests of group differences in shape using the FULL con-
figuration, as well as RED-4, confirm the strong effect of
sex (accounting for ca. 40% of variance) and suggest neg-
ligible differences between western patas and eastern
patas (Table 7). Mean differences are never significant
and account for less than 3% of shape variance. The inter-
action between sex and taxon is also small (R
=ca. 4%)
and does not reach significance. This supports the appro-
priateness of controlling for sex, as patterns do not differ
statistically between the two groups. As for other tests,
however, nonsignificance may be due to the low power
imposed by small samples.
Cross-validated classification accuracy ranges, on aver-
age, from 55% to 65%. This is only slightly better than
chance (median baseline =4852%), and never above the
95th percentile of 6672% required for significance. Thus,
the XbgPCA classification also indicates negligible differ-
ences in shape regardless of the configuration and type
of data.
Indeed, the congruence between 2D and 3D data is
almost perfect in terms of conclusions about significance
but also, and more importantly in terms of estimates of
the magnitude of the differences, with very similar R
and hit rates. In fact, differences in results of tests for dif-
ferences between taxa are slightly larger between the first
and second digitization of 2D data than between 2D and
3D data. For instance, for the effect of taxon, the FULL-0
FIGURE 7 Median of absolute covariances of sex-corrected shape coordinates for individuals (light gray), ME (dark gray long dash),
and random error(histogram of medians from 100 runs of simulation with dotted line marking their 95th percentile): (a) FULL-0;
(b) FULL-1; (c) RED-4
difference between 2D replicates is 0.4%, whereas for
3D versus 2D in FULL-1 and RED-4 it is, respectively,
0.2% and <0.1%. Similarly, with hit rates, the first and
second 2D digitization show a difference of 7% (with the
first digitization having higher classification accuracy),
whereas the corresponding differences between 3D and
2D in FULL-1 and RED-4 are, respectively, 4% and 0%
(with 3D shapes being marginally more accurate in group
prediction only in FULL-1).
Scatterplots of ordinations summarizing RED-4
tests with an almost complete overlap of western patas
and eastern patas (Figure 9). PCAs show a small sepa-
ration of their respective means both in 3D and 2D data
(Figure 9a1,b1) and slight differences in patterns of
variation between the two taxa. These are suggested by
the orientation and elongation of the confidence enve-
between 2D and 3D. In contrast, XbgPCA scatterplots
(Figures 9a2,b2) show almost identical patterns both in
2D and 3D, with very close means and overlapping
confidence envelopes consistently vertically stretched
(i.e., in the main direction of nonbetween group vari-
ance). Ordinations (not shown) for FULL-1 suggest
similar conclusions of strong congruence with mostly
minor differences between 2D and 3D data.
Shape diagrams of RED-4 mean shapes of western
patas and eastern patas in 2D and 3D (Figure 10) must be
magnified 10 times to visualize small differences. We do
not describe these nonsignificant differences, as they are
tiny. In contrast, it is interesting to observe that, even in
spite of the huge magnification, 3D and 2D produce an
almost perfect match in shape changes in all anatomical
regions of the ventral cranium except the basisphenoid-
basioccipital region. Here, 2D shows a widening of the
bone and slight enlargement of the occipital foramen in
western patas compared to eastern patas, whereas 3D
suggests the opposite. Without magnification, however,
the 2D and 3D patterns look almost identical, both show-
ing very minor differences between taxa.
3.4.2 | Differences between taxa in
magnitude of sex-corrected shape variance
None of the tests (first or second 2D digitization or 2D
vs. 3D) show appreciable differences in shape variance
between western patas and eastern patas (Table 8), although
the latter, with its larger N, consistently has slightly larger
values. 2D, however, tends to moderately overestimate this
small difference showing larger R
6%) and variance ratios. This suggests that eastern patas vary
approximately 10% more than western patas. In contrast, 3D
shapes have smaller R
s (ca. 1%), with variance in eastern
patas only 3% larger, on average, than in western patas.
Thus, although the agreement between 2D and 3D results is
slightly less precise than between the first and second 2D
digitization (unlike what we found with group mean differ-
ences in Section 3.4.1), the bias in 2D is small and does not
affect the conclusions of the tests.
3.4.3 | Static allometric trajectories of sex-
corrected shapes in western patas and eastern
Results of tests of taxonomic differences in static allome-
try are also highly congruent between 2D and 3D data
(Table 9). None of the factors in the multivariate
ANCOVAs is significant in any of the datasets except for
centroid size, which is always highly significant
(p< .01) and accounts for 1011% of variance in the
total configuration (FULL-0 and FULL-1), and slightly
more (13%) in RED-4. The effect of taxon, as well as the
effect of the interaction of taxon and centroid size,
FIGURE 8 Centroid size of RED-4 estimated in 2D (a) and 3D
(b) for sex-corrected eastern patas and western patas. The shape of
the violin plots, the distribution of points in the jitter plots, and the
similar box plots all indicate an excellent congruence of the two
types of data
which tests whether allometries differ between western
patas and eastern patas, are not significant. Indeed, they
account for very small amounts of shape variance (2
4%). Nevertheless, in the highly dimensional shape
spaces, the angles formed by the allometric trajectories
of the two patas taxa are large (ca. 4950on average).
Angles are very similar in 3D and 2D being, respec-
tively, 5355in FULL-1 and 4850in RED-4. In
fact, the discrepancy in estimates of the angles of allo-
metric vectors is larger in the comparison of the first
and second 2D digitization, with a difference of 5(53
vs. 58), compared to just 2in the TTD datasets.
4.1 |Aim and context
ME in GMM has received more attention in the last
decade, as shown by Fruciano (2016) in his detailed
TABLE 7 Multivariate analysis of variances (ANOVAs) for shape differences in 3D and 2D, and leave-one out cross-validated
classifications using sex-corrected shapes
2D or 3D Type of shape data
ANOVA bgPCA Random baseline
Factor df SS MS FR
pHit rate Median 95th
2D FULL-0 1st digitization Sex 1 0.03108 0.031081 18.51 39.4% .0001
Taxon 1 0.00222 0.002215 1.32 2.8% .2337 62.1% 52.2% 69.2%
Sex by taxon 1 0.00355 0.003553 2.12 4.5% .0809
Residuals 25 0.04198 0.001679 53.3%
Total 28 0.07882
2nd digitization Sex 1 0.03229 0.032290 21.02 42.9% .0001
Taxon 1 0.00184 0.001839 1.20 2.4% .2720 55.2% 48.3% 69.2%
Sex by taxon 1 0.00278 0.002775 1.81 3.7% .1248
Residuals 25 0.03840 0.001536 51.0%
Total 28 0.07531
Sex 1 0.03101 0.031005 20.76 42.3% .0001
Taxon 1 0.00193 0.001925 1.29 2.6% .2365 62.1% 55.2% 69.0%
Sex by taxon 1 0.00302 0.003016 2.02 4.1% .0981
Residuals 25 0.03734 0.001494 51.0%
Total 28 0.07329
Sex 1 0.02742 0.027423 19.01 40.9% 0.0001
Taxon 1 0.00153 0.001533 1.06 2.3% .3305 62.1% 48.3% 65.7%
Sex by taxon 1 0.00203 0.002026 1.40 3.0% .2046
Residuals 25 0.03607 0.001443 53.8%
Total 28 0.06705
Sex 1 0.03602 0.036022 20.34 42.2% .0001
Taxon 1 0.00201 0.002010 1.14 2.4% .2745 65.5% 51.7% 69.0%
Sex by taxon 1 0.00302 0.003021 1.71 3.5% .1283
Residuals 25 0.04427 0.001771 51.9%
Total 28 0.08532
Sex 1 0.03334 0.033341 18.98 40.6% 0.0001
Taxon 1 0.00189 0.001889 1.08 2.3% .3131 62.1% 51.7% 72.4%
Sex by taxon 1 0.00289 0.002886 1.64 3.5% .1391
Residuals 25 0.04392 0.001757 53.5%
Total 28 0.08204
2D versus 3D matrix correlation for sex-corrected Euclidean shape distances r=0.58.
