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Many ecological and evolutionary studies seek to explain patterns of shape variation and its covariation with other variables. Geometric morphometrics is often used for this purpose, where a set of shape variables are obtained from landmark coordinates following a Procrustes superimposition.We introduce geomorph: a software package for performing geometric morphometric shape analysis in the r statistical computing environment.Geomorph provides routines for all stages of landmark-based geometric morphometric analyses in two and three-dimensions. It is an open source package to read, manipulate, and digitize landmark data, generate shape variables via Procrustes analysis for points, curves and surfaces, perform statistical analyses of shape variation and covariation, and to provide graphical depictions of shapes and patterns of shape variation. An important contribution of geomorph is the ability to perform Procrustes superimposition on landmark points, as well as semilandmarks from curves and surfaces.A wide range of statistical methods germane to testing ecological and evolutionary hypotheses of shape variation are provided. These include standard multivariate methods such as principal components analysis, and approaches for multivariate regression and group comparison. Methods for more specialized analyses, such as for assessing shape allometry, comparing shape trajectories, examining morphological integration, and for assessing phylogenetic signal, are also included.Several functions are provided to graphically visualize results, including routines for examining variation in shape space, visualizing allometric trajectories, comparing specific shapes to one another and for plotting phylogenetic changes in morphospace.Finally, geomorph participates to make available advanced geometric morphometric analyses through the r statistical computing platform.

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APPLICATION

geomorph: an R package for the collection and analysis

of geometric morphometric shape data

Dean C. Adams

1,2

*andErikOt



arola-Castillo

1,3

Department of Ecology, Evolution, and Organismal Biology, Iowa State University, Ames, IA 50011, USA;

Department of

Statistics, Iowa State University, Ames, IA 50011, USA; and

Department of Human Evolutionary Biology, Department of

Statistics, Harvard University, Cambridge, MA 02138, USA

Summary

1. Many ecological and evolutionary studies seek to explain patterns of shape variation and its covariation with

other variables. Geometric morphometrics is often used for this purpose, where a set of shape variables are

obtained from landmark coordinates following a Procrustes superimposition.

2. We introduce geomorph: a software package for performing geometric morphometric shape analysis in the R

statistical computing environment.

3. Geomorph provides routines for all stages of landmark-based geometric morphometric analyses in two and

three-dimensions. It is an open source package to read, manipulate, and digitize landmark data, generate shape

variables via Procrustes analysis for points, curves and surfaces, perform statistical analyses of shape variation

and covariation, and to provide graphical depictions of shapes and patterns of shape variation. An important

contribution of geomorph is the ability to perform Procrustes superimposition on landmark points, as well as

semilandmarks from curves and surfaces.

4. A wide range of statistical methods germane to testing ecological and evolutionary hypotheses of shape varia-

tion are provided. These include standard multivariate methods such as principal components analysis, and

approaches for multivariate regression and group comparison. Methods for more specialized analyses, such as

for assessing shape allometry, comparing shape trajectories, examining morphological integration, and for

assessing phylogenetic signal, are also included.

5. Several functions are provided to graphically visualize results, including routines for examining variation in

shape space, visualizing allometric trajectories, comparing speciﬁc shapes to one another and for plotting

phylogenetic changes in morphospace.

6. Finally, geomorph participates to make available advanced geometric morphometric analyses through the R

statistical computing platform.

Key-words: macroevolution, statistics, evolutionary biology

Introduction

The comparison of anatomical features of organisms, and

understanding how variation in those features associates with

variation in other traits, has long been of interest to ecologists

and evolutionary biologists. In recent years, the quantitative

study of anatomical form has matured into the ﬁeld of mor-

phometrics: the study of shape variation and its covariation

with other variables (Bookstein 1991; Rohlf & Marcus 1993;

Adams, Rohlf & Slice 2004; Zelditch et al. 2004; Adams, Rohlf

& Slice 2013). One common approach to shape analysis, geo-

metric morphometrics (GM), utilizes the coordinates of land-

marks to record the relative positions of morphological points,

boundary curves and surfaces as the basis of shape quantiﬁca-

tion. Geometric morphometric shape analyses are typically

accomplished through a series of steps that can be called the

Procrustes paradigm (Adams, Rohlf & Slice 2013). First, a set

of two- or three-dimensional landmark coordinates are

obtained on each specimen, which record the relative positions

of anatomically-corresponding (or homologous) locations.

Next, a generalized Procrustes analysis (GPA: Gower 1975;

Rohlf & Slice 1990) is used to superimpose the specimens to a

common coordinate system by holding constant variation in

their position, size and orientation (an additional step is

included to standardize points on curves and surfaces:

Bookstein et al. 1999; Gunz, Mitteroecker & Bookstein 2005).

