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\begin{document}

\title{Insect Morphometry is Reproducible Under Average Investigation Standards}



\author[1]{Sandor Csosz}%
\author[2]{Bernhard Seifert}%
\author[3]{Istvan Mikó}%
\author[4]{Brendon Boudinot}%
\author[5]{Marek Borowiec}%
\author[6]{Brian Fisher}%
\author[5]{Matthew Prebus}%
\author[7]{Jayanthi Puniamoorthy}%
\author[8]{Jean Claude Rakotonirina}%
\author[8]{Nicole Rasoamanana}%
\author[2]{Roland Schultz}%
\author[9]{Carolyn Trietsch}%
\author[10]{Jonah Ulmer}%
\author[11]{Zoltán Elek}%
\affil[1]{MTA}%
\affil[2]{Senckenberg Museum of Natural History Görlitz}%
\affil[3]{University of New Hampshire Department of Biological Sciences}%
\affil[4]{University of California Davis Department of Entomology and Nematology}%
\affil[5]{University of Idaho}%
\affil[6]{California Academy of Sciences}%
\affil[7]{National University of Singapore}%
\affil[8]{Madagascar Biodiversity Center}%
\affil[9]{Pennsylvania State University University Park}%
\affil[10]{Staatliches Museum für Naturkunde Stuttgart}%
\affil[11]{MTA-ELTE-MTM, Ecology Research Group}%


\vspace{-1em}



  
  \date{May 16, 2024}


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\selectlanguage{english}
\begin{abstract}
Morphometric research is being applied to a growing number and variety
of organisms. Discoveries achieved via morphometric approaches are often
considered highly transferable, in contrast to the tacit and
idiosyncratic interpretation of discrete character states. The
reliability of morphometric workflows in insect systematics has never
been a subject of focused research, but such studies are sorely needed.
In this paper, we assess the reproducibility of morphometric studies of
ants where the mode of data collection is a shared routine. We compared
datasets generated by eleven independent gaugers, i.e. collaborators,
who measured 21 continuous morphometric traits on the same pool of
individuals according to the same protocol. The gaugers possessed a wide
range of morphometric skills, had varying expertise among insect groups,
and differed in their facility with measuring equipment. We used
Intraclass correlation coefficients (ICC) to calculate repeatability and
reproducibility values (i.e., intra-, and inter-gauger agreements), and
we performed a multivariate Permutational Multivariate Analysis of
Variance (PERMANOVA) using the Morosita index of dissimilarity with 9999
iterations. The calculated average measure of intraclass correlation
coefficients of different gaugers ranged from R = 0.784 to R = 0.9897
and a significant correlation was found between the repeatability and
the morphometric skills of gaugers (p = 0.016). There was no significant
association with the magnification of the equipment in the case of these
rather small ants. The inter-gauger agreement, i.e. the reproducibility,
varied between R=0.872 and R=0.471 (mean R=0.690), but all gaugers
arrived at the same two-species conclusion. A PERMANOVA test revealed no
significant gauger effect on species identity (R2 =0.69, p=0.58). Our
findings show that morphometric studies are reproducible when observers
follow the standard protocol; hence, morphometric findings are widely
transferable, and will remain a valuable data source for alpha taxonomy.%
\end{abstract}%



\sloppy


\section*{Keywords}

{\label{keywords}}

measurement error, repeatability, morphology, entomology, taxonomy,
species delimitation



\section*{Introduction}

{\label{introduction}}

The phenotype of organisms varies continuously during development and
through evolutionary time. Continuous morphological variation is
captured for numerous purposes in the life sciences via the practice of
morphometry: the measurement of the size and shape of anatomical forms.
Morphometry has yielded novel findings in evolution (Esquerr\selectlanguage{ngerman}é et al.,
2020) and has been used to assess fluctuating asymmetry (Palmer, 1993;
Klingenberg, 2015), ontogeny (Cs\selectlanguage{polish}ő\selectlanguage{english}sz \& Majoros, 2009; Shingleton et al.,
2007), ecomorphism (Mahendiran et al. 2018; Tomiya \& Meachen, 2018;
Anderson et al., 2019), and in human clinical practice (Bartlett \&
Frost, 2008). Among other applications, morphometric data are also key
for alpha taxonomy, the discipline of formally differentiating and
describing species and higher taxa. This is exemplified by the
development of phenetics in the twentieth century (Michener \& Sokal,
1957; Sokal \& Sneath, 1963) and by numerous modern studies in other
frameworks, such as for plants (Savriama, 2018; Chuanromanee, Cohen \&
Ryan, 2019), animals (Villemant, Simbolotti \& Kenis, 2007; In\selectlanguage{ngerman}äbnit,
2019), and other organisms (Fodor et al., 2015; McMullin et al., 2018).
Continuous data are also valuable, for modeling evolutionary histories
(e.g., Parins-Fukuchi, 2017, 2020). Thus, the morphometric approach
constitutes a fundamental and crucial practice for the study of
phenotypes in biodiversity research.

Morphology is traditionally considered to comprise both continuous and
discrete traits (Artistotle, 350; Thompson, 1917; Rensch, 1947; Remane,
1952). Discrete states were established as the basic comparative units
in animal alpha taxonomy from its formalization (Linnaeus 1758), and
have become a key means of scoring data for phylogenetic analysis,
particularly after Hennig (1950, 1966). The reproducibility of scoring
discrete states is an issue, however, as qualitative perception of
phenotype not only requires specific training and considerable
experience but can also be plagued by arbitrariness (Bond \& Beamer,
2006), meaning that variation may simply come from individual
(mis-)interpretation. The qualitative approach commonly uses verbal
species descriptions that are often subjective or difficult to
articulate. Therefore, information transfer, if at all reliable, is
based on one-to-one knowledge sharing mechanisms, and requires
logically-structured linguistic hierarchies such as the Hymenoptera
Anatomy Ontology (Yoder, Mikó, Seltmann, Bertone \& Deans, 2010).

In contrast to this relatively idiosyncratic approach, morphometry is
considered transferable. It converts variation of shape, size of
anatomical traits, and number and arrangement of anatomical elements
into numerical values, allowing for the dissemination of reproducible,
phenotype-based knowledge. Today, an increasing number of
morphology-based insect alpha-taxonomists use morphometric data and
provide numeric keys to species (Steiner Schlick-Steiner \& Moder, 2006;
Cs\selectlanguage{polish}ő\selectlanguage{english}sz Heinze \& Mik\selectlanguage{ngerman}ó 2015; Seifert, 2018). If observers arrive at the
same conclusion by measuring traits according to the same protocol,
findings are believed to be reliable and transferable. If one can
measure a trait, anyone else should be able to reproduce it.

However, measurements come with error. Agreement among different
observers and within a single observer's measurements is affected by a
number of sources, such as the skills of the observer (if human input is
required), the precision and accuracy of the equipment, clear
interpretation and appropriate understanding of the character recording
protocol, and other parameters. All of the uncertainty factors mentioned
above are common in practice, and the fact that it is impossible to
control every source of measurement variation challenges
morphometry-based research (Wolak, Fairbairn \& Paulsen, 2012).
Understanding of the degree to which measurement errors may affect the
transferability of findings is urgently needed. During the last few
decades, reproducibility issues have been studied in vertebrate
systematics (e.g., Oxnard, 1983, Corruccini, 1988; Yezerinac, Lougheed
\& Handford, 1992; Helm and Albrecht, 2000; Takacs Vital, Ferincz \&
Staszny, 2016; Fox, Veneracion \& Blois, 2020), clinical research (e.g.,
Bland \& Altman, 1986; Ridgway et al., 2008; Phexell et al., 2019),
social science (e.g., Salganik et al. 2020), molecular phylogeny and
genetic clustering (e.g., Huelsenbeck, 1998; Jones et al., 1998;
DeBiasse \& Ryan, 2019), and morphometric data generally (Andrew et al.,
2015). However, to date, reproducibility assessments of morphometric
data in entomology are extremely limited (Mutanen \& Pretorius, 2007;
Johnson et al., 2013).