2D versus 3D matrix correlation for sex-corrected Euclidean shape distances r=0.54.
review, but also as summarized, in the specific context
of TTD errors, by Cardini and Chiapelli (2020). The
renewed interest in ME is welcome, as the field has
encountered increasing success over the years (Adams
et al., 2013), but most of its focus has been on new
methods and innovative applications (Cardini &
Loy, 2013). Much less attention has been devoted to
the centrality of accurate data (Cardini, 2020a) and
other less fashionabletopics, including ME. Arnqvist
and Martensson (1998) wrote their important and
highly cited contribution on ME in GMM almost
20 years before Fruciano's (2016) much needed update.
Exactly 20 years have passed since Roth's (1993) early,
but largely ignored, warning on the potential problems
of 2D studies and the publication of a series of papers
FIGURE 9 Scatterplots summarizing RED-4 sex-corrected shape variance (percentages of total in parentheses) of eastern patas and
western patas ventral crania with 2D and 3D data in separate shape spaces (95% confidence envelopes are shown as well as mean shapes
[filled circles] for the two groups). In the PCA (a1b1), 2D and 3D both suggest a large overlap between eastern patas and western patas,
although with a more elongated scatter for western patas, especially in 2D. The XbgPCAs (a2b2, with res-PC1 representing the main axis of
nonbetween group variance) confirm, regardless of the type of data, the lack of appreciable mean differences and the almost complete
overlap of the two groups
FIGURE 10 RED-4 average sex-corrected shapes of (a) eastern
patas and (b) western patas magnified 10. 3D means (lighter and
thinner lines) were manually superimposed on 2D means (darker
and thicker lines) to emphasize differences. Despite the huge
magnification, they overlap almost perfectly except in the
basisphenoid-basioccipital region
on TTD errors (see Cardini & Chiapelli, 2020 for refer-
ences) initiated by
Alvarez and Perez (2013) and
Cardini (2014).
ME is especially important for a careful assessment
of small taxonomic differences among closely related
taxa. 2D photographs, as we explained in the Introduc-
tion, are a very convenient source of information for
taxonomic studies using morphological data. They are
relatively easy to acquire and low cost. However, if
measurements on photographs provide an inaccurate
representation of the real 3D structures, results can be
misleading. The validity of 2D data is generally taken
for granted and hardly mentioned in most GMM ana-
lyses using photographs. Yet, this implicit assumption
is crucial, should be discussed and, whenever possible,
tested at least with a small sample in order to explore
the appropriateness of the TTD approximation in rela-
tion to the specific study question.
As the main research on TTD errors has been concisely
presented by the recent paper of Cardini and
Chiapelli (2020), we refer readers to that article for an
overview of the main findings and approaches. Here we
focus our discussion on a comparison with two other stud-
ies (Cardini, 2014; Cardini & Chiapelli, 2020) that, as in
this paper, consistently used all three main methods to
explore TTD congruence. Thus, we discuss findings using
the approach of Cardini (2014), which tests TTD error
within a common 2D3D shape space, as well as findings
from correlational analyses and the comparison of results
from tests run in parallel in 2D and 3D. These previous
studies are not only more directly comparable to our study
of patas, but also provide a complementary point of
view on cranial TTD approximation in different groups
of mammals. Cardini (2014) used marmots as a case study.
Marmots are are rodents with an adult body mass of about
37 kg (Armitage, 1999) and crania about 8 cm in length
(Cardini, unpublished). Cardini and Chiapelli (2020), in
contrast, analyzed much larger animals, the living equids,
which are typical representatives of the terrestrial mega-
fauna, with a body mass at least 25 times (Clauss
et al., 2009) that of the largest marmot and crania 50 cm
or more in length. In terms of size, patas crania are some-
what in between. Although much smaller than equids,
patas have an average adult body mass (ca. 7 kg for female
and 12 kg for male E. p. patas; Isbell, 2013) about twice
that of marmots, and cranial lengths of 811 cm.
Patas are, to our knowledge, the first example of an in
depth study of TTD errors in primates. Thus, we work
with representatives of a different order of placentals
(Primates), but within the same evolutionary and taxo-
nomic context as Cardini (2014) and Cardini and
Chiapelli (2020), who focused on the relatively small vari-
ation typical of microevolutionary studies of adults
within the same species or, at the boundary between
micro- and macroevolution, within the same genus. The
analyses we performed on patas are, nevertheless, more
extensive, as they include differences in the magnitude
and structure of shape variancecovariance, as well as an
exploratory examination of the covariance structure of
ME. In the next sections, starting with size followed by
TABLE 8 Tests for differences in magnitude of sex-corrected shape variation between western and eastern patas analyzed separately for
the first and second replicate (2D digitizations) or 3D and 2D data
Configuration Test statistics
1st replicate or 3D 2nd replicate or 2D
Statistic pR
(%) Ratio Statistic pR
FULL-O Fratio 1.014 .3265 3.6% 0.444 .5119 1.6%
VAR1 0.9 0.00026 .4440 0.9 0.00016 .6428
VAR2 0.9 0.00419 .4628 1.0 0.00231 .6877
VAR3 0.9 0.00799 .3860 0.9 0.00783 .4888
FULL-1 Fratio 0.234 .6365 0.9% 0.667 .4278 2.4%
VAR1 1.0 0.00006 .8142 0.9 0.00018 .5668
VAR2 1.0 0.00074 .8533 0.9 0.00293 .5989
VAR3 1.0 0.00291 .6749 0.9 0.00593 .5071
RED-4 Fratio 0.305 .5856 1.1% 1.652 .2094 5.8%
VAR1 1.0 0.00007 .7896 0.8 0.00024 .3593
VAR2 1.0 0.00107 .7962 0.9 0.00451 .3423
VAR3 1.0 0.00150 .7948 0.9 0.00689 .3150
Ratio between VAR in western and eastern patas; ratios <1 indicate larger variance in eastern patas.