From the Procrustes-aligned coordinates, a set of shape vari-

ables is obtained (Bookstein 1991; Dryden & Mardia 1998;

Rohlf 1999), which can be used in multivariate statistical anal-

yses to address a wide range of biological questions. Finally,

graphical methods are used to visualize patterns of shape varia-

tion and facilitate descriptions of shape changes.

*Corresponding author. E-mail: dcadams@iastate.edu

Methods in Ecology and Evolution 2013, 4, 393–399 doi: 10.1111/2041-210X.12035

Because geometric morphometric methods provide a more

comprehensive quantiﬁcation of biological shape as compared

to alternative approaches, their use in ecological and evolu-

tionary studies has increased dramatically in recent years. For

instance, geometric morphometric methods are now com-

monly used in studies of evolutionary quantitative genetics

(Klingenberg, Debat & Roﬀ 2010; Adams 2011; Mart 

ınez-

Abad 

ıas et al. 2012), to reveal phenotypical changes associated

with species interactions (Adams 2004; Langerhans et al. 2004;

Adams, West & Collyer 2007), to describe patterns of ﬂuctuat-

ing and directional asymmetry (Klingenberg, Barluenga &

Meyer 2002; Schaefer et al. 2006), to identify convergent and

parallel evolution (Stayton 2006; Adams 2010; Adams & Nistri

2010; Piras et al. 2010), to discover phylogenetic and

macroevolutionary trends (Sidlauskas 2008; Klingenberg &

Gidaszewski 2010; Monteiro & Nogueira 2011) and to reveal

ontogenetic patterns in human evolution (Bookstein et al.

2003; Mitteroecker et al. 2004; Mitteroecker & Bookstein

2008), among other applications. Consequently, several soft-

ware packages are now available for applying geometric mor-

phometrics to particular problems. However, freely available

software implementing all of the steps of the Procrustes para-

digm in a single computer package, including the digitization

of specimens and the analysis of both ﬁxed landmarks and slid-

ing semilandmarks in two- and three-dimensions, is generally

lacking.

The purpose of geomorph is to ﬁll this gap. Geomorph

(Adams & Ot

arola-Castillo 2012) is a freely available software

package for performing geometric morphometric shape analy-

sis in the Rstatistical computing environment. It can be

installed from the Comprehensive RArchive Network, CRAN.

In geomorph, routines for all stages of landmark-based geo-

metric morphometric analyses are provided, including: digitiz-

ing landmarks on two and three-dimensional objects; reading

and manipulated landmark data ﬁles; generating shape vari-

ables via Procrustes analysis for points, curves and surfaces;

performing statistical analyses of shape variation and covaria-

tion; and providing graphical depictions of shapes and patterns

of shape variation. A variety of statistical methods for shape

analyses germane to ecological and evolutionary studies are

included. Geomorph extends the capabilities of landmark-

based shape analysis in Rover prior packages and routines

(e.g. the 'shapes' package: Dryden 2012 and Morphometrics

With R: Claude 2008), by incorporating both semilandmark

methods and the digitization of specimens directly within R.

However, because geomorph utilizes previously developed

data structures implemented in these packages, one may com-

bine functions across packages to expand the breadth of shape

analyses available within the Rcomputing environment. Below

we describe some of the major features of geomorph to demon-

strate some of its functionalities.

Description

ThegeomorphpackageiswrittenintheR scientiﬁc computing

language (R Development Core Team 2012). The functions in

geomorph are designed to enhance all aspects of a landmark-based

geometric morphometric shape analysis. Currently imple-

mented functions are listed in Table 1, which is arranged by

workﬂow. In the coming years, we will incorporate additional

functions to further expand the utility of geomorph.

DATA INPUT AND DIGITIZING

Previously digitized landmark data stored as text ﬁles in the

*.tps or *.nts formats can be read into geomorph using read-

land.tps,readland.nts,orreadmulti.nts.The

resulting data are then stored in Ras a three-dimensional array

for subsequent morphometric analyses (p landmarks 9 k

dimensions 9N specimens). Previously digitized data stored

in other formats (such as those used by MORPHOJ: Klingenberg

2011 and MORPHOLOGIKA: O'Higgins & Jones 1998) may be

read using read.morphologika and the base functions of R

(e.g. read.csv ,read.table ). The data matrix can then be

converted to a three-dimensional array for use in geomorph

using the function arrayspecs .

A major feature of geomorph is the ability to digitize land-

mark data directly from two- and three-dimensional images in

R(Fig. 1). Digitizing two-dimensional landmarks from a

*.jpeg image is accomplished using the function digitize2d .

For three-dimensional data, digital surface images in the form

of *.ply or *.vrml ﬁles may be read into geomorph using

read.ply and read.vrml respectively. From these, the

coordinates of points, curves and surfaces may be digitized

using one or more functions in geomorph (for list of functions

see Table 1). When semilandmarks on surfaces are desired,

these points are digitized using a template (following Gunz,

Mitteroecker & Bookstein 2005). Here, a set of ﬁxed land-

marks are ﬁrst digitized on a specimen; then a series of equally

spaced points are identiﬁed mathematically, and treated as a

semilandmarks representing the shape of the surface (using the

function buildtemplate ). The remaining specimens are

then digitized by matching this template to their surface scans

using the function digitsurface , which allows for a one-to-

one correspondence between semilandmarks across specimens.