In order to address the question ``to what extent is insect morphometry
reproducible?'', we compiled a broad database of morphometric data and
performed robust statistical analyses. We used ants, a group in which
the application of morphometric data has a long tradition (e.g., Brown,
1943; Brian \& Brian, 1949), as a model organism. Morphometry has been
employed widely in recent myrmecological studies (e.g., Ward, 1999;
Baroni Urbani, 1998; Seifert, 1992, 2003, 2019; Cs\selectlanguage{polish}ő\selectlanguage{english}sz Heinze \& Mik\selectlanguage{ngerman}ó,
2015; Wagner et al., 2017) as the primary method of interpreting
anatomical forms and their variation. Eleven participants of diverse
levels of skill and expertise, working with different taxonomic routines
over three continents and six countries, were asked to perform repeated
measurements on the same set of ant specimens, according to the same
measurement protocol, with their own equipment. The wide range of
morphometric skills and the quality of microscopes used provided us with
an overview of the level of reproducibility of morphometric
interpretation as it works in daily practice. Our findings are a first
step in exploring the reproducibility of morphometric data across
entomology.

Terminology {[}Textbox 1.{]}

A number of terms (e.g. ``accuracy'', ``precision'', ``reliability'',
``repeatability'', and ``reproducibility'') commonly used in association
with repeatability studies are defined differently in the literature. To
increase the fluency of scientific discourse, we propose to adopt the
standard terminology of the National Institute for Standards and
Technology (NIST, Taylor \& Kuyatt, 2001) of the USA and terms proposed
by (Bartlett \& Frost, 2008) in biological systematics:

\selectlanguage{english}* Accuracy describes the average closeness of the measurement(s) to the
value of the measurand (= subject or quantity to be measured) (Fig. 1).
Accuracy is affected by systematic and random error. We follow the
terminology proposed by the NIST in using the phrase ''the value of the
measurand'' instead of the often-applied ''true value of the measurand''
(or ''a true value'') (Taylor \& Kuyatt, 2001).

\selectlanguage{english}* Precision refers to the closeness of the measurements between pairs of
measurements made on the same measurand and applying the same protocol.
Precise measurements are tightly clustered, but are not necessarily
accurate, i.e. close to the value of the measurand (Fig. 1). Precision
is affected by random error.

\selectlanguage{english}* Reliability refers to the amount of measurement error that occurs
between observed measurements compared to the inherent amount of
variability that occurs between measurands (Bartlett \& Frost, 2008).

\selectlanguage{english}* Repeatability refers to the degree of agreement between repeat
measurements made on the same measurand under the same conditions, i.e.
made by the same observer, using the same microscope, following the same
measurement protocol (Taylor \& Kuyatt, 2001). Repeatability can be
assessed via intra-class correlation (ICC, see Lessells \& Boag, 1987).

\selectlanguage{english}* Reproducibility refers to the degree of agreement between measurements
made on the same measurand under changing conditions, such as changing
principle, method of measurement, observer, instrument, etc. (Taylor \&
Kuyatt, 2001).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Fig. 1. Precision versus accuracy.

Sources of errors {[}Textbox 2.{]}

Recognized sources of error in morphometry include three broad classes
of observational errors:

1. Random errors, which occur irregularly and hence are unpredictable.
Such errors arise in three different ways: random oscillations of the
apparatus, mechanical vibrations, and minor positional changes of the
subject at every single measurement. This type of error results in
dissimilar outcomes, which can be detected by replicated observations.
Random error primarily affects precision.

2. Systematic errors, which can be subdivided into a) observational
error, which arises from an individual's bias, unclear description of
measuring procedures, lack of proper setting of the equipment, or false
data recording due to parallax errors (Seifert, 2002); b) instrumental
error caused by factors such as imperfect calibration, etc., and c)
environmental error that can be ascribed to the effects of the external
conditions on the measurements, e.g., temperature, illumination, etc.
Systematic errors primarily influence a measurement's accuracy, but
these sources are predictable.

3. Gross errors, arising from false readings, mistakes in recording data
by an observer (e.g., reading or recording 88 instead of 38), or
mistakenly set magnification. This type of error seriously affects both
precision and accuracy. This source of error can be eliminated by
careful reading or recording. This type of error can also be recognized
post hoc via comparing the repeated measurements in a pairwise matrix
scatterplot (Baur \& Leuenberger, 2011).

\section*{Materials and Methods}

{\label{materials-and-methods}}

\subsection*{The research objects --}

{\label{the-research-objects}}

As an ideal stress-test basis for evaluating repeatability of
morphometric studies in insect systematic research, we selected ten
specimens each of a cryptic species pair, \emph{Nesomyrmex devius}(Cs\selectlanguage{polish}ő\selectlanguage{english}sz
\& Fisher, 2016) and \emph{N. hirtellus} (Cs\selectlanguage{polish}ő\selectlanguage{english}sz \& Fisher, 2016), for a
total of twenty ant specimens. Every trait under observation shows
overlapping ranges (Seifert 2009); thus, these species can be classified
in multivariate fashion only. Today, cryptic species pairs are
considered the most difficult cases and pose extraordinary challenges to
systematic biology.

The material is deposited in the California Academy of Sciences, San
Francisco, California, U.S.A. The full list of material morphometrically
examined in this work is listed in Supplementary Table S1 (available on
Dryad at\emph{https://doi.org/10.5061/dryad.q83bk3jfq}). Because two
specimens suffered a certain degree of damage during the projects due to
consecutive postal shipments, making the subsequent gaugers unable to
measure them, final analyses were done on only 18 individuals. The ant
specimens used in this study comply with the regulations for export and
exchange of research samples outlined in the Convention on Biological
Diversity and the Convention on International Trade in Endangered
Species of Wild Fauna and Flora. For field work conducted in Madagascar,
permits to research, collect, and export ants were obtained from the
Ministry of Environment and Forest as part of an ongoing collaboration
between the California Academy of Sciences and the Ministry of
Environment and Forest, Madagascar National Parks and Parc Botanique et
Zoologique de Tsimbazaza (Approval Numbers: N\selectlanguage{ngerman}° 0142N/EA03/MG02, N°
340N-EV10/MG04, N° 69 du 07/04/06, N° 065N-EA05/MG11, N° 047N-EA05/MG11,
N° 083N-A03/MG05, N° 206 MINENVEF/SG/DGEF/DPB/SCBLF, N° 0324N/EA12/MG03,
N° 100 l\textbackslash{}fEF/SG/DGEF/DADF/SCBF, N° 0379N/EA11/MG02, N°
200N/EA05/MG02). Authorization for export was provided by the Director
of Natural Resources.

\subsection*{Gaugers --}

{\label{gaugers}}

We addressed the question of whether or not the morphometric
measurements performed by eleven gaugers (``measurers'') could be
considered repeatable based on statistical thresholds. Eleven volunteers
from three continents and six countries, who all have different levels
of taxonomic training and skill, were asked to perform a pair of
measurements on the same set of ant specimens with their own equipment.
Eight of the volunteers are myrmecologists and three are
non-myrmecologists (two are wasp specialists and one is a
dipterologist). The wide range of the observers' morphometric skills and
the different levels of laboratory facilities and equipment, especially
the types of microscopes used, provided an overview of morphometric
reproducibility as it works in daily practice. Data belonging to gaugers
appear anonymously in this paper, but in order to provide the most
important information regarding their skills and their equipment's
quality, gaugers are coded in triad format as follows: expertise in
field, estimated total number of specimens measured in their career, and
the maximum magnification of the microscope used in the present study
separated by underscores (e.g. MYRM\_9000\_100x).