the main analysis on shape, we summarize the most
important findings and compare them with previous
4.2 |Centroid size: Excellent TTD
approximation, and the importance of
coplanar landmarks
ANOVAs, correlations, and summary plots all con-
firmed that 2D data provide estimates of centroid size
which are almost perfectly congruent with those from
3D measurements. This is in agreement with Car-
dini (2014) and Cardini and Chiapelli (2020), hence
our focus on cranial shape. Indeed, 2D centroid size is
accurate and shows no strong bias in patas ventral
crania. For instance, using all landmarks (FULL-1), the
average deviation in western patas and eastern patas is
within ±12 mm of the corresponding 3D estimates,
which in relative terms translates to an inaccuracy of
less than 1%. For comparison, the same differences in
mean centroid size between the first and second 2D
replicates (FULL-0) are, on average, about 0.5 mm, but
that is only 2D digitization error on the same
TABLE 9 Multivariate ANCOVAs for allometry using sex-corrected shape and size in 3D and 2D
2D or 3D Type of shape data
Factor df SS MS fR
2D FULL-0 1st digitization Taxon 1 0.00202 0.002019 1.26 4.2% .2302
CS 1 0.00469 0.004687 2.93 9.8% .0073
Taxon by CS 1 0.00107 0.001068 0.67 2.2% .7470
Residuals 25 0.03997 0.001599 0.84
Total 28 0.04774 1.000000
2nd digitization Taxon 1 0.00168 0.001676 1.16 3.9% .2820
CS 1 0.00448 0.004479 3.11 10.4% .0058
Taxon by CS 1 0.00088 0.000883 0.61 2.1% .7924
Residuals 25 0.03598 0.001439 0.84
Total 28 0.04302
FULL-1 Taxon 1 0.00176 0.001755 1.25 4.2% 0.2472
CS 1 0.00449 0.004487 3.19 10.6% .0046
Taxon by CS 1 0.00087 0.000874 0.62 2.1% .7783
Residuals 25 0.03517 0.001407 0.83
Total 28 0.04229
RED-4 Taxon 1 0.00140 0.001397 1.08 3.5% 0.3484
CS 1 0.00515 0.005145 3.99 13.0% .0002
Taxon by CS 1 0.00082 0.000819 0.63 2.1% .7838
Residuals 25 0.03227 0.001291 0.81
Total 28 0.03963
3D FULL-1 Taxon 1 0.00183 0.001832 1.13 3.7% .2978
CS 1 0.00538 0.005382 3.31 10.9% .0001
Taxon by CS 1 0.00149 0.001493 0.92 3.0% .5369
Residuals 25 0.04059 0.001624 0.82
Total 28 0.04930
RED-4 Taxon 1 0.00172 0.001722 1.08 3.5% .3487
CS 1 0.00607 0.006067 3.82 12.5% .0001
Taxon by CS 1 0.00123 0.001227 0.77 2.5% .7188
Residuals 25 0.03968 0.001587 0.81
Total 28 0.04869 1.000000
photographs and would probably be about twice as
large (see the relative discussion in Section 2) if speci-
mens had been repositioned and rephotographed. Thus,
TTD error in patas cranial size is only slightly larger
than expected in replicates of 2D landmarks and smaller
than TTD inaccuracies in marmots (Cardini, 2014) and
equids (Cardini & Chiapelli, 2020), in which 2D centroid
size was precise but on average tended to slightly
(ca. 2% or less) over-estimate (marmot lateral and ven-
tral cranial views) or under-estimate (marmot hemi-
mandibles and equid ventral crania) 3D centroid size.
Two-dimensional centroid size is, in fact, expected to be
biased and typically underestimate the size of a 3D structure
because distances between landmarks and their centroid
are smaller when variation in depth cannot be measured.
Depending on its position, however, relative to the land-
marks, the scale factor in a photograph may consistently
bias measurements in two directions (downward, if placed
higher than most landmarks, and upward, if lower). For
instance, the position of the scale factor below the land-
marks was the likely explanation for centroid size over-
estimates in marmot crania (Cardini, 2014). Measuring
condylobasal length, directly in 3D, and using this measure
to rescale landmarks from 2D photographs, may avoid
issues with the scale factor in the photograph and contrib-
ute to reducing error in estimates of size. For accuracy it is
evenmoreimportantthatlandmarks are mostly coplanar.
In the ventral crania of patas, only one landmark (inion,
Figures 2 and 3) lies well outside the main plane defined by
the configuration. It is not always easy to know precisely
which landmarks might be less coplanar than others. Car-
dini (2014) argued that the zygomatic arches may often be
taxon and the orientation of the cranium. In side view, for
example, it is very common to have landmarks on the
midplane, as well as around teeth, orbits, and zygoma
(Alhajeri, 2018; Boh
orquez-Herrera et al., 2017; Borges
et al., 2017; Cardini et al., 2005; Chemisquy, 2015; Chevret
et al., 2020; D'Anatro & Lessa, 2006; dos Reis et al., 2002;
Evin et al., 2008; Fornel et al., 2010; Lalis et al., 2009;
Loveless et al., 2016; Marcy et al., 2016; Milenvi
et al., 2010; Myers et al., 1996; Panchetti et al., 2008;
Pandolfi et al., 2020; Samuels, 2009; Scalici et al., 2018;
Yazdi, 2017; Yazdi et al., 2012). These inevitably span multi-
ple depths and may strongly distort estimates of size and
shape in closely related species. Thus, coplanarity seems
crucialinstudiesofsmalldifferences and, together with
rescaling the raw coordinates using a 3D distance, likely
explains why the inaccuracy in centroid size estimates is so
small in our dataset and the error seems random, with no
consistent bias. This observation strengthens the conclusion
of previous research on marmots and equids that, at least in
crania of mammals of medium or large size, centroid size
can be accurately measured using photographs as long as
the photographic setting is reasonably standardized, the
landmarks are mostly coplanar, and the scaling factor is
4.3 |Magnitude of TTD error in shape
Unlike for size, the magnitude of TTD error for shape is
large. Individual variation within sex-corrected patas is
only 45 times larger than differences between 2D and
3D, which is similar to findings in marmot crania
(Cardini, 2014) but slightly more than in equids
(Cardini & Chiapelli, 2020) (with individual variance
about four - marmots - and three - equids - times TTD
error variance). Only in the relatively flat marmot hemi-
mandibles were individual differences much larger
(approximately nine times) than TTD error (Cardini, 2014)
but, in that dataset, individual variance was slightly
inflated by the inclusion of a few young animals in a sam-
ple of mostly adult animals. Thus, overall, it seems that
TTD error, especially within fairly homogeneous samples
of adult mammal crania, accounts for a large proportion
of shape variance within a species or, in the case of patas,
between putative subspecies.
Individual variation was, nevertheless, significantly
larger than TTD error in all three studies, but signifi-
cance on its own does not mean that ME is negligible.
The ANOVA test simply rejects the null hypothesis that
differences among individuals are as large as differ-
ences between 2D and 3D, but cannot rule out the pos-
sibility that the latter are large enough to make 2D
results inaccurate. In fact, if individual variation is only
about 35 times larger than TTD error, then the inac-
curacy in the approximation of 3D shapes in 2D has an
effect size about as large as interspecific differences
within a genus of mammal. For instance, individual
differences within a species of marmot (Cardini, 2014)
or equid (Cardini & Chiapelli, 2020) are about 2.55.5
times larger than interspecific variation, which is the
same range as when individual variation is compared
with TTD error.
The relatively modest congruence of 2D and 3D
shapes is evident also by the moderate correlations
between corresponding matrices of Procrustes shape dis-
tances. In the ventral crania of equids (Cardini &
Chiapelli, 2020), rranged from about 0.5 to 0.6 (respec-
tively, within plains zebra or Equus regardless of species),
while in marmots (Cardini, 2014) it ranged from 0.5 to
0.7 for crania and up to 0.84 for hemi-mandibles. If we
only consider cranial data, which are more directly com-
parable across taxa, these correlations are only slightly
smaller than in patas (r0.70.8). The difference is
unlikely to be a consequence of the smaller size of the
patas sample. Cardini and Chiapelli (2020) showed that
small random subsamples of either plains zebras or the
total Equus sample produce a larger range of values of
matrix correlations (i.e., lower precision) but, on average,
estimates are very similar to (actually, very slightly
smaller than) those observed including all specimens.
Indeed, in small samples, unlike R
that is biased upward
(Cramer, 1987), rtends to be underestimated, especially
when in the range of approximately 0.50.8 (Zimmerman
et al., 2003). Thus, at least compared to the homogeneous
intraspecific sample of plains zebras, the larger rof sex-
corrected patas ventral cranial shapes might be explained
by either a really smaller TTD error or by potentially
larger differences among individuals (or by a mix of these
two effects). That our small sample of patas might span a
range of differences larger than found within a single spe-
cies is consistent with the recent revision of the genus,
that suggests that Erythrocebus is a species complex
(De Jong & Butynski, 2020a,b, 2021; De Jong et al., 2020;
Gippoliti & Rylands, 2020). A comparatively larger vari-
ability among specimens in the sample is also a likely
reason why individual differences in patas are 45 times
larger than TTD error, but only three times larger in
plains zebras and other equids.