Finally, because geometric morphometric analyses require that

all specimens have the same set of landmarks, incomplete spec-

imens require some additional treatment. For incomplete spec-

imens the function estimate.missing canbeusedto

estimate the location of missing landmarks. This function

implements thin-plate spline interpolation (following Gunz

et al. 2009), which maps the locations of landmarks on a com-

plete specimen to their corresponding locations on the speci-

men with missing landmarks. This approach is particularly

useful for biological disciplines where missing landmarks and

partial specimens are common; such as palaeontology, archae-

ology and biological anthropology.

PROCRUSTES SUPERIMPOSITION AND DATA ANALYSIS

The workhorse of geometric morphometrics is GPA, which

superimposes specimens to a common coordinate system by

holding constant variation in their position, size, and orienta-

tion. In geomorph, GPA is accomplished using the function

394 D. C. Adams and E. Ot 

arola-Castillo

gpagen.Importantly,gpagen is a general function which

can be used to superimpose sets of landmark as well as semi-

landmarks, the latter of which can be used to capture the shape

of boundary curves and of surfaces. Here an additional step is

incorporated into the Procrustes algorithm where semiland-

marks on curves are slid along their tangent vectors, and semi-

landmarks on surfaces are slid within their tangent planes,

until their positions minimize the shape diﬀerence between

specimens (based on either Procrustes distance [the default] or

bending energy: Bookstein 1997; Bookstein et al. 1999; Gunz,

Mitteroecker & Bookstein 2005; Rohlf 2010). Aligned speci-

mens can then be projected into a linear tangent space for sub-

sequent statistical analysis using the option Proj = TRUE .

A number of functions in geomorph provide statistical

assessment of patterns of shape variation. For instance, plot-

TangentSpace performs a principal components analysis of

the shape data and provides a graphical view of the resulting

scatter. Hypothesis-testing for ANOVA and regression models is

accomplished in procD.lm , which uses the Procrustes

distances among specimens to quantify explained and

Table 1. Major functions of the geomorph package

Function name Description

Data Input, Data Collection, and Data Preparation Functions

arrayspecs Convert landmark data

matrix into array (p9 k9 N)

buildtemplate Build 3D surface template

curves2d Select points to 'slide' along

two-dimensional curves

digit.curves Select points to 'slide' along

three-dimensional curves

digit.ﬁxed Digitize ﬁxed 3D landmarks only

digitize2d Digitize 2D landmarks

digitsurface Digitize 3D ﬁxed landmarks and

surface semilandmarks

editTemplate Edit 3D template

estimate.missing Estimate locations of missing

landmarks using the

thin-plate spline

read.ply Read landmark data from ply ﬁles

read.vrml Read landmark data from vrml ﬁles

readland.nts Read landmark data from nts ﬁle

readland.tps Read landmark data from tps ﬁle

read.morphologika Read 3D landmark data from

Morphologika ﬁle

readmulti.nts Read landmark data from

multiple nts ﬁles

two.d.array Convert (p9 k9 N ) data array

into 2D data matrix

Data Analysis Functions

compare.modular.partitions Compare modular signal to

alternative landmark subsets

gpagen Generalized Procrustes analyis of

points, curves, and surfaces

morphol.integr Quantify morphological integration

between two modules

mshape Estimate mean shape for a set of

aligned specimens

physignal Assessing phylogenetic signal in

morphometric data

procD.lm Procrustes ANOVA/regression for

shape data

(a) (b)

Fig. 1. Example of landmark digitizing from three-dimensional image (data from Serb et al. 2011). (a) A surface scan of a scallop, read into R as a

*.ply ﬁle. (b) A set of digitized points obtained from the surface scan. Here, 15 points were digitized along the edge of the specimen (red), and 100

equally-spaced semilandmark surface points (blue) were then obtained using the function digitsurface .

Table 1. (continued)

Function name Description

trajectory.analysis Quantify and compare shape change

trajectories

Plots and Graphical Functions

plotAllometry Plot allometric patterns in landmark

data

plotAllSpecimens Plot landmark coordinates for all

specimens

plotGMPhyloMorphoSpace Plot phylogenetic tree and specimens

in tangent space

plotRefToTarget Plot shape diﬀerences between a

reference and target specimen

plotspec Plot 3D specimen, ﬁxed landmarks

and surface semilandmarks

plotTangentSpace Plot specimens in tangent space

geomorph 395

unexplained components of shape variation, which are statisti-

cally evaluated via permutation (Goodall 1991). Comparisons

of trajectories of shape change or motion paths may be

obtained using trajectory.analysis (Adams & Cerney

2007; Adams & Collyer 2009), and patterns of morphological

integration explored using the functions morphol.integr

and compare.modular.partitions . Recent methods

for assessing phylogenetic signal in morphometric data

(Klingenberg & Gidaszewski 2010) are implemented in phy-

signal. Finally, because R is a statistical computing language,

the function arrayspecs canbeusedtoreformattheshape

data to a matrix of specimens by variables, so that other statis-

tical routines in Rmay be utilized.