\subsection*{The morphometric character recording protocol
--}

{\label{the-morphometric-character-recording-protocol}}

Gaugers were asked to measure 21 continuous morphometric characters in
each specimen twice in order to collect data for testing both
intra-gauger error, equivalent to repeatability, and inter-gauger error
rate, equivalent to reproducibility. Every gauger was provided the same
measurement protocol, including visual and verbatim trait definitions to
follow (Fig. 2 and Table 1). The protocol was assembled based on an
existing set of characters used in published papers (Seifert, 2006,
2018; Cs\selectlanguage{polish}ő\selectlanguage{english}sz \& Fisher, 2016; Schlick-Steiner et al., 2006; Wagner et
al., 2017). In the current work, we addressed the question of to what
extent random and systematic errors affect the rate of reproducibility.
Therefore, all gaugers were encouraged to eliminate extraordinary
differences due to gross error (occurring due to misreading, mistyping
or erroneously set magnification) by comparing the values of the
repeated observations.

Table 1. Verbatim trait definitions for morphometric character
recording.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Trait abbreviation: description & Character definition & Reference to
Fig. 2\tabularnewline
\midrule
\endhead
CL: Head capsule length & Maximum cephalic length in median line. The
head must be carefully tilted to the position with the true maximum. &
Fig. 2a\tabularnewline
CW: Width of head including eyes & Maximum width of the head including
compound eyes. & Fig. 2a\tabularnewline
CWb: Width of head capsule & Maximum width of head capsule posterior of
the eyes. & Fig. 2a\tabularnewline
EL: Eye length & Maximum diameter of compound eye. All structurally
visible ommatidiae, pigmented or not, are included. & (Not
illustrated)\tabularnewline
FRS: Frontal carinae width & Distance of the frontal carinae immediately
caudal of the posterior intersection points between frontal carinae and
the torular lamellae. If these dorsal lamellae do not laterally surpass
the frontal carinae, the deepest point of scape corner pits may be taken
as reference line. These pits take up the inner corner of scape base
when the scape is fully switched caudad and produce a dark triangular
shadow in the lateral frontal lobes immediately posterior of the dorsal
lamellae of scape joint capsule. & Fig. 2b\tabularnewline
ML: Mesosoma length & Measured from caudalmost point of propodeal lobe
to transition point between anterior pronotal slope and anterior
pronotal shield (preferentially measured in lateral view; if the
transition point is not well defined, use dorsal view and take the
centre of the dark-shaded borderline between pronotal slope and pronotal
shield as anterior reference point). In gynes: length from caudalmost
point of propodeal lobe to the most distant point of steep anterior
pronotal face. & Fig. 2c\tabularnewline
STPL: Propodeal spine tip erection & Maximum distance from the center of
the propodeal stigma to the margin of lateral metapleural lobe. & Fig.
2d\tabularnewline
MW: mesosoma width & In workers: maximum width the pronotum excluding
the pronotal spines. & Fig. 2e\tabularnewline
NOH: Maximum height of the petiolar node & Measured from the uppermost
point of the petiolar node perpendicular to a reference line set from
the petiolar spiracle to the imaginary midpoint of the transition
between dorso-caudal slope and dorsal profile of caudal cylinder of the
petiole (Fig. 1D). Do not erroneously take as reference point the
dorso-caudal corner of the helcium, which is sometimes visible. Nodal
spines, if present, are excluded. If there is a dorsal plane of node
(i.e., no convexity in frotal section), take care that left and right
highest points of node are superimposing and use also position of setae
bases for correct adjustment. & Fig. 2d\tabularnewline
NOL: Length of the petiolar node & In lateral view NOL is measured
orthogonally from the reference line fitted to the margin of caudal
cylinder to the centre of petiolar spiracle. Take care that left and
right profiles of caudal slope of node are superimposing and use also
position of setae bases for correct adjustment. & Fig. 2d\tabularnewline
PoOC: Postocular distance & Use a cross-scaled ocular micrometer and
adjust the head to the measuring position of CL. Caudal measuring point:
median occipital margin; frontal measuring point: median head at the
level of the posterior eye margin. & Fig. 2a\tabularnewline
PEH: Maximum petiole height & Measured perpendicular to a ventral
reference line defined as follows: the chord spanning between caudal
corner of ventral petiole profile and the caudal end of the subpetiolar
process. If there is a dorsal plane of node (i.e., no convexity in
frontal section), take care that left and right highest points of node
are superimposing and use also position of setae bases for correct
adjustment. & Fig. 2f\tabularnewline
PEL: Petiolar lenght & Diagonal petiolar length in lateral view;
measured from the tip of subpetiolar process to dorso-caudal corner of
caudal cylinder. Do not erroneously take as reference point the
dorso-caudal corner of the helcium, which is sometimes visible. & Fig.
2f\tabularnewline
PEW: Petiole width & Maximum width of petiole in dorsal view. Nodal
spines - if any - are not considered. & Fig. 2g\tabularnewline
PPH: Postpetiole height & Maximum height of the postpetiole in lateral
view. Measured perpendicularly to a line defined by the linear section
of the segment border between dorsal and ventral petiolar sclerite (Fig.
1F). Take care that the lowest point of left and right part of sternites
are superimposing and use also position of setae bases for correct
adjustment. & Fig. 2f\tabularnewline
PPL: Postpetiole length & The longest anatomical line that is
perpendicular to the posterior margin of the postpetiole and is between
the posterior postpetiolar margin and the anterior postpetiolar margin
(Fig. 4). Take care that the left and right part of frontal face of node
are superimposing and use also position of setae bases for correct
adjustment. & Fig. 2d\tabularnewline
PPW: Postpetiole width & Postpetiole width. Maximum width of postpetiole
in dorsal view. & Fig. 2g\tabularnewline
SL: Scape length & Maximum length of the scape excluding the neck of
articulatory condyle. & Fig. 2a\tabularnewline
SPST: Spine length & Distance between the centre of propodeal stigma and
spine tip. The stigma centre refers to the midpoint defined by the outer
cuticular ring but not to the centre of real stigma opening that may be
positioned excentrically. & Fig. 2d\tabularnewline
SPBA: Spine base width & The smallest distance of the lateral margins of
the spines at their base. This should be measured in dorsofrontal view,
since the wider parts of the ventral propodeum do not interfere with the
measurement in this position. If the lateral margins of spines diverge
continuously from the tip to the base, a smallest distance at base is
not defined. In this case, SPBA is measured at the level of the bottom
of the interspinal meniscus. & Fig. 2g\tabularnewline
SPTI: Propodeal spine tip distance & Distance of propodeal spine tips in
dorsal view; if spine tips are rounded or thick take the centers of
spine tips as reference points. & Fig. 2g\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Fig. 2. Illustrations for morphometric characters.

\subsection*{Data analysis --}

{\label{data-analysis}}

Distribution patterns of objects (i.e. specimens represented by 21
characters measured by the eleven different gaugers) were displayed in a
scatterplot via Principal Component Analysis (PCA; Venables \& Ripley,
2002) using a standardization to zero mean and the variance unit
(Legendre \& Gallagher, 2001). A Permutational Multivariate Analysis of
Variance (PERMANOVA) was performed using the Morosita index of
dissimilarity with 9999 iterations (Anderson, 2001).

Reliability depends on the magnitude of the error in the measurements to
the inherent variability between subjects. These measures of variability
can be expressed as standard deviations (SDs). Reliability is defined as
a quadratic term of the measured values divided by the sum of the
quadratic term of the measured plus the square standard deviation. It is
formally described by Bartlett and Frost (2008) as

\emph{(SD of subject's true values)\textsuperscript{2}} (SD subjects'
true values)\textsuperscript{2} + (SD measurement
error)\textsuperscript{2}.