Configurations with a smaller number of landmarks
may have lower correlations of 2D and 3D Procrustes
shape distances. This was seen in equids, although the
effect was small and almost negligible (Cardini &
Chiapelli, 2020). In fact, a configuration of just about two
dozen landmarks, as in Cardini and Chiapelli (2020) and
in this study of patas, does not allow a proper assessment
of whether having more or fewer landmarks has an effect
on the goodness of the TTD approximation. Indeed, fewer
landmarks do not automatically lower 2D accuracy, as
we have shown that a careful selection of a subset of
landmarks can slightly improve the correspondence
between 2D and 3D shapes of patas.
On the other hand, the choice of landmarks, and
therefore their number is, strictly functional to the
specific study question (Cardini, 2020a, 2020b;
Klingenberg, 2008; Oxnard & O'Higgins, 2009). If the
aim is individual identification, as in forensics and
some other disciplines, a larger set of points might be a
good choice for capturing the often minute anatomical
details that differentiate each individual. However, for
taxonomic comparisons and many other applications
in evolutionary biology or ecology, where the purpose
is to accurately describe variability within and among
taxa, a better choice could be a smaller but carefully
designed set of points which capture the main differ-
ences in relative proportions of a structure, leaving out
noisy details of dubious relevance for population biol-
ogy. This type of trade-off might explain why Car-
dini (2014) found that ventral crania, with their larger
set of landmarks, had a larger proportion of individuals
clustering as sister replicates in phenograms of shape
distances (ca. 60% vs. ca. 4055% in lateral and dorsal
views of the cranium), despite a lower correspondence
between 2D and 3D distances (matrix r0.5 vs. ca.
0.60.8 in other views), as well as between variance
covariance matrices (matrix r0.5 vs. ca. 0.7 in other
views). On the effect of the number and type of land-
marks on 2D accuracy, there is not enough evidence at
present to make any recommendation. We speculate
that sometimes an increase in precision at the level of
the individual comes at the cost of a reduction in over-
all accuracy in the quantification of inter-individual
similarity relationships, but this will have to be
assessed in future research.
Cardini (2014) and Cardini and Chiapelli (2020) did
in the common shape space. Therefore, we cannot say if
any difference they reported was significant or not, but
in marmots, as in patas, 3D shape variance was consis-
tently larger than 2D variance. One exception, however,
is that 2D scans of hemi-mandibles showed slightly
more variance in 2D. A larger (ca. 827%) 2D shape var-
iance was also found in equids. This is unexpected,
because 2D shape has, in fact, zero variation on the
Zaxis (the third fakecoordinate added to superim-
pose data in a common shape space). Variance should,
therefore, be larger in 3D, as in patas and most of the
marmot datasets (e.g., Cardini, 2014). So, why was 2D
shape variance larger in ventral crania of equids, as
well as in the scanned marmot hemi-mandibles? It
could be because of difficulties of standardizing the ori-
or relate to the type of instrument used for acquiring
images. For instance, hemi-mandibles laid on a flat-bed
scanner are less easy to be consistently and precisely
tively irregular surface of the lingual side. Thus, the
inaccuracies in replicating the orientation of different
specimens adds some extra variance to the data. This
also explained why scans of marmot hemi-mandibles
had a larger ME than photographs (Cardini, 2014). In
the case of equids, it is also possible that, besides issues
with standardizing the orientation, photographic distor-
tions have contributed to variance inflation. This seems
likely, because the distance between the camera and
the specimen was relatively short and a wide-angle
zoom had to be used to photograph these large crania
(Mullin & Taylor, 2002). Marmot and patas crania not
only are easier to position but also, being much smaller,
allow the operator to increase the distance between the
specimen and the camera to reduce distortions in the
photographs (Cardini & Tongiorgi, 2003). Both incon-
sistencies in the orientation of the cranium and photo-
graphic distortions may have inflated 2D shape
variance and contributed to making TTD error in
equids (Cardini & Chiapelli, 2020) larger than in mar-
mots (Cardini, 2014) and patas.
4.4 |Can we reconcile a modest TTD
approximation with accurate 2D results?
Considering the large proportion of variance accounted
for by TTD error in patas, and the low percentage (50%)
of individuals clustering as sisterreplicates in the
phenograms, despite the moderately large 2D3D correla-
tions of Procrustes shape distances and variance
covariance matrices, a complete congruence between
tests performed in parallel on 2D and 3D shapes is unex-
pected. Yet, our series of tests of biological hypotheses
shows an almost perfect correspondence in results of 2D
and 3D shape analyses. Even more surprisingly, this hap-
pens not only for factors with a large effect (such as sex
differences or centroid size in the ANCOVAs), but also
for those accounting for very small proportions of vari-
ance (e.g., taxonomic differences in means, variances,
and allometric trajectories). There are a few exceptions
where estimates in 2D deviate slightly more from the
corresponding 3D estimates, but even in these instances
the conclusions from the tests are the same.
Several of the factors we tested show a very small
effect size and do not reach significance. Power is low in
our small samples and robust answers require many
more specimens, but this is of secondary interest in this
methodological study on the degree of congruence between
2D and 3D results. In fact, having mostly tiny deviations
between 2D and 3D estimates of small R
s, as well as
between estimates of classification accuracy using shape, is
counter-intuitive. Like sampling error, ME is also likely to
have a stronger impact on estimates of small differences. In
our study, the variance explained by the factors being
tested is often half the variance accounted for by TTD
error, or even less than half. For instance, for RED-4, with
a TTD error approximately equal to one-fifth of individual
variance (Table 4), the variance explained by taxonomic
differences was 2.3% both in 2D and 3D, which is just
1/23rd of individual variation (Table 7). RED-4 cross-
validated hit rates (Table 7) were identical (62%), although
with small differences in the 95th percentiles for the ran-
dom baseline of classification accuracy (66% in 2D and 72%
in 3D). Even this discrepancy is, however, small and proba-
bly partly relates to the modest number of randomizations.
With more randomizations, baselines percentages would
likely converge toward more similar values.
That, in spite of the excellent congruence in the tests
and summary plots (Figures 8 and 9), the visualization of
mean shape differences between western patas and east-
ern patas suggest some differences between 2D and 3D
(Figure 10) is understandable. The differences between
these two taxa are small and had to be magnified 10 times
to make them visible. Thus, it is probably more surprising
that the visualization is almost identical for the rostrum,
and only differs in the cranial base region. This differ-
ence, visible only after magnifying changes many times
is, in fact, a good reminder not to over-interpret small
and nonsignificant variation.
With highly congruent 2D and 3D results of tests,
summary plots, and shape diagrams, an obvious question
is: How might this happen when the magnitude of the
TTD error is as large as, or larger than, the size of most of
the effects being tested? This apparent contradiction is
not new. Cardini and Chiapelli (2020) found the same in
equids, where the error was even larger than in patas and
yet results of the tests of biologicalhypotheses were
perfectly congruent in terms of significance, magnitude,
and even patterns in ordinations and shape diagrams.
Thus, individuals are not in the same exact relative posi-
tions in the 2D shape space as in the 3D one, but the dif-
ferences do not seem to lead to inaccurate inferences
when samples are tested. Cardini and Chiapelli (2020)
speculated that this paradox can be explained if TTD
error adds a moderate amount of random noise to a
strong pattern of truebiological covariance. We show,
however, that TTD error is not random. Its covariance
structure is stronger than expected by chance because of
sampling error (Figures 6 and 7) and seems also larger
than with digitizing error (Figures 5 and 6).