GRAPHICS AND VISUALIZATION

Geomorph provides numerous functions for visualizing the

results of shape analyses for both two-dimensional and three-

dimensional data. For instance, one can visualize the shape

changes between two specimens, as either landmark displace-

ments or thin-plate spline deformation grids, with the function

plotRefToTarget. Evolutionary changes in shape along a

phylogeny can be viewed in shape space using plotGMPhy-

loMorphoSpace, and changes as a function of size (i.e. allo-

metric trajectories) may be viewed using the function

plotAllometry. Other visualization options are described

in Table 1.

EXAMPLES

Here we provide several illustrative examples to demonstrate

the use of geomorph. All examples can be reproduced using

thedatathatcomewiththepackage.First,weloadgeomorph

in R:

>library(geomorph)

Next, we call the data set 'plethoodon ', and plot the origi-

nal landmark data (Fig. 2a):

>data(plethodon)

>plotAllSpecimens(plethodon$land)

We then perform a Procrustes superimposition and plot the

aligned landmark coordinates. In this case, the resulting shape

variables are stored as a data frame 'Y.gpa ' and graphical

links between landmarks (included in the data set 'pleth-

odon') are plotted to aid visual interpretation (Fig. 2b).

>Y.gpa<-gpagen(plethodon$land)#GPA-alignment

plotAllSpecimens(Y.gpa$coords,links=plethodon

$links)

If sliding semilandmarks are included, additional parame-

ters of gpagen must be speciﬁed. This can be seen in the fol-

lowing example, using three-dimensional landmark data

(Fig. 2C):

>data(scallops)

>Y.gpa2<-gpagen(A=scallops$coorddata,

curves=scallops$curvslide,

surfaces=scallops$surfslide)

Next, we will perform several additional analyses that relate

to particular biological hypotheses. First, to visualize patterns

of shape variation in shape space we perform a principal com-

ponents analysis:

>plotTangentSpace(Y.gpa$coords)

The resulting plot of the ﬁrst two dimensions of tangent

space explains 67% of the total shape variation, and reveals

several distinct clusters of specimens, implying that shape

diﬀerences may be present (Fig. 3a). Indeed, for this data

example, specimens represent two species in two distinct envi-

ronments and a statistical evaluation using MANOVA reveals sig-

niﬁcant shape diﬀerences between species, between sites and in

the interaction between the two factors:

>y<-two.d.array(Y.gpa$coords)

>procD.lm(y~plethodon$species*plethodon$site,

iter=99)

[1] No specimen names inresponse matrix. Assuming

specimens in same order.

df SS.obs MS P .val

plethodon$species 1 0 02925784 002925784 0 001

plethodon$site 1 0 06437484 006437484 0 001

plethodon$species

:plethodon$site

10 03088502 003088502 0001

Total 39 0 19693973 NA NA

The shape diﬀerences between group mean can be visualized

graphically, by obtaining the average landmark coordinates

for each group and the overall mean, and plotting the diﬀer-

ences as thin-plate spline transformation grids:

>ref<-mshape(Y.gpa$coords)

>gp1.mn<-mshape(Y.gpa$coords[,,1:20])

>plotRefToTarget(ref,gp1.mn,mag=2,

links=plethodon$links)

Here, the shape diﬀerences have been ampliﬁed by a factor

of two to aid in the description of shape diﬀerences and facili-

tate biological interpretation (Fig. 3b).

Multivariate patterns of allometry can also be visualized,

using one of three visualization options (Mitteroecker et al.

2004; Drake & Klingenberg 2008; Adams & Nistri 2010). The

example data set 'rats' can be used to illustrate the approach

(Fig. 3c):

>data(rats)

>rat.gpa<-gpagen(ratland)

> plotAllometry(rat.gpa$coords,rat.gpa$Csize,

method=CAC)

This data set exhibits signiﬁcant allometry, as is found from

multivariate regression:

>procD.lm(two.d.array(rat.gpa$coords)~rat.gpa

$Csize,iter=999)

[1] No specimen names inresponse matrix. Assuming

specimens in same order.

df SS.obs MS P .val

rat.gpa$Csize 1 0 6403531 0 6403531 0 001

Total 163 0 8423871 NA NA

As a ﬁnal example, one may combine phylogenetic data with

shape data to estimate the degree of phylogenetic signal in

396 D. C. Adams and E. Ot 

arola-Castillo

(a) (b)

(c)

Fig. 2. Plot of landmark data (a) before and (b) after Procrustes superimposition obtained using the functions plotAllSpecimens (a) and gpa-

gen (b). Data represent head shape based on landmarks on 40 salamander specimens from the genus Plethodon (subset of data originally described

in: Adams 2004, 2010). (c) A plot of superimposed scallop specimens represented by three-dimensional landmark coordinates.