This measure of reliability is also known as intraclass correlation
(ICC). If reliability is high, measuring error is small in comparison to
the true differences between subjects, so that subjects can be
relatively well distinguished (in terms of the quantity being measured)
on the basis of the error-prone measurements (Bartlett \& Frost, 2008).

To estimate the within-subject SD, we applied a one-way analysis of
variance (ANOVA) to model the data containing the repeat measurements
made on subjects. In addition, we also tested the effect of the gaugers'
expertise and their equipment's performance on the accuracy of ICC
estimation by using Spearman's rank correlation. The analyses were
carried out in R 3.6.2 (R Core Team, 2019) by using the ``Vegan''
package (version 2.5-6, Oksanen et al., 2019) for PCA and PERMANOVA and
``car package'' (version 3.0-7, Fox \& Weisberg 2019). Repeatability was
calculated for each gauger respectively in order to assess whether the
gauger's skills or equipment quality played major roles in measurement
consistency.

\section*{Results}

{\label{results}}

\subsection*{Agreement in classification between gaugers
--}

{\label{agreement-in-classification-between-gaugers}}

The classification of the 18 pairs of independent observations made by
eleven gaugers was successful for the two taxa according to the
cumulative PCA analysis that involved all gaugers' observations in the
same analysis. Each gauger arrived at the two-species hypothesis with
only two misidentified observations (less than 1\%) out of the total 198
(Fig. 3a); a single misclassification appeared in two different gaugers
respectively. The results of the PCA revealed that the species identity
was responsible for the differences based on the morphological traits,
and was not ascribed to gauger effect (Fig. 3b). The PCA results were
based on the inertia 5489, and the variance explained by the 1st axis
was 62.59\%, while the variance for the 2nd axis was 10.32\%; thus, the
overall explained variance was 72.91\%. These patterns were also
revealed by the PERMANOVA performed using the Morosita index of
dissimilarity with 9999 iteration, where the gaugers were shown to have
no significant effect on the species identity based on the measured
morphological traits (R\textsuperscript{2}=0.69, p=0.58).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Fig. 3a,b. Ordination biplot for Principal Component Analysis based on
(A) species identity and (B) the accuracy of the measurement.

\subsection*{Reproducibility (inter-gauger agreement)
--}

{\label{reproducibility-inter-gauger-agreement}}

The Intraclass Correlation Coefficients (ICCs) indicated that the
reproducibility of the examined 21 morphometric characters varied
between R=0.872 and R=0.471 (mean R=0.690) when the inter-gauger
agreement was considered across the 11 gaugers (Table 2).
Reproducibility of 16 characters out of the total 21 were acceptable.
Five morphometric traits (EL, FRS, NOL, PoOC, PPL) were found to be
slightly reproducible, with intraclass correlation coefficient (R)
scores between 0.471 to 0.526 (Table 2). These scores belong to
physically smaller traits in the observed character pool, hence we
examined to what extent absolute character size affects the
reproducibility. The general linear model returned no significant
correlation (R = 0.3617, p = 0.1071) between the trait size and ICC
scores.

Table 2. Repeatability scores (R) calculated for each character.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
character & R & lower bound & upper bound & n & average trait size
(\selectlanguage{greek}µ\selectlanguage{english}m)\tabularnewline
\midrule
\endhead
CL & 0.8113 & 0.7050 & 0.9176 & 18 & 648.45\tabularnewline
PoOC & 0.5292 & 0.3511 & 0.7074 & 18 & 250.95\tabularnewline
CW & 0.8073 & 0.6993 & 0.9154 & 18 & 565.60\tabularnewline
CWb & 0.6278 & 0.4629 & 0.7927 & 18 & 540.93\tabularnewline
FRS & 0.5259 & 0.3476 & 0.7043 & 18 & 243.82\tabularnewline
SL & 0.6826 & 0.5306 & 0.8346 & 18 & 387.69\tabularnewline
EL & 0.5116 & 0.3324 & 0.6907 & 18 & 155.03\tabularnewline
MW & 0.7970 & 0.6846 & 0.9095 & 18 & 407.84\tabularnewline
PEW & 0.8434 & 0.7519 & 0.9349 & 18 & 264.86\tabularnewline
PPW & 0.7836 & 0.6655 & 0.9016 & 18 & 300.48\tabularnewline
SPBA & 0.8724 & 0.7955 & 0.9494 & 18 & 223.93\tabularnewline
SPTI & 0.7864 & 0.6695 & 0.9032 & 18 & 265.74\tabularnewline
ML & 0.7561 & 0.6275 & 0.8847 & 18 & 762.78\tabularnewline
PEL & 0.5951 & 0.4244 & 0.7658 & 18 & 330.85\tabularnewline
NOL & 0.5087 & 0.3294 & 0.6880 & 18 & 180.08\tabularnewline
STPL & 0.6159 & 0.4487 & 0.7831 & 18 & 243.49\tabularnewline
PEH & 0.7283 & 0.5900 & 0.8666 & 18 & 249.68\tabularnewline
NOH & 0.6140 & 0.4465 & 0.7815 & 18 & 154.87\tabularnewline
PPH & 0.8169 & 0.7131 & 0.9207 & 18 & 228.55\tabularnewline
SPST & 0.8013 & 0.6907 & 0.9120 & 18 & 217.51\tabularnewline
PPL & 0.4709 & 0.2909 & 0.6508 & 18 & 185.64\tabularnewline
\bottomrule
\end{longtable}

\subsection*{Repeatability (intra-gauger agreement)
--}

{\label{repeatability-intra-gauger-agreement}}

A geometric mean of intraclass coefficients were calculated for every
gauger in order to evaluate their personal performance in association
with their skills and equipment quality. The calculated average measure
of intraclass correlation coefficients of different gaugers ranged from
R = 0.7840 to R = 0.9897 (Table 3). The non-parametric Spearman's Rank
correlation revealed a significant correlation between ICC scores and
gaugers' morphometric skills, represented by the estimated number of
individuals measured in their personal career (n = 11, R = 0.70, t=
2.94, p = 0.016) and a non-significant association between the
repeatability parameters and the maximum magnification of the microscope
(n = 11, R = 0.56, t = 2.03, p = 0.073) applied by the gauger (Fig. 4).

Table 3. Repeatability scores (R) calculated for gaugers.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
no. & gauger code & ICC (\emph{R}) & expertise & magnification &
field\tabularnewline
1 & MYRM\_9000\_100x & 0.93645 & 9000 & 100 &
myrmecologist\tabularnewline
2 & DIPT\_0\_100x & 0.817519 & 0 & 100 & dipterologist\tabularnewline
3 & MYRM\_60000\_360x & 0.989691 & 60000 & 360 &
myrmecologist\tabularnewline
4 & MYRM\_5000\_288x & 0.971863 & 5000 & 288 &
myrmecologist\tabularnewline
5 & MYRM\_500\_50x & 0.831945 & 500 & 50 & myrmecologist\tabularnewline
6 & MYRM\_450\_50x & 0.903117 & 450 & 50 & myrmecologist\tabularnewline
7 & MYRM\_500\_50x & 0.816274 & 500 & 50 & myrmecologist\tabularnewline
8 & WASP\_1000\_230x & 0.884679 & 1000 & 230 & parasitic
wasps\tabularnewline
9 & WASP\_0\_230x & 0.856756 & 0 & 230 & parasitic wasps\tabularnewline
10 & MYRM\_300\_100x & 0.784024 & 300 & 100 &
myrmecologist\tabularnewline
11 & MYRM\_300\_100x & 0.87304 & 300 & 100 &
myrmecologist\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Fig. 4. The correlogram of the studied variables for testing
repeatability by the Spearman rank correlation test.