A degree of covariance in TTD error is, in fact, more
plausible than an expectation of random error. If large
relative to the size of the effects being tested, random
error would significantly disrupt the correspondence of
2D with 3D similarity relationships. Instead, if there are
no huge photographic deformations and the orientation
of the specimens is well standardized, the distortions in
the photographs due to the flattening of the third dimen-
sion should be relatively similar in all individuals
(at least within species or genera, where the amount of
biological variation is typically small). For instance, land-
marks on the zygomatic arch will be on a plane which is
slightly below that of landmarks on the palate and this
should happen in all individuals and samples. Thus, the
TTD distortion is not purely random and does introduce
a certain amount of covariance, which partly modifies
the truepattern of covariation. Although not as small
as for digitizing error (Table 5, Figures 6 and 7), TTD
covariances are, on average, more than three times
smaller than individual covariance. Thus, after mean-
centering, which removes the main bias between 2D and
3D shape due to the lack of information in the third
dimension in 2D, the TTD error distorts the structure of
variance and covariance, but the distortion is modest
compared to the much stronger truevariancecovariance.
At least within genera of mammals, using cranial data, this
inaccuracy seems to moderately alter the precise position of
specimens in the shape space without having a strong
impact on the general patterns of differences. It does not,
therefore, alter the results of tests in 2D compared to the
same tests in 3D.
Whether this interpretation is correct, and whether
it can be generalized, remain open questions. Future
studies will have to assess TTD error in other mammals
and other organisms, and in other structures (e.g., post-
cranial bones or other views of the cranium), but also
in relation to different hypothesesfor instance, tests
of evolutionary trends or patterns of modularity and
integration. For modularity/integration, where an accu-
rate estimate of variancecovariance is crucial and
Procrustes GMM already faces methodological issues
(Cardini, 2019, 2020b), it will be particularly important
to determine if a partial modification of the 3D pattern
of covariance in 2D analyses adds a further layer of
complexity and potential inaccuracy.
4.5 |Support for the accuracy of 2D
Procrustes GMM using mostly coplanar
landmarks, and considerations on the
importance of standardizing
Our research lends support to the observation that, at
least when adult crania of closely related mammals are
analyzed, results of 2D Procrustes GMM may be accurate
despite TTD errors. This conclusion requires additional
evidence but suggests that the eraof 2D GMM is not
yet over. 3D data are becoming easier to obtain and are
more detailed and accurate whenever a structure is not
flat. Collection of 3D data, however, requires instru-
ments, such as 3D scanners, that are more expensive and
typically slower and less portable than a digital camera.
3D photogrammetry, like 2D GMM, requires only a digi-
tal camera, but each specimen typically needs hundreds
of photographs for accurate 3D reconstructions. This
means longer time for collecting data and more computa-
tional power for processing them (Evin et al., 2016;
Falkingham, 2012; Giacomini et al., 2019; Katz &
Friess, 2014; Muñoz Muñoz et al., 2016). In addition,
landmarking on 3D models is time-consuming and likely
to take longer than digitizing the same landmarks on 2D
photographs. Overall, it seems that 2D GMM offers a
good alternative to 3D for a variety of applications. These
include the measurement and testing of small taxonomic
differences in morphology (this study, and Cardini &
Chiapelli, 2020), but also the study of subtle covariation
between genes and form (Navarro & Maga, 2016). Yet,
accuracy cannot be taken for granted (e.g., Buser et al.,
2018; Hedrick et al., 2019). Whether TTD error is negligi-
ble should be carefully considered before using 2D
methods. This is even more crucial in studies of popula-
tion, subspecies, or species differences, because the evi-
dence they produce contributes to decisions on taxonomic
status. These decisions, in turn, may influence the deter-
mination of conservation priorities (Mace, 2004).
Besides exploring the goodness of the TTD approxima-
tion in a preliminary study using, for instance, the truss
method (Carpenter et al., 1996; Claude, 2008) to rapidly
obtain low-cost 3D landmarks in a representative subsam-
ple (Cardini & Chiapelli, 2020), researchers must carefully
plan how to obtain enough relevant information for the
specific aim of their study, while minimizing TTD errors.
The number, type, and position of landmarks (or semi-land-
marks) are important, but this is not specific to 2D GMM
(Cardini, 2020b). For 2D GMM, however, using fewer
quasi-coplanar landmarks, and excluding those off the main
plane of other landmarks, may be a useful expedient to
reduce inaccuracies. Yet, one might want to first try includ-
ing fewer coplanar landmarks, check the congruence with
3D in a subsample and, based on this, decide whether to
include or exclude the landmarks which are off the main
plane. In patas, for instance, we found a small but measur-
able improvement in the TTD approximation by excluding
inion. There might be cases, however, when the exclusion
regions with crucial anatomical information. This could be
one reason why 2D data on hystricognath (porcupine)
hemi-mandibles, with a lateral flaring that makes them
highly three-dimensional, have larger inaccuracies in 2D
than those of the relatively flat sciurognath (squirrel) hemi-
mandibles (
Alvarez & Perez, 2013; Cardini, 2014; Cardini &
Chiapelli, 2020).
The design of a highly standardized protocol for
photographing specimens is fundamental for 2D GMM.
Although our 2D data produced results largely congruent
with 3D despite the poor standardization of the photo-
graphs, it is better to minimize potential sources of inac-
curacy that can be easily controlled, such as the
photographic settings. The orientation of the structure, or
more precisely of the plane where most landmarks lie,
must be kept as consistent as possible across all individ-
uals. This requires not only determining in advance what
landmarks to employ, but also how to place specimens
in the most appropriate position. Cardini and Ton-
giorgi (2003), for instance, built a small table whose
inclination can be adjusted in order to check, using a
spirit-level, that the lens and the specimen plane are par-
allel. This table has a frame of millimeter paper around
its margins. The frame, thus, provides a scaling factor,
but also helps to verify that the photograph shows no
barrel-shaped deformations around the main central
area. Marmot hemi-mandibles were placed horizontally
on their buccal side on the small table, so that they
always leaned the same way. This accurate placement may
study structure. In the case of marmot hemi-mandibles, all
but one landmark were on their outline in side-view and all
were within a depth of <1 cm. This made it easier to stan-
dardize orientation without the use of plasticine. Finally,
Cardini and Tongiorgi (2003) locked the camera on a porta-
kept it as distant as possible (ca. 1 m) from the hemi-
mandible in order to minimize photographic deformations.
To keep the scale of photographic reproduction constant,
they slightly adjusted, for each specimen, the height of the
camera. Differences in height were very small (the lens
aperture was kept at a minimum, and thus the width of
field was just enough for the hemi-mandible to be in focus).
This standardizes even more the distance of the camera to
end of the diastema). They also worked with similar light
settings in all photographs, and used diffuse lights to reduce
shadows, since shadows can make some anatomical details
harder to see.
Unlike the now obsolete analogical camera of Cardini
and Tongiorgi (2003), modern high resolution digital cam-
eras, held on a tripod and with a high-quality lens, simplify
this protocol. Standardizing the orientation of crania is,
however, less simple than with mandibles. For ventral
views, one could replace the lid of a box with a frame of
millimeter paper and have a plasticine doughnutat the
bottom of the box to support the cranium upside-down. By
remodeling the plasticine, the height of the cranium can be
adjusted to match that of the millimeter paper, and a small
spirit level on, for instance, the palate used to verify that it
is parallel to the lens of the camera.
Every operator will have to adjust the photographic
settings to their specific aim and study structure, plan-
ning everything in advance and anticipating all potential
problems. This may be a tedious operation with much
trial and error before the protocol is found. The careful
settings of Cardini and Tongiorgi (2003) are one of the
reasons why the TTD error in photographs of marmot
hemi-mandibles was so small (Cardini, 2014), being
about one-third and half that found in crania of plains
zebras, marmots, and patas. In fact, photographs had a
TTD error even smaller than in 2D shapes from high res-
olution scans of the same individuals (Cardini, 2014).