(a) (b)

Fig. 3. Example of some of the graphical output from geomorph. (a) Principal components plot of shape variation using the function plotTan-

gentSpace, (b) shape diﬀerences between the average (reference) and a target specimen displayed as a thin-plate spline deformation grid from the

function plotRefToTarget , (c) allometric trajectories viewed as the common allometric component (CAC: Mitteroecker et al. 2004) versus size

using the function plotAllometry , (d) projection of phylogeny into shape space for viewing evolutionary shape changes obtained with the func-

tion physignal .

geomorph 397

shape. This function provides a view of shape space with the

phylogeny superimposed (Fig. 3d):

>data(plethspecies)

>Y.gpa<-gpagen(plethspecies$land)#GPA-

alignment

>physignal(plethspecies$phy,Y.gpa$coords,

iter=99)

$phy.signal

[1] 0 002659967

$pvalue

[1] 0 02

Additional examples illustrating how to implement other

functions are found in the geomorph help ﬁles.

Conclusions

The past several decades have seen a major increase in the

development and use of landmark-based geometric morpho-

metric methods in ecological and evolutionary studies. During

this same time, the R statistical language has become the stan-

dard platform for statistical and computational analyses in

many biological disciplines. The package geomorph leverages

both of these advances by providing comprehensive software

for performing the latest morphometric shape analyses in R.

Users may read, manipulate and digitize two- and three-

dimensional landmark data within R, generate shape variables

from landmark and semilandmark data, perform statistical

analyses to address ecological and evolutionary hypotheses

and obtain graphical depictions of shapes and patterns of

shape variation. Importantly, geomorph can perform Procrus-

tes superimposition on landmark points, and semilandmarks

on curves and surfaces in two or three dimensions, providing a

more comprehensive quantiﬁcation and analysis of biological

shape variation. Full descriptions of all geomorph functions,

as well as examples of their use, are available from the online

help ﬁles.

CITATION OF GEOMORPH

Scientists using geomorph in a published paper should cite this

article. Users can also cite the phytools package directly. Cita-

tion information can be obtained by typing:

> citation(geomorph)at the command prompt.

Acknowledgements

This work was sponsored in part by NSF grant DEB-1118884 to DCA, and by a

Harvard Fellowship to EOC. Three anonymous reviewers provided valuable

comments that greatly improved this work.

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... 1.4, Appendix 1-table 1). The CFMR was derived from a Procrustes superimposition (R package 'geomorph' v.3.0.5; Adams et al., 2013) of four fossil specimens which showed low levels of overall distortion and a mandible orientation suitable for extraction of individual MAs (Appendix 1-figure 9). For comparison of species and inference of the dietary niche, a PCA and, due to the detection of significant phylogenetic signal, a pPCA (R package 'phytools' v.0.6-44; ...

... Phylogenetic signal was assessed using the K statistic as implemented in geomorph v.3.0.5 (Adams et al., 2013) with 10,000 random permutations. This test statistic was found to be the most efficient approach to test for phylogenetic signal (Pavoine and Ricotta, 2013). ...

A high portion of the earliest known insect fauna is composed of the so-called 'lobeattid insects', whose systematic affinities and role as foliage feeders remain debated. We investigated hundreds of samples of a new lobeattid species from the Xiaheyan locality using a combination of photographic techniques, including reflectance transforming imaging, geometric morphometrics, and biomechanics to document its morphology, and infer its phylogenetic position and ecological role. Ctenoptilus frequens sp. nov. possessed a sword-shaped ovipositor with valves interlocked by two ball-and-socket mechanisms, lacked jumping hind-legs, and certain wing venation features. This combination of characters unambiguously supports lobeattids as stem relatives of all living Orthoptera (crickets, grasshoppers, katydids). Given the herein presented and other remains, it follows that this group experienced an early diversification and, additionally, occurred in high individual numbers. The ovipositor shape indicates that ground was the preferred substrate for eggs. Visible mouthparts made it possible to assess the efficiency of the mandibular food uptake system in comparison to a wide array of extant species. The new species was likely omnivorous which explains the paucity of external damage on contemporaneous plant foliage.

... A Generalized Procrustes Analysis (GPA) was performed on the resulting landmark configurations of every specimen in order to homogenize their positions in the Cartesian coordinate system by superimposing them (Gower, 1975;Rohlf & Slice, 1990), using the function "gpagen" of the geomorph v. 3.3.1 R package (Adams & Otárola-Castillo, 2013). This step also enabled us to isolate the shape component from the size component (Zelditch et al., 2012). ...