\section*{Discussion}

{\label{discussion}}

Morphometric characters proved reproducible in terms of inter-gauger
agreement. The eleven gaugers successfully arrived at the same
two-species conclusion despite a great variety of morphometric skills
and microscopic equipment of differing quality. The PERMANOVA test
revealed no significant gauger effect on the species identity
(R\textsuperscript{2} =0.69, p=0.58). The ratio of misidentifications on
specimen level over all gaugers was only 1.0\% within a total of 198
determinations. The non-parametric Spearman's Rank correlation revealed
that gauger ICC scores and morphometric skills were significantly
correlated, whereas repeatability parameters and maximum magnification
used by the gauger were not significantly correlated. These results
indicate that both observer experience (Fig. 4) and better optical
resolution in microscopes reduces measurement error and increases
repeatability (Table 3, Fig. 4).

In analyzing mean intra-gauger agreement character-wise, the mean ICC
scores (R) varied between 0.471 in the least reproducible character and
0.872 in the most reproducible character. This rather low average
reproducibility may have different causes. One of these may be the
absolute physical size of a trait. Traits with smaller sizes tended to
have lower ICC scores, but when we tested this with a generalized linear
model (GLM) analysis there was no significant correlation between trait
size and ICC score. This non-significance may be explained by the rather
large minimum trait size (155 \selectlanguage{greek}µ\selectlanguage{english}m) in the \emph{Nesomyrmex} test
organisms where the given differences in resolution and magnification of
the optical systems did not play a major role. The situation might
change dramatically if, for instance, 25-\selectlanguage{greek}µ\selectlanguage{english}m long antennal segments of
tiny \emph{Plagiolepis} ants were to be measured. The solution of such a
task requires measurement conditions as they were given in the gaugers
MYRM\_60000\_360x and MYRM\_5000\_288x.

If mean trait size does not contribute much to the rather low ICC scores
in the present study, these data are probably better explained by a
combination of ten error sources as they were specified for
stereomicroscopy by Seifert (2002). It is impossible to analyze which of
these caused major disturbances in this study. All observers received
verbal and picture-assisted character definitions (see Fig. 2 and Table
1) but were given no further advice or protocols on how to minimize
stereomicroscopic measuring errors. Firstly, whether all observers
avoided the parallax error is unknown. Secondly, whether all observers
used an X-Y-Z-stage for spatial positioning of specimens (see Fig. 1 in
Seifert, 2002) and which position stability this stage had are also
unknown. In spatial positioning, it is important to place the two
endpoints of a measurement in the same visual plane, which is more
accurate the lower the depth of focus or the higher the magnification of
the optical system. Thirdly, the performance and reliability (e.g.,
ratchet-step error) of the zoom microscopes used by gaugers in this
study are unknown. Fourthly, it is unknown how the observers made their
readings (by one tenth of a graduation mark, by entire graduation marks,
by digital read-out systems, etc.). A fifth important error source is
observer-specific, ambiguous translation of character definitions. These
factors highlight the importance of presenting unambiguous character
definitions and proposing accurate measurement procedures (see
supplementary file SI4, the measuring protocol of the most advanced
observer).

To conclude, besides the above-mentioned uncertainties that are common
in regular practice in insect taxonomic research, morphometry has proven
reproducible in our test setting. The best morphology, we believe, may
be done through multi-modal means, such as combining multiple
microscopic and morphometric methods (e.g., Richter et al., 2018; Sarnat
et al., 2019; Hita-Garcia et al., 2019; Boudinot, 2019; Keklikoglou et
al., 2019; Braga et al., 2019). Given the same size range of measured
traits, the same range of observers' skill, and the same range of
equipment, we expect the same reproducibility for other groups of
arthropods, provided these have a similar exoskeleton stability and that
specimens belong to a comparable developmental stage. Apart from this,
we encourage research teams to replicate this study with taxa of
different size classes, such as with tiny parasitic wasps and larger
grasshoppers or crickets. The requirements for equipment will change,
but we are keen to know if the basic conclusions prove comparable to our
results with \emph{Nesomyrmex} ants.

\par\null

\section*{Acknowledgements}

{\label{acknowledgements}}

First, we would like to thank Michele Esposito, from CASC, for her
enduring support with databasing, imaging processing, proofreading, and
her overall support in the lab. The fieldwork that provided the
specimens used in this study could not have been completed without the
help of the Ministry of Environment and Forest, the Madagascar National
Parks, and the Parc Botanique et Zoologique de Tsimbazaza, and the
gracious support of the Malagasy people. The authors wish to thank Dr.
Bethan Davies for her permission to use the graphics in Figure 1.

This study was supported by the National Science Foundation under Grant
No. DEB-0072713, DEB-0344731, and DEB-0842395. Finally, SC was partly
supported by the Schlinger Fellowship at the California Academy of
Sciences.

The ant specimens used in this study comply with the regulations for
export and exchange of research samples outlined in the Convention on
Biological Diversity and the Convention on International Trade in
Endangered Species of Wild Fauna and Flora. For field work conducted in
Madagascar, permits to research, collect, and export ants were obtained
from the Ministry of Environment and Forest as part of an ongoing
collaboration between the California Academy of Sciences and the
Ministry of Environment and Forest, Madagascar National Parks and Parc
Botanique et Zoologique de Tsimbazaza (Approval Numbers: N\selectlanguage{ngerman}°
0142N/EA03/MG02, N° 340N-EV10/MG04, N° 69 du 07/04/06, N°
065N-EA05/MG11, N° 047N-EA05/MG11, N° 083N-A03/MG05, N° 206
MINENVEF/SG/DGEF/DPB/SCBLF, N° 0324N/EA12/MG03, N° 100
l\textbackslash{}fEF/SG/DGEF/DADF/SCBF, N° 0379N/EA11/MG02, N°
200N/EA05/MG02). Authorization for export was provided by the Director
of Natural Resources.

\section*{Author contribution:}

{\label{author-contribution}}

SC, BS, BLF and IM conceived the ideas and designed methodology; MB, MP,
JP, JCR, NR, RS and JMU collected the data; ZE and SC analysed the data;
SC, IM, BS, BEB, BLF, CT and ZE led the writing of the manuscript. All
authors contributed critically to the drafts and gave final approval for
publication.

\section*{Data availability}

{\label{data-availability}}

Data available from the Dryad Digital
Repository\emph{https://doi.org/10.5061/dryad.q83bk3jfq}.

\section*{References}

{\label{references}}

Anderson, A. M., Friis, C., Gratto-Trevor, C. L., Morrison, R. G.,
Smith, P. A., \& Nol, E. (2019). Consistent declines in wing lengths of
Calidridine sandpipers suggest a rapid morphometric response to
environmental change. PloS One, 14(4), e0213930.
doi:10.1371/journal.pone.0213930.

Anderson, M. J. (2001). A new method for non-parametric multivariate
analysis of variance. Austral Ecology, 26, 32--46.
doi:10.1111/j.1442-9993.2001.01070.pp.x.

Andrew, R. L., Albert, A. Y. K., Renaut, S., Rennison, D. J., Bock, D.
G., Vines, T. (2015). Assessing the reproducibility of discriminant
function analyses. \emph{PeerJ,} 3:e1137. doi:10.7717/peerj.1137

Artistotle, 350. Historia Animalium, translated by Thompson, D.W.,
edited by Smith, J.A., Ross, W.D. London, Oxford University Press.

Baroni Urbani, C. (1998). The number of castes in ants, where major is
smaller than minor and queens wear the shield of the soldiers. Insectes
Sociaux, 45, 315--333. doi:10.1007/s000400050091.

Bartlett, J. W., Frost, C. (2008). Reliability, repeatability and
reproducibility: analysis of measurement errors in continuous variables.
Ultrasound in Obstetrics \& Gynecology, 31, 466--475.
doi:10.1002/uog.5256.

Baur, H., Leuenberger, C. (2011). Analysis of ratios in multivariate
morphometry. Systematic Biology, 60, 813--825.
doi:10.1093/sysbio/syr061.