4.6 |What's next? The potential of 2D
GMM for taxonomic assessment
A simple question inspired this study: Can 2D photo-
graphs of the ventral side of adult crania be used for a
morphometric analysis of taxonomic variation in patas?
The answer is yes.The TTD error is similar, or even
slightly smaller, than in previous analyses using the same
methods on ventral crania of adults of some other species
of mammal (Cardini, 2014; Cardini & Chiapelli, 2020).
The magnitude of the TTD error, however, is not small
when compared to differences among crania of adults of
closely related species/subspecies. In these studies, it can
be as large as one/fourth to one/fifth of individual varia-
tion, thus leading to a low percentage of 2D-3D sister rep-
licates in the phenograms. Nonetheless, results of all
taxonomic tests produced virtually identical results in 2D
and 3D, which indicates that 2D GMM accurately cap-
tures patterns of group differences and should be appro-
priate for a quantitative assessment of morphological
variability in patas.
We performed this study with two aims. The more
general aim was to better understand whether and when
2D might be accurate despite the almost inevitable distor-
tion of the third dimension in highly 3D structures such
as mammal crania. The second, more specific, aim was to
confirm (as we hoped) that we can now go on with a
proper taxonomic study and, thus, assess the degree of
variability in the adult crania across the geographic distri-
bution of Erythrocebus. Most 2D studies consider the
appropriateness of 2D GMM as a given. This, however, is
often risky assumption. For example, what if 2D is inac-
curate and one finds that out after an extensive data col-
lection or, even later, after others fail to replicate 2D
results using 3D landmarks?
Ventral crania provide a small piece of morphometric
evidence. For an accurate taxonomic assessment we need to
wait until results are corroborated by genetic data. Yet, for
now, the 2D study we are preparing to carry out appears a
promising approach to start improving our knowledge of
the taxonomy of this genus of African primate. For robust
morphometric findings on small taxonomic differences,
however, we will need large samples representing all the
main populations of patas. A recent GMM analysis of more
than 4,000 adult crania from many genera of mammals
(Cardini et al., 2021) suggests that a minimum number
(within population and split by sex, for highly dimorphic
taxa such as primates) might be in the range of 2540 speci-
mens. This number tends to, on average, produce estimates
of means and variancecovariance matrices close to those
found in much larger samples of the same species and also
strongly reduces errors in species identification based on
cranial shape. As specimens are stored among many
museums, photographing enough specimens is daunting,
but not impossible. Visiting collections with patas crania
will be expensive and time-consuming. Developing a stan-
dardized and reproducible protocol that yields minimal
interoperator differences would allow others to obtain pho-
tographs from those museums that we are unable to visit.
This collaboration would, thus, generate the largest
Our study of patas has an interest that goes beyond the
taxonomy and conservation of this group. Besides African
primates (Butynski et al., 2013; Estrada et al., 2017), numer-
ous mammals worldwide are in rapid decline and threat-
ened with extinction (Ceballos et al., 2017; Schipper
et al., 2008), some of which may hide more diversity than
we presently recognize (Ceballos & Ehrlich, 2009). This par-
tially cryptic variation, to some extent, reflects the choice of
species definition and differences in taxonomic philosophy
(e.g., Groves, 2001; Groves et al., 2017; Zachos, 2016, 2018).
Yet, compared to the taxonomies presented in Wilson
and Reeder (2005), the majority of the about 1,000 new
species of mammal proposed in the recent taxonomic
revision of Burgin et al. (2018) originates from the redefini-
tion of previously known taxa based on updated scientific
knowledge. Some of these new taxa may go unrecognized
using different criteria and, therefore, lack robust support.
For morphological and other phenotypic data there is
also a chance that differences are plastic and do not
reflect genetic divergence and adaptive change. Most
likely, however, the majority of the newtaxa represent
unique components of biological diversity regardless of
their taxonomic rank. Being the result of an irreproduc-
ible evolutionary history with generations of individuals
selected by a variety of environmental pressures, preserv-
ing their genetic diversity could be key to enhancing their
chance of survival in a rapidly changing, mostly deterio-
rating, natural landscape. With this variability, at least
some populations might be resilient and able to adapt
(Sgrò et al., 2011), and thus preserve diversity, but also
phenotypic disparity and ecological functions (Mace,
2004; Mace & Purvis, 2008). Taxonomic uncertainties are
just one of several problems in measuring biodiversity
(Hortal et al., 2015) as more knowledge and conservation
actions may not be enough to save species from extinction
(Costello et al., 2013; Ellison, 2016; Kim & Byrne, 2006;
Robinson, 2006), but without knowledge we will cer-
tainly end up losing diversity that we have never recog-
nized (Kim & Byrne, 2006; Lees & Pimm, 2015; Tedesco
et al., 2014).
We are in debt to all of the museums and curators who
provided access to their specimens, to Riccardo Poloni
and Carmelo Fruciano for their advice on, respectively,
digital photography and some of the tests of ME, and to
Stefan Schlager for his help with the bgPCA in Morpho.
We are particularly grateful to Vida Jojic for her help
with references on ME, as well as for taking the time to
add information and results on the specific aspects of ME
that we are interested in. Finally, we are most grateful to
the Associate Editor, Tim D. Smith, for his excellent sug-
gestions and extensive work on the manuscript, and to
three anonymous reviewers for their careful and bal-
anced reviews, which greatly improved the paper. Finan-
cial support for data collection came from a grant of the
Leverhulme Trust to Sarah Elton, whom we thank, and
to a SYNTHESYS fellowship to AC.
Open Access Funding provided by Universita degli
Studi di Modena e Reggio Emilia within the CRUI-CARE
Andrea Cardini: Conceptualization; data curation;
study design, methodology and analysis; writing original
draft, reviews and revisions. Yvonne A. de Jong
and Thomas M. Butynski: Conceptualization; data
curation; writing original draft, reviews and revisions.
Andrea Cardini
Yvonne A. de Jong
Thomas M. Butynski
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How to cite this article: Cardini, A., de Jong, Y.
A., & Butynski, T. M. (2021). Can morphotaxa be
assessed with photographs? Estimating the
accuracy of two-dimensional cranial geometric
morphometrics for the study of threatened
populations of African monkeys. The Anatomical
2D: related to landmarks digitized on photographs. Each
landmark is described by a pair of X and Y coordinates.
3D: related to landmarks digitized directly on crania.
Each landmark is described by a triplet of X, Y and Z
coordinates. Both for 2D and 3D, the coordinates can
be raw (in mm, including differences in position and
size) or Procrustes shape coordinates (after the super-
imposition has standardized size and positional
FULL-0: all 25 landmarks digitized twice on the photo-
graphs in order to assess 2D digitization error; results
from this dataset are emphasized using a light gray
background in the tables.
FULL-1: all 25 landmarks digitized on the photographs
(averages of the two replicates of FULL-0) and re-
digitized directly on the 3D crania.
RED-2: reduced configuration using the same data as
in FULL-1 but after removing landmarks 11, 15,
16, and 18 (and the corresponding mirror-reflected
paired landmarks).
RED-3: same as FULL-1 after removing landmarks
7, 11, and 23 (and the corresponding mirror-reflected
paired landmarks).
RED-4: same as FULL-1 after removing landmarks
11, 15, 16, 18, and 23 (and the corresponding mirror-
reflected paired landmarks).
GMM: geometric morphometrics. Here, specifically
referred to the set of methods based on the Procrustes
superimposition of anatomical landmarks.
ME: measurement error.
Variance metrics used for multivariate shape data:
VAR1: the sum of variances of the shape coordinates.