... Convex hulls were used in order to highlight the distribution of locomotor modes in the morphospace using the function "shape-Hulls" from the geomorph v. 3.3.1 R package (Adams & Otárola-Castillo, 2013). Isolating the shape variation linked to differences in locomotor mode also enabled us to compute 3D visualizations that highlighted which features varied the most along this axis. ...

The evolutionary history of archosaurs and their closest relatives is characterized by a wide diversity of locomotor modes, which has even been suggested as a pivotal aspect underlying the evolutionary success of dinosaurs vs. pseudosuchians across the Triassic–Jurassic transition. This locomotor diversity (e.g., more sprawling/erect; crouched/upright; quadrupedal/bipedal) led to several morphofunctional specializations of archosauriform limb bones that have been studied qualitatively as well as quantitatively through various linear morphometric studies. However, differences in locomotor habits have never been studied across the Triassic–Jurassic transition using 3D geometric morphometrics, which can relate how morphological features vary according to biological factors such as locomotor habit and body mass. Herein, we investigate morphological variation across a dataset of 72 femora from 36 different species of archosauriforms. First, we identify femoral head rotation, distal slope of the fourth trochanter, femoral curvature, and the angle between the lateral condyle and crista tibiofibularis as the main features varying between bipedal and quadrupedal taxa, all of these traits having a stronger locomotor signal than the lesser trochanter's proximal extent. We show a significant association between locomotor mode and phylogeny, but with the locomotor signal being stronger than the phylogenetic signal. This enables us to predict locomotor modes of some of the more ambiguous early archosauriforms without relying on the relationships between hindlimb and forelimb linear bone dimensions as in prior studies. Second, we highlight that the most important morphological variation is linked to the increase of body size, which impacts the width of the epiphyses and the roundness and proximodistal position of the fourth trochanter. Furthermore, we show that bipedal and quadrupedal archosauriforms have different allometric trajectories along the morphological variation in relation to body size. Finally, we demonstrate a covariation between locomotor mode and body size, with variations in femoral bowing (anteroposterior curvature) being more distinct among robust femora than gracile ones. We also identify a decoupling in fourth trochanter variation between locomotor mode (symmetrical to semi‐pendant) and body size (sharp to rounded). Our results indicate a similar level of morphological disparity linked to a clear convergence in femoral robusticity between the two clades of archosauriforms (Pseudosuchia and Avemetatarsalia), emphasizing the importance of accounting for body size when studying their evolutionary history, as well as when studying the functional morphology of appendicular features. Determining how early archosauriform skeletal features were impacted by locomotor habits and body size also enables us to discuss the potential homoplasy of some phylogenetic characters used previously in cladistic analyses as well as when bipedalism evolved in the avemetatarsalian lineage. This study illuminates how the evolution of femoral morphology in early archosauriforms was functionally constrained by locomotor habit and body size, which should aid ongoing discussions about the early evolution of dinosaurs and the nature of their evolutionary "success" over pseudosuchians. We studied femoral shape variation by applying 3D geometric morphometrics to a large sample of archosauriforms predominantly from the Late Triassic. We identified a set of anatomical features varying with locomotor mode (quadrupedal/bipedal) or body size. We also showed that morphological variation linked to locomotor mode had a strong phylogenetic signal and that femoral shape specialization to body size was convergent between avemetatarsalians (=dinosaur lineage) and pseudosuchians (=crocodile lineage).

... Male and female morphological differences: To investigate the bill shape differences between males and females, we used the function "procD.lm" from the R package "geomorph" (Adams and Otárola-Castillo 2013) to perform a Procrustes ANOVA (randomised residuals, 1000 iterations) with sex as an explanatory variable. We also used linear models to test whether the separated PC1 and PC2, which explained the different aspects of bill shape were related to sex. ...

The New Zealand huia (Heteralocha acutirostris) had the most extreme bill sexual dimorphism among modern birds. Given the quick extinction of the species, the cause of the dimorphism could only be hypothesised to reflect different trophic niches and reduce male/female competition. We tested that hypothesis by combining museum specimens, geometric morphometrics, and isotopic analyses. We used geometric morphometrics to describe bill shape; measured bulk (δ 15 N bulk) and (δ 13 C bulk) values from feather as proxies of the birds' foraging habitat and diet; and compared compound-specific stable isotopes analyses (CSIA) of nitrogen in amino acids (δ 15 N AA) in male-female pairs to estimate their trophic position. Sexes had significantly different, but overlapping feather δ 15 N bulk and δ 13 C bulk values, but δ 15 N AA indicated identical trophic positions and δ 15 N bulk was not related to bill shape. Trophic position was less variable among females, consistent with a specialised foraging behaviour and, thus, supporting a partial male/female foraging segregation.