Bland, J. M., Altman, D. (1986). Statistical methods for assessing
agreement between two methods of clinical measurement. Lancet, 327,
307--310. doi:10.1016/S0140-6736(03)15270-1.

Bond, J. E., Beamer, D. A. (2006). A morphometric analysis of
mygalomorph spider carapace shape and its efficacy as a phylogenetic
character (Araneae). Invertebrate Systematics, 20, 1--7.
doi::10.1071/IS05041.

Boudinot, B. E. (2019). Toward phylomics in entomology: Current
systematic and evolutionary morphology. Insect Systematics and
Diversity, 3(6), 1--4. doi:10.1093/isd/ixz019.

Braga, J., Zimmer, V., Dumoncel, J., Samir, C., de Beer, F., Zanolli,
C., Pinto, D., Rohlf, F. J., Grine, F. E. (2019). Efficacy of
diffeomorphic surface matching and 3D geometric morphometrics for
taxonomic discrimination of Early Pleistocene hominin mandibular molars.
Journal of Human Evolution, 130, 21--35.
doi:10.1016/j.jhevol.2019.01.009.

Brian, M. V., Brian, A. D. (1949). Observations on the taxonomy of the
ants \emph{Myrmica rubra} L. and \emph{M. laevinodis} Nylander
(Hymenoptera: Formicidae). Transactions of the Entomological Society of
London, 100(14), 393--409.

Brown, W. L. Jr. (1943). A new metallic ant from the pine barrens of New
Jersey. Entomological News, 54, 243--248.

Chuanromanee, T. S., Cohen, J. I., Ryan, G. L. (2019). Morphological
Analysis of Size and Shape (MASS): An integrative software program for
morphometric analyses of leaves. Applications in Plant Science,
7(9):e11288.~doi:10.1002/aps3.11288.

Corrucini, R. S. (1988). Morphometric replicability using chords and
cartesian coordinates of the same landmarks. Journal of Zoology, 215,
389--394. doi:10.1111/j.1469-7998.1988.tb02847.x.

Cs\selectlanguage{polish}ő\selectlanguage{english}sz, S., Heinze, J., Mik\selectlanguage{ngerman}ó, I. (2015). Taxonomic synopsis of the
Ponto-Mediterranean ants of \emph{Temnothorax nylanderi} species-group.
PLoS One, 10(11), e0140000. doi:10.1371/journal.pone.0140000.

Cs\selectlanguage{polish}ő\selectlanguage{english}sz, S., Majoros, G. (2009). Ontogenetic origin of
mermithogenic\emph{Myrmica} phenotypes (Hymenoptera, Formicidae).
Insectes Sociaux, 56, 70--76. doi:10.1007/s00040-008-1040-3.

DeBiasse, M. B., Ryan, J. F. (2019). Phylotocol: Promoting transparency
and overcoming bias in phylogenetics. Systematic Biology, 68, 672--678.
doi:10.7287/peerj.preprints.26585v4.

Esquerr\selectlanguage{ngerman}é, D., Donnellan, S., Brennan, I. G., Lemmon, A. R, Lemmon, E.
M., Zaher, H., Grazziotin, G. G., Keogh, J. S. (2020). Phylogenomics,
biogeography and morphometrics reveal rapid phenotypic evolution in
pythons after crossing Wallace's line. Systematic Biology, syaa024.
doi:10.1093/sysbio/syaa024.

Fodor, E., Hâru\selectlanguage{polish}ţ\selectlanguage{english}a, O., Milenkovi\selectlanguage{polish}ć, \selectlanguage{english}I., Lyubenova, A., Tziros, G., Ke\selectlanguage{polish}č\selectlanguage{english}a,
N., Slavov, S., Diamandis, S., Kostov, K. (2015). Geometric morphometry
of \emph{Phytophthora plurivora sporangia} . Annals of Forest Research,
58, 275--294. doi:10.15287/afr.2015.411.

Fox, J., Weisberg, S. (2019). \emph{An R Companion to Applied
Regression, Third edition.} Sage, Thousand Oaks CA.
https://socialsciences.mcmaster.ca/jfox/Books/Companion/.

Fox, N. S., Veneracion, J. J., Blois, J. L. (2020). Are geometric
morphometric analyses replicable? Evaluating landmark measurement error
and its impact on extant and fossil \emph{Microtus} classification.
Ecology and Evolution, 10, 3260--3275. doi:10.1002/ece3.6063.

Gotzek, D., Brady, S. G., Kallal, R. J., LaPolla, J. S. (2012). The
importance of using multiple approaches for identifying emerging
invasive species: the case of the rasberry crazy ant in the United
States. PLoS One, 7(9), e45314. doi:10.1371/journal.pone.0045314.

Helm, B., Albrecht, H. (2000). Human handedness causes directional
asymmetry in avian winglength. \emph{Animal Behaviour,} 60, 899--902.
doi:10.1006/anbe.2000.1534c.

Hennig, W. (1950). Grundz\selectlanguage{ngerman}üge einer Theorie der phylogenetischen
Systematil. Berlin, Deutscher Zentralverlag.

Hennig, W. (1966). Phylogenetic Systematics, translated by Davis, D.,
Zangerl, R. Urbana, University of Illinois Press.

Huelsenbeck J. P. (1998). Systematic bias in phylogenetic analysis: is
the Strepsiptera problem solved? Systematic Biology, 47, 519--537.

Hita-Garcia, F., Lieberman, Z., Audisio, T. L., Liu, C., Economo, E. P.
(2019). Revision of the highly-specialized ant genus
\emph{Discothyrea}(Hymenoptera: Formicidae) in the Afrotropics with
x-ray microtomography and 3D cybertaxonomy. Insect Systematics and
Diversity, 3, 1--84.

\emph{http://www.antarcticglaciers.org/glacial-geology/dating-glacial-sediments-2/precision-and-accuracy-glacial-geology/}accessed
2020-03-05.

\emph{https://www.nist.gov/pml/nist-technical-note-1297/nist-tn-1297-appendix-d1-terminology/}accessed
2020-03-05.

Inäbnit, T., Jochum, A., Kampschulte, M., Martels, G., Ruthensteiner,
B., Slapnik, R., Nesselhauf, C., Neubert, E. (2019). An integrative
taxonomic study reveals carychiid microsnails of the troglobitic
genus\emph{Zospeum} in the Eastern and Dinaric Alps (Gastropoda,
Ellobioidea, Carychiinae). Organisms Diversití and Evolution
19:135--177.

Johnson, L., Mantle, B.L., Gardner, J.L., Backwell, P.R.Y. (2013).
Morphometric measurements of dragonfly wings: the accuracy of pinned,
scanned and detached measurement methods. ZooKeys, 276:77--84.

Jones, C. J., Edwards, K. J., Castiglione, S., Winfield, M. O., Sala, F,
Van der Wiel, C, \ldots{} Karp, A. (1998). Reproducibility testing of
AFLPs by a network of European laboratories. pp. 191--192 in Karp A.,
Isaac, P.G. and Ingram D.S. (Eds) Molecular tools for screening
biodiversity. London, New York, Melbourne, Madras, Chapman \& Hall.

Keklikoglou, K., Faulwetter, S., Chatzinikolaou, E., Wils, P., Brecko,
J., Kva\selectlanguage{polish}č\selectlanguage{english}ek, \ldots{} Arvanitidis, C. (2019). Micro-computed tomography
for natural history specimens: a handbook for best practice protocols.
European Journal of Taxonomy, 522:1--55.

Klingenberg, C. P. (2011). MorphoJ: an integrated software package for
geometric morphometrics. Molecular Ecology Resources, 11:353--357.

Klingenberg, C. P. (2015). Analyzing fluctuating asymmetry with
geometric morphometrics: concepts, methods, and applications. Symmetry,
7:843--934.

Legendre, P., Gallagher, E. D. (2001). Ecologically meaningful
transformations for ordination of species data. Oecologia, 129:271--280.