VAR2: the mean of pairwise Procrustes shape dis-
tances among all individuals in a sample.
VAR3: the 90th percentile of the same set of pairwise
Procrustes distances used in VAR2.
varcov: matrix of variances and covariances of the Pro-
crustes shape coordinates.
TTD: 2D to 3D approximation.
XbgPCA: cross-validated between group PCA (principal
component analysis).
... The tarsometatarsi of the selected waterfowl species was analyzed by means of 2D geometric morphometrics. The effectiveness of 2D geometric morphometrics approaches from photographs was recently assessed, even to detect small differences (Cardini, de Jong, & Butynski., 2021). Herein, the shape of the tarsometatarsi was captured by a configuration of 11 landmarks and two marginal curves with six semilandmarks each ( Figure 1) using the software tpsUtil ver. ...
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Anseriformes is a diverse group of birds that comprises screamers, the Magpie Goose, and swans ducks and geese, with a relatively rich fossil record. Waterfowl live in close relation to water bodies, but show a diversity of locomotory habits, being typically categorized as walkers, dabblers, and divers. Owing to its functional significance and high preservation potential, the tarsometatarsus has been considered to be a ‘key’ element upon which to base ecomorphological inferences in fossil waterfowl. For instance, based on features of the tarsometatarsus the Miocene flightless duck Cayaoa bruneti and the Oligocene‐Miocene large waterfowl Paranyroca have been inferred as divers. Herein we use a geometric morphometric approach and comparative methods to assess the phylogenetic and ecomorphological signals in the shape and size of waterfowl tarsometatarsi in relation to their locomotory habits. We also apply phylogenetic flexible discriminant analysis (pFDA) to test the inferred diving habits in the extinct waterfowl Cayaoa and Paranyroca. Extant waterfowl species are largely distributed according to their locomotory habit along the main axis of variation in the shape space, a pattern mirrored by the phylogenetic generalized least squares model, which shows that a third of the shape variation is significantly explained by the habit. The pFDA reclassifies correctly almost all extant species and classified with high posterior probabilities the fossil Cayaoa and Paranyroca as a diver and as a dabbler, respectively. Our quantitative multivariate approach confirms the tarsometatarsus as a useful source of data upon which reliably assesses locomotory habits of fossil waterfowl.
Distinct life stages may experience different selection pressures influencing phenotypic evolution. Morphological evolution is also constrained by early phenotypes, since early development forms the phenotypic basis of later development. This work investigates evolutionary-developmental modification in three life stages and both sexes of 24 Rhipicephalus species using phylogenetic comparative methods for geometric morphometrics of basis capituli (basal mouthpart structure used for host attachment), and scutum or conscutum areas (proxy for overall body size). Findings indicate species using large hosts at early life stages have distinct basis capituli shapes, correlated with host size, enabling attachment to the tough skins of large hosts. Host-truncate species (one- and two-host) generally retain these adaptive features into later life stages, suggesting neoteny is linked to the evolution of host truncation. In contrast, species using small hosts at early life stages have lost these features. Developmental trajectories differ significantly between host-use strategies (niches), and correlate with distinct clades. In two-host and three-host species using large hosts at early life stages, developmental change is heterotopically accelerated (greater cell mass development) before the first off-host period where selection probably favours large individuals able to better resist dehydration when questing (waiting) for less abundant, less active hosts. In other species, development is heterotopically reduced (neotenic), possibly because dehydration risk is bypassed by prolonged host attachment (one-host species – heterotopic neoteny), or is allometrically repatterned possibly by using highly abundant and active hosts (three-host species using small hosts at early life stages – allometric repatterning). These findings highlight complex trade-offs between on- and off-host factors of free-living ectoparasite ecology, which mediate responses to diverse selection pressures varied by life stage and host-use strategy. It is proposed that these trade-offs shape evolutionary-developmental morphology and diversity of Rhipicephalus ticks.
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The IUCN Red List of Threatened Species 2022. Available at:
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Hippopotamidae are a group of large-sized mammals of interest for testing evolutionary traits in time and space. Variation in skull shape within Hippopotamidae is here investigated by means of shape analysis (Ge-ometric Morphometrics) and modern statistical approaches. Two-dimensional shape analysis is applied to dorsal and lateral views of extant and extinct Hippopotamidae species sufficiently preserved to allow their morphology to be captured by landmark and semi-landmark digitization. The results show that Hippopotamus gorgops and H. antiquus display similar shapes, while Hexaprotodon palaeindicus falls within the morphospace occupied by H. amphibius, suggesting similar morphology. The cranial shape of the Sicilian hippopotamus (H. pentlandi) still resembles that of H. amphibius in lateral view, suggesting that adaptation to the insular domain was yet not fully attained. Madagascan hippopotamu-ses (H. madagascariensis and H. lemerlei) are close to the pygmy hippo, Choeropsis liberiensis, in PC1 values; nevertheless, the cranial shape of the Madagascan hippos seems not to be closely related to the cranial shape of C. liberiensis. Despite the morphological convergences within the group, while cranial shape in Hippopotamidae is phylogenetically structured, this does not hold for size. Although further investigations are needed to test the influence of ecological and palaeo-ecological parameters on the general shape to provide additional information for understanding Hippopotamidae evolution and adaptation, the present study provides an insight into the evolutionary framework of Hippopotamidae.
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Quantifying phenotypes is a common practice for addressing questions regarding morphological variation. The time dedicated to data acquisition can vary greatly depending on methods and on the required quantity of information. Optimizing digitization effort can be done either by pooling datasets among users, by automatizing data collection, or by reducing the number of measurements. Pooling datasets among users is not without risk since potential errors arising from multiple operators in data acquisition prevents combining morphometric datasets. We present an analytical workflow to estimate within and among operator biases and to assess whether morphometric datasets can be pooled. We show that pooling and sharing data requires careful examination of the errors occurring during data acquisition, that the choice of morphometric approach influences amount of error, and that in some cases pooling data should be avoided. The demonstration is based on a worked example (Sus scrofa teeth) using a combinations of 18 morphometric approaches and datasets for which we identified and quantified several potential sources of errors in the workflow. We show that it is possible to estimate the analytical power of a study using a small subset of data to select the best morphometric protocol and to optimize the number of variables necessary for analysis. In particular, we focus on semi-landmarks, which often produce an inflation of variables in contrast to the number of available observations use in statistical testing. We show how the workflow can be used for optimizing digitization efforts and provide recommendations for best practices in error management.
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In the context of geometric morphometric analyses of modularity and integration using Procrustes methods, some researchers have recently claimed that “high-density geometric morphometric data exceed the traditional landmark-based methods in the characterization of morphology and allow more nuanced comparisons across disparate taxa” and also that, using “high-density” data (i.e., with dozens or hundreds of semilandmarks), “potential issues [with tests of modularity and integration] are unlikely to obscure genuine biological signal”. I show that the first claim is invalidly tautological and, therefore, flawed, while the second one is a speculation. “High-density” geometric morphometrics is a potentially useful tool for the quantification of continuous morphological variation in evolutionary biology, but cannot be said to represent absolute accuracy, simply because more measurements increase information, but do not by default imply that this information is accurate. Semilandmarks are an analytical expedient to break the continuity of regions devoid of clearly corresponding landmarks, but the shape variables which they generate are a function of the specific choice of the placement and possible mathematical manipulation of these points. Not only there are infinite ways of splitting a curve or surface into discrete points, but also none of the methods to slide the semilandmarks increases the accuracy of their mapping onto the underlying biological homology: indeed, none of them is based on a biological model, and the assumption of universal equivalence between geometric and biological correspondence is unverified, if at all verifiable. Besides, in the specific context of modularity and integration using Procrustes geometric morphometrics, the limited number of scenarios simulated until now may provide interesting clues, but do not yet allow strong statements and clear generalizations. The Procrustes superimposition does alter the ‘true’ covariance structure of the data and sliding semilandmarks further contributes to this change. Although we hope that this might only add a negligible source of inaccuracy, and simulations using landmarks (but no semilandmarks yet) suggest that this might be the case, it is too early to confidently share the view, expressed by the promoters of high-density methods, that this is “Not-Really-a-Problem”. The evidence is very preliminary and the dichotomy may not be this simple, with the magnitude (from negligible to large) and direction (inflation of modularity, integration, or both) of a potential bias in the tests likely to vary in ways specific to the data being analysed. We need more studies that provide robust and generalizable evidence, without indulging in invalid tautology and over-interpretation. With both landmarks and semilandmarks, what is measured should be functional to the specific hypothesis and we should be clear on where the treatment of the data is pure mathematics and where there is a biological model that supports the maths.