... Intraobserver error for the landmark configuration was assessed using the methods of White et al. (2020) and was found to be significantly lower than intrataxonomic and intertaxonomic distances (SOM S2; SOM Table S4; SOM Fig. S1), meaning that intraobserver error should not significantly affect the outcomes of this study. Generalized Procrustes analysis The data were put through a generalized Procrustes analysis (GPA) with a partial Procrustes fit (Rohlf and Slice, 1990;Rohlf, 1999) using the 'gpagen' function in the 'geomorph' package v. 3.3.1 (Adams et al., 2013) in R v. 3.6.1 (R Core Team, 2014). During this process, the semilandmarks were slid to minimize bending energy. ...

This study assessed variation in the supraorbital and orbital region of the Middle Pleistocene hominins (MPHs), sometimes called Homo heidelbergensis s.l., to test whether it matched the expectations of intraspecific variation. The morphological distinctiveness and relative variation of this region, which is relatively well represented in the hominin fossil record, was analyzed quantitatively in a comparative taxonomic framework. Coordinates of 230 3D landmarks (20) and sliding semilandmarks (210) were collected from 704 specimens from species of Homo, Australopithecus, Paranthropus, Gorilla, Pan, Papio, and Macaca. Results showed that the MPHs had expected levels of morphological distinctiveness and intragroup and intergroup variation in supraorbital and orbital morphology, relative to commonly recognized non-hominin catarrhine species. However, the Procrustes distances between this group and H. sapiens were significantly higher than expected for two closely related catarrhine species. Furthermore, this study showed that variation within the MPH could be similarly well contained within existing hypodigms of H. sapiens, H. neanderthalensis, and H. erectus s.l. Although quantitative assessment of supraorbital and orbital morphology did not allow differentiation between taxonomic hypotheses in later Homo, it could be used to test individual taxonomic affiliation and identify potentially anomalous individuals. This study confirmed a complicated pattern of supraorbital and orbital morphology in the MPH fossil record and raises further questions over our understanding of the speciation of H. sapiens and H. neanderthalensis and taxonomic diversity in later Homo.

... The landmark data were imported into the software R v.3.5.2 (R Core Team, 2011). Using the plotAllSpecimens function of Geomorph v.3.2.1 (Adams and Otárola-Castillo, 2013) in R, we notice great variability for each anatomical landmark, resulting from two main shapes of the vomer. The majority of bird possesses a fused vomer that is bilaterally symmetric and roof-shaped in transection, with a horizontal orientation within the pterygoid-palatine complex (Fig. 1B). ...

Crown birds are subdivided into two main groups, Palaeognathae and Neognathae, that can be distinguished, among other means, by the organization of the bones in their pterygoidpalatine complex (PPC). Shape variation of the vomer, which is the most anterior part of the PPC, was recently analysed with help of geometric morphometrics to discover morphological differences between palaeognath and neognath birds. Based on this study, the vomer was identified as sufficient to distinguish the two main groups (and even some inclusive neognath groups) and their cranial kinetic system. As there are notable size differences between the skulls of Palaeognathae and Neognathae, we here investigate the impact of allometry on vomeral shape and its implication for taxonomic classification by re-analysing the data of the previous study. Different types of multivariate statistical analyses reveal that taxonomic identification based on vomeral shape is strongly impaired by allometry, as the error of correct identification is high when shape data is corrected for size. This finding is evidenced by a great overlap between palaeognath and neognath subclades in morphospace. Correct taxonomic identification is further impeded by the convergent presence of a flattened vomeral morphotype in multiple neognath subclades. As the evolution of cranial kinesis has been linked to vomeral shape in the original study, the correlation between shape and size of the vomer across different bird groups found in the present study questions this conclusion. In fact, cranial kinesis in crown birds results from the loss of the jugal-postorbital bar in the temporal region and ectopterygoid in the PPC and the combination of a mobilized quadratezygomatic arch complex and a flexible PPC. Therefore, we can conclude that vomer shape itself is not a suitable proxy for exploring the evolution of cranial kinesis in crown birds and their ancestors. In contrast, the evolution of cranial kinesis needs to be viewed in context of the braincase, quadrate-zygomatic arch and the whole pterygoid-palatine complex.