Lessells, C. M., Boag, P. T. (1987). Unrepeatable repeatabilities, a
common mistake. Auk, 104:116--121.

Lewis, P. O. (2001). A likelihood approach to estimating phylogeny from
discrete morphological character data. Systematic Biology, 50:913--925.

Linnaeus, C. (1758). Systema naturae per regna tria naturae, secundum
classes, ordines, genera, species, cum characteribus, differentiis,
synonymis, locis. Tomus I. Editio decima, reformata. Holmiae {[}=
Stockholm{]}, Laurentii Salvii.

L\selectlanguage{ngerman}ösel, P., Heuveline, V. (2016). Enhancing a diffusion algorithm for 4D
image segmentation using local information. Proceedings of International
Society for Optics and Photonics, 9784:1--11, doi: 10.1117/12.2216202.

Mahendiran, M., Parthiban, M., Azeez, P. A., Nagarajan, R. (2018). In
situ measurements of animal morphological features: A non-invasive
method. Methods in Ecology and Evolution, 9:613--623.

McMullin, R. T., Maloles, J. R., Selva, S. B., Newmaster, S. G. (2018).
A synopsis of \emph{Chaenotheca} in North America, including a new
species from southern Ontario, \emph{C. selvae} , supported by
morphometric analyses. Botany, 96:547--553.

Michener, C. D., Sokal, R. R. (1957). A quantitative approach to a
problem in classification. Evolution, 11:130--162.

Miller, M. I., Priebe, C. E., Qiu, A., Fischl, B., Kolasny, A., Brown,
T., \ldots{} Buckner R. L. (2009). Collaborative computational anatomy:
an MRI morphometry study of the human brain via diffeomorphic metric
mapping. Human Brain Mapping, 30:2132--2141.

Mutanen, M., Pretorius, E. (2007). Subjective visual evaluation vs.
traditional and geometric morphometrics in species delimitation: a
comparison of moth genitalia. Systematic Entomology, 32:371--386.

Nakagawa, S., Schielzeth, H. (2010). Repeatability for Gaussian and
non-Gaussian data: a practical guide for biologists. Biological Reviews,
85:935--956.

Oksanen, J., Blanchet, F. G., Friendly, M., Kindt, R., Legendre, P.,
McGlinn, D., \ldots{} Wagner, H. (2019). vegan: Community Ecology
Package. R package version 2.5--6.
https://CRAN.R-project.org/package=vegan

Oxnard, C. E. (1983). Multivariate statistics in physical anthropology:
testing and interpretation. Zeitschrift für Morphologie und
Anthropologie, 73:237--278.

Parins-Fukuchi, C. (2017). Use of continuous traits can improve
morphological phylogenetics. Systematic Biology, 67:328--339.

Parins-Fukuchi, C. (2020). Mosaic evolution, preadaptation, and the
evolution of evolvability in apes. Evolution, 74:297--310.

Phexell, E., Åkesson, A., Söderberg, M., Bolejko, A. (2019). Intra-and
inter-rater reliability in a comparative study of cross-sectional and
spiral computed tomography pelvimetry methods. Acta Radiologica Open,
8:2058460119855187.

R Core Team (2019). R: A language and environment for statistical
computing. R Foundation for Statistical Computing, Vienna, Austria. URL
https://www.R-project.org/.

Randers, J. (2012). 2052 -- A Global Forecast for the Next Forty Years.
Chelsea Green Publishing, Vermont, 416 pp.

Remane, A. (1952). Die grundlagen des natürlichen Systems, der
vergleichenden Anatomie und der Phylogenetik. Akademische
Verlagsgesellschaft Geest und Portig, Leipzig.

Rensch, B. (1947). Neuere Probleme der Abstammunglehre die
Transspezifische Evolution. Ferdinand Enke, Stuttgart. Pp. 407.

Richter, A., Keller, R. A., Rosumet, F. B., Economo, E. P., Hita Garcia,
F., Beutel, R. G. (2019). The cephalic anatomy of the ant
species\emph{Wasmannia affinis} (Formicidae, Hymenoptera, Insecta) and
its evolutionary implications. Arthropod Structure \& Development,
49:26--49.

Ridgway, G. R., Henley, S. M. D., Rohrer, J. D., Scahill, R. I., Warren,
J. D., Fox, N. C. (2008). Ten simple rules for reporting voxel-based
morphometry studies. NeuroImage, 40:149--1435.

Salganik, M. J. Lundberg, I., Kindel, A. T., Ahearn, C. E., Al-Ghoneim,
K., Almaatouq, A., \ldots{} Datta, D. et al. (2020). Measuring the
predictability of life outcomes with a scientific mass collaboration.
Proceedings of the National Academy of Sciences, 117:8398--8403.

Sarnat, E. M., Hita-Garcia, F., Dudley, K., Liu C., Fischer, G.,
Economo, E. P. (2019). Ready Species One: exploring the use of augmented
reality to enhance systematic biology with a revision of
Fijian\emph{Strumigenys} (Hymneoptera: Formicidae). \emph{Insect Syst.
Diversity} 3:1--43.

Savriama, Y. (2018). A step-by-step guide for geometric morphometrics of
floral symmetry. Frontiers in Plant Science, 9, 1433.
doi:10.3389/fpls.2018.01433

Schlick-Steiner, B. C., Seifert, B., Stauffer, C., Christian, E.,
Crozier, R. H., Steiner, F. M. (2007). Without morphology, cryptic
species stay in taxonomic crypsis following discovery.
TREE\emph{,}22:391--392.

Schlick-Steiner, B. C., Steiner, F. M., Moder, K., Seifert, B., Sanetra,
M., Dyreson, E., Stauffer, C., Christian, E. (2006). A multidisciplinary
approach reveals cryptic diversity in Western
Palearctic\emph{Tetramorium} ants (Hymenoptera: Formicidae). Molecular
Phylogenetics and Evolution, 40:259--273.

Schlick-Steiner, B. C., Steiner, F. M., Seifert, B., Stauffer, C.,
Christian, E., Crozier R. H. (2010). Integrative taxonomy: a multisource
approach to exploring biodiversity. Annual Review of Entomology,
55:421--438.

Seifert, B. (1992). A taxonomic revision of the Palaearctic members of
the ant subgenus \emph{Lasius} s.str. (Hymenoptera: Formicidae).
-\emph{Abh. Ber. Naturkundemus. Görlitz.} 66:1--67.

Seifert, B. (2002). How to distinguish most similar insect species -
improving the stereomicroscopic and mathematical evaluation of external
characters by example of ants. Journal of Applied Entomology,
126:445--454.

Seifert, B. (2003). The ant genus \emph{Cardiocondyla} (Insecta:
Hymenoptera: Formicidae) - a taxonomic revision of the \emph{C. elegans}
, \emph{C. bulgarica} , \emph{C. batesii} , \emph{C. nuda} ,\emph{C.
shuckardi} , \emph{C. stambuloffii} , \emph{C. wroughtonii} ,\emph{C.
emeryi} , and \emph{C. minutior} species groups. \emph{Ann. Naturhist.
Mus. Wien, B Bot. Zool.} 104:203--338.

Seifert, B. (2009). Cryptic species in ants (Hymenoptera: Formicidae)
revisited: we need a change in the alpha-taxonomic approach.
Myrmecological News, 12:149--166.

Shingleton, A. W., Frankino, W. A., Flatt, T., Nijhout, H. F., Emlen, D.
J. (2007). Size and shape: the developmental regulation of static
allometry in insects. BioEssays, 29(6):536--548.

Sokal, R. R., Sneath, P. H. N. A. (1963). Principles of Numerical
Taxonomy. San Francisco, W. H. Freeman.