Technical Report
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De Jong, Y.A. & Butynski, T.M. 2020. Erythrocebus patas ssp. pyrrhonotus. The IUCN Red List of Threatened Species 2020: e.T92252480A92252486.
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The complex taxonomy and biogeography of the highly polytypic and widespread gentle monkey Cercopithecus mitis continue to be debated. Tanzania and Kenya, together, support eight of the currently recognized 17 subspecies of C. mitis. This paper reviews the taxonomy of the eight subspecies of C. mitis recognized for Kenya and Tanzania and presents an overview of their geographic distribution and pelage coloration and pattern. This paper also describes a new, endemic, subspecies of C. mitis for Tanzania, offers two hypotheses for its origin and phylogenetic affinities, and assesses its conservation status and conservation needs. Cercopithecus mitis in the Lake Manyara-Ngorongoro Region of central north Tanzania (i.e., the "Manyara Population") has often been referred to as "C. m. stuhlmanni × C. m. albogularis hybrids" and as representative of a "hybrid swarm." To better understand the taxonomic and conservation status of this population, four field surveys totaling 25 days were undertaken in southwest Kenya and central north Tanzania. The aim was to determine the geographic distribution of this population and to obtain detailed descriptions and photographs of as many individuals as possible. In addition, the literature was searched, and 88 C. mitis specimen skins were directly examined at four museums. We found no evidence to support the contention that C. mitis of the Lake Manyara-Ngorongoro Region are hybrids or represent a hybrid swarm. The Manyara C. mitis is geographically isolated from other C. mitis by >90 km of semi-arid habitat, is phenotypically distinct from other C. mitis, and presents little intra-population variation. As such, the diagnosable phenotypic characters of this population appear to be fixed, genetic, and heritable.
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Geometric morphometric analyses are frequently employed to quantify biological shape and shape variation. Despite the popularity of this technique, quantification of measurement error in geometric morphometric datasets and its impact on statistical results is seldom assessed in the literature. Here, we evaluate error on 2D landmark coordinate configurations of the lower first molar of five North American Microtus (vole) species. We acquired data from the same specimens several times to quantify error from four data acquisition sources: specimen presentation, imaging devices, interobserver variation, and intraobserver variation. We then evaluated the impact of those errors on linear discriminant analysis‐based classifications of the five species using recent specimens of known species affinity and fossil specimens of unknown species affinity. Results indicate that data acquisition error can be substantial, sometimes explaining >30% of the total variation among datasets. Comparisons of datasets digitized by different individuals exhibit the greatest discrepancies in landmark precision, and comparison of datasets photographed from different presentation angles yields the greatest discrepancies in species classification results. All error sources impact statistical classification to some extent. For example, no two landmark dataset replicates exhibit the same predicted group memberships of recent or fossil specimens. Our findings emphasize the need to mitigate error as much as possible during geometric morphometric data collection. Though the impact of measurement error on statistical fidelity is likely analysis‐specific, we recommend that all geometric morphometric studies standardize specimen imaging equipment, specimen presentations (if analyses are 2D), and landmark digitizers to reduce error and subsequent analytical misinterpretations.
The "Critically Endangered" southern patas monkey Erythrocebus baumstarki, thought to be endemic to Tanzania, has been resurrected to species level based on its geographic isolation, and on the coloration and pattern of its pelage. This study presents the first evidence for E. baumstarki in Kenya and reviews its historic and current geographic distributions based on the literature, museum specimens, online platforms, responses to requests for site records, and our own fieldwork. The distribution of E. baumstarki in the early 20th century was roughly 66,000 km2 . This has declined about 85% to around 9700 km2 at present (post-2009). The current "Extent of Occurrence" is only about 2150 km2 . This species was extirpated from Kenya in about 2015 and from the Kilimanjaro Region in Tanzania in about 2011. At present, E. baumstarki appears to be restricted to the protected areas of the western Serengeti, with the western Serengeti National Park being the stronghold. The number of individuals remaining is probably between 100 and 200, including between 50 and 100 mature individuals. The ultimate threat to E. baumstarki is the very rapidly increasing human population, while the main proximate threats are the degradation, loss, and fragmentation of natural habitats, and the related competition with people and livestock for habitat and water, particularly during droughts. Other problems are hunting by poachers and domestic dogs, and probably loss of genetic variation and climate change. This article provides recommendations for reducing the threats and promoting the recovery of E. baumstarki. We hope this article heightens awareness of the dire conservation status of E. baumstarki and encourages an increase in research and conservation action for this monkey.
Water voles from the genus Arvicola display an amazing ecological versatility, with aquatic and fossorial populations. The Southern water vole (Arvicola sapidus) is largely accepted as a valid species, as well as the newly described Arvicola persicus. In contrast, the taxonomic status and evolutionary relationships within Arvicola amphibius sensu lato had caused a long‐standing debate. The phylogenetic relationships among Arvicola were reconstructed using the mitochondrial cytochrome b gene. Four lineages within A. amphibius s.l. were identified with good support: Western European, Eurasiatic, Italian, and Turkish lineages. Fossorial and aquatic forms were found together in all well‐sampled lineages, evidencing that ecotypes do not correspond to distinct species. However, the Western European lineage mostly includes fossorial forms whereas the Eurasiatic lineage tends to include mostly aquatic forms. A morphometric analysis of skull shape evidenced a convergence of aquatic forms of the Eurasiatic lineage toward the typically aquatic shape of A. sapidus. The fossorial form of the Western European lineage, in contrast, displayed morphological adaptation to tooth‐digging behavior, with expanded zygomatic arches and proodont incisors. Fossorial Eurasiatic forms displayed intermediate morphologies. This suggests a plastic component of skull shape variation, combined with a genetic component selected by the dominant ecology in each lineage. Integrating genetic distances and other biological data suggest that the Italian lineage may correspond to an incipient species (Arvicola italicus). The three other lineages most probably correspond to phylogeographic variations of a single species (A. amphibius), encompassing the former A. amphibius, Arvicola terrestris, Arvicola scherman, and Arvicola monticola.
The study of phenotypic variation in time and space is central to evolutionary biology. Modern geometric morphometrics is the leading family of methods for the quantitative analysis of biological forms. This set of techniques relies heavily on technological innovation for data acquisition, often in the form of 2D or 3D digital images, and on powerful multivariate statistical tools for their analysis. However, neither the most sophisticated device for computerized imaging nor the best statistical test can produce accurate, robust and reproducible results, if it is not based on really good samples and an appropriate use of the 'measurements' extracted from the data. Using examples mostly from my own work on mammal craniofacial variation and museum specimens, I will show how easy it is to forget these most basic assumptions, while focusing heavily on analytical and visualization methods, and much less on the data that generate potentially powerful analyses and visually appealing diagrams.