Steiner, F.,M., Schlick-Steiner, B.,C., Moder, K. (2006).
Morphology-based cyber identification engine to identify ants of
the\emph{Tetramorium caespitum} /\emph{impurum} complex (Hymenoptera:
Formicidae). Myrmecologische Nachrichten, 8:175--180.

Takacs, P., Vital, Z., Ferincz, Á., Staszny, Á. (2016). Repeatability,
reproducibility, separative power and subjectivity of different fish
morphometric analysis methods. PLoS One, 11:e0157890.

Taylor, B. N, Kuyatt, C. E. (2001). Guidelines for Evaluating and
Expressing the Uncertainty of NIST Measurement Results, {[}Online{]}.
Available: http://physics.nist.gov/TN1297 {[}2020, March 5{]}. National
Institute of Standards and Technology, Gaithersburg, MD. Originally
published as Guidelines for Evaluating and Expressing the Uncertainty of
NIST Measurement Results, Barry N. Taylor and Chris E. Kuyatt, NIST
Technical Note 1297 (1994 Edition).

Thompson, D. W. (1917). \emph{On Growth and Form.} Cambridge University
Press, London.

Tomiya, S., Meachen, J. A. (2018). Postcranial diversity and recent
ecomorphic impoverishment of North American gray wolves. Biological
Letter, 14:20170613.

Venables, W. N., Ripley, B. D. (2002). \emph{Modern Applied Statistics
with S} . Springer-Verlag.

Villemant, C., Simbolotti, G., Kenis, M. (2007). Discrimination
of\emph{Eubazus} (Hymenoptera, Braconidae) sibling species using
geometric morphometrics analysis of wing venation. Systematic
Entomology, 32:625--634.

Yoder, M. J., Mikó, I., Seltmann, K. C., Bertone, M. A., Deans, A. R.
(2010). A gross anatomy ontology for Hymenoptera. PLoS ONE, 5:e15991.

Ward, P. S. (1999). Systematics, biogeography and host plant
associations of the Pseudomyrmex viduus group (Hymenoptera: Formicidae),
Triplaris-and Tachigali-inhabiting ants. Zoological Journal of the
Linnean Society, 126:451--540.

Wolak, M. E., Fairbairn, D. J., Paulsen, Y. R. (2012). Guidelines for
estimating repeatability. Methods in Ecology and Evolution, 3:129--137.

Wright, A. M. (2019). A systematist's guide to estimating Bayesian
phylogenies from morphological data. Insect Systemaics and
Diversity\emph{,} 3:1--14.

Yezerinac, S. M., Lougheed, S. C., Handford, P. (1992). Measurement
error and morphometric studies: statistical power and observer
experience. Systematic Biology, 41:471--482.

Table legends

Table 1.

Verbatim trait definitions for morphometric character recording.
Abbreviations, definitions and descriptions of morphometric characters
are given. This standard protocol was followed by each gauger.

Table 2.

Intraclass correlation coefficients (R), upper and lower bounds, number
of cases (n) and average trait sizes are given for each observed
characters. Descriptions for abbreviations of morphometric characters
are as follows: CL: Head capsule length, CW: Width of head including
eyes, CWb: Width of head capsule, FRS: Frontal carinae width ML:
Mesosoma length; MW: mesosoma width; NOH: Maximum height of the petiolar
node, NOL: Length of the petiolar node, PEH: Maximum petiole height,
PEL: Petiolar lenght, PEW: Petiole width, PoOC: Postocular distance,
PPH: Postpetiole height; PPL: Postpetiole length, PPW: Postpetiole
width, SL: Scape length, SPBA: Spine base width, SPST: Spine length,
SPTI: Propodeal spine tip distance, STPL: Propodeal spine tip erection.

Table 3.

Repeatability scores (R) calculated for gaugers. Gauger information in
the table follows this format: experience in an insect group, estimated
number of individuals measured in a career, maximum magnification of the
microscope used, separated by underscores. ICC: intraclass correlation
coefficient calculated from the repeated measurements. The gaugers are
aligned according to the sequence of their contribution. Gauger alphabet
codes in triad format: A: MYRM\_9000\_100x, B: DIPT\_0\_100x, C:
MYRM\_5000\_288x, D: MYRM\_60000\_360x, E: MYRM\_500\_50x, F:
MYRM\_500\_50x, G: MYRM\_450\_50x, H: WASP\_1000\_230x, I:
WASP\_0\_230x, J: MYRM\_300\_100x, K: MYRM\_300\_100x.

Figure captions

Fig. 1.

Precision versus accuracy. The bullseye represents the value of the
measurand. Accuracy is indicated by closeness to the
bullseye---measurements closer to the bullseye are more accurate.
Precise measurements are tightly clustered. Accurate and precise
measurements are tightly clustered in the bullseye. Graphics produced
and used with permission from Dr. Bethan Davies (antarcticglaciers.org).

Fig. 2.

Illustrations for morphometric characters. Head in dorsal view (a) with
measurement lines for CL: Head capsule length, CW: Width of head
including eyes, CWb: Width of head capsule, PoOC: Postocular distance
and SL: Scape length; frontal region of the head dorsum (b) with
measurement lines for FRS: Frontal carinae width (red accessory lines
and arrows identify the torular lamella); lateral view of mesosoma (c)
with measurement line for ML: Mesosoma length; lateral view of
propodeum, petiole, and postpetiole (d) with measurement lines for STPL:
Propodeal spine tip erection, NOH: Maximum height of the petiolar node,
NOL: Length of the petiolar node, PPL: Postpetiole length, and SPST:
Spine length; dorsal view of mesosoma (e) with measurement lines for MW:
mesosoma width; lateral view of propodeum, petiole, and postpetiole (f)
with measurement lines for PEH: Maximum petiole height, PEL: Petiolar
lenght, and PPH: Postpetiole height; dorsal view of propodeum, petiole,
and postpetiole (g) with measurement lines for SPBA: Spine base width,
SPTI: Propodeal spine tip distance, PEW: Petiole width, and PPW:
Postpetiole width. Detailed verbatim trait definitions for characters
are given in Table 1.

Fig. 3a,b.

Ordination biplot for Principal Component Analysis based on (a) species
identity and (b) the accuracy of the measurement. Black and red dots
represent repeated observations on the same objects, while black dots
represent \emph{Nesomyrmex devius} , and red dots represent \emph{N.
hirtellus} . Convex hulls for spatial distribution of observations
within morphospace represent (a) species and (b) gaugers. Descriptions
for abbreviations of morphometric characters (red letters) are as
follows: CL: Head capsule length, CW: Width of head including eyes, CWb:
Width of head capsule, FRS: Frontal carinae width ML: Mesosoma length;
MW: mesosoma width; NOH: Maximum height of the petiolar node, NOL:
Length of the petiolar node, PEH: Maximum petiole height, PEL: Petiolar
lenght, PEW: Petiole width, PoOC: Postocular distance, PPH: Postpetiole
height; PPL: Postpetiole length, PPW: Postpetiole width, SL: Scape
length, SPBA: Spine base width, SPST: Spine length, SPTI: Propodeal
spine tip distance, STPL: Propodeal spine tip erection. Gauger alphabet
codes (B) in triad format: A: MYRM\_9000\_100x, B: DIPT\_0\_100x, C:
MYRM\_5000\_288x, D: MYRM\_60000\_360x, E: MYRM\_500\_50x, F:
MYRM\_500\_50x, G: MYRM\_450\_50x, H: WASP\_1000\_230x, I:
WASP\_0\_230x, J: MYRM\_300\_100x, K: MYRM\_300\_100x. Compositional
differences between treatments expressed as the results of the PERMANOVA
(coefficient of determination, F and p values, details in the text).

Fig. 4.

The correlogram of the studied variables for testing repeatability by
the Spearman rank correlation test. The size of each bubble is
proportional to the estimated correlation value (r). The heat chart on
the right shows the color correspondence for r values.

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