The integrative taxonomy approach has recently been widely suggested in systematic studies. Lines of evidence such as the geometric morphometrics and ecological analyses have been useful for discriminating between genetically well-differentiated species. Within the genus Reithrodontomys, R. mexicanus is one of the more taxonomically complex species, being considered a cryptic species complex. R. cherrii was considered a subspecies of R. mexicanus, until molecular evidence raised it to the species-level. Herein, we evaluate these two forms using morphological and ecological data based on the premise that they constitute genetically differentiated species. We carried out geometric morphometric analyses on dorsal and ventral views of the skull. Landmark and semi-landmark configurations for both views of the skull were selected based on previous studies of cricetid rodents. We tested the presence of sexual dimorphism, and the skull shape and size differences between species on both cranial views. Additionally, we characterized the environmental space of each species habitat using bioclimatic variables , elevation, and the Normalized Difference Vegetation Index (NDVI). Females and males of R. mexicanus and R. cherrii did not show sexual dimorphism in shape or size of both skull views. We found significant differences between the two species in both shape and size of the skull. Cranial structures of the ventral view were more useful to differentiate both species. R. mexicanus exhibited a broader environmental space than R. cherrii, with relatively similar values of temperature and elevation, but not of precipitation. The pairwise comparison showed significant differences in the majority of the environmental variables analyzed. Although for each view, we found statistical differences in the skull shape of R. cherrii and R. mexicanus, the ventral side showed major resolutive power differentiating both species. Our findings suggest that R. cherrii tends to have a larger skull than R. mexicanus. However, the morphological and pelage coloration similarity between these species reported in the past, could explain the previous inclusion of R. cherrii as a subspecies of R. mexicanus. R. mexicanus occurs in a variety of vegetation-types coinciding with the broader environmental space that it occupies compared to that of R. cherrii. The natural areas where both species are distributed were associated with high NDVI values. Our results complement the molecular evidence and, under an integrative taxonomy approach, support R. cherrii as a different species from R. mexicanus.

Parallel phenotypic divergence is the independent differentiation between phenotypes of the same lineage or species occupying ecologically similar environments in different populations. We tested in the Antarctic limpet Nacella concinna the extent of parallel morphological divergence in littoral and sublittoral ecotypes throughout its distribution range. These ecotypes differ in morphological, behavioural and physiological characteristics. We studied the lateral and dorsal outlines of shells and the genetic variation of the mitochondrial gene Cytochrome Oxidase subunit I from both ecotypes in 17 sample sites along more than 2,000 km. The genetic data indicate that both ecotypes belong to a single evolutionary lineage. The magnitude and direction of phenotypic variation differ between ecotypes across sample sites; completely parallel ecotype-pairs (i.e., they diverge in the same magnitude and in the same direction) were detected in 84.85% of lateral and 65.15% in dorsal view comparisons. Besides, specific traits (relative shell height, position of shell apex, and elliptical/pear-shape outline variation) showed high parallelism. We observed weak morphological covariation between the two shape shell views, indicating that distinct evolutionary forces and environmental pressures could be acting on this limpet shell shape. Our results demonstrate there is a strong parallel morphological divergence pattern in N. concinna along its distribution, making this Antarctic species a suitable model for the study of different evolutionary forces shaping the shell evolution of this limpet.

Peter B. Berendzen
Sam R. Holmes
Jeremy R. Abels
Corinthia Black

The Ozark minnow, Notropis nubilus, is a small stream fish that has a disjunct distribution in the Ozark Plateau and upper Mississippi River basin. Three reciprocally monophyletic and deeply divergent lineages have been hypothesized within the species based on molecular data. These lineages are allopatric and isolated from each other. The objective of this study was to test the hypothesis that these lineages and the disjunct population in the upper Mississippi River basin are morphologically distinct. Meristic and geometric morphometric data were used to identify and quantify morphological diversity within the Ozark minnow. Analyses of the meristic data and a principal component analysis of the morphometric data were unable to find any noticeable differences in morphology among groups. However, canonical variates analyses of the morphometric data and linear models were able to define statistically significant differences in shape. Analyses of all-individuals were able to identify shape differences between all groups. Males-only analyses were less conclusive, but there was some indication that males may be diverging more quickly than all-individuals. The detection of subtle variation in shape implies selection is not a strong factor in morphological divergence and observed differences are most likely due to morphological drift. This indicates that the lineages within the Ozark minnow are likely on the trajectory for speciation. The allopatric nature of these clades makes the Ozark minnow an interesting model for the study of morphological drift and speciation. This article is protected by copyright. All rights reserved.

Adam Cossette
Andy D. Grass
Thomas DeGuzman

To explore shape variability among crocodylian skull tables, an analysis using geometric morphometric methods is conducted with the inclusion of extant and fossil taxa. Skull tables are variable and the differences likely play a role in hydrodynamics, species recognition, and biomechanical adaptations. Comparisons of allometric change within taxa are explored revealing that adults significantly diverge from juvenile skull table morphologies in most species and these changes happen in a stereotyped way. In all analyses, adults of the smallest extant taxa plot alongside the juveniles of related taxa and heterochrony may explain the maintenance of these morphologies into adulthood. When landmarks representing the supratemporal fenestrae are included, longirostrine taxa are broadly separated from one another due to variation in the size of the supratemporal fenestrae. The hypotheses of previous studies suggesting that the size of the supratemporal fenestrae is influenced by snout length—with longer snouts corresponding to larger fenestrae—must be re‐evaluated. Although species of the crocodyloids Tomistoma and Euthecodon approach or exceed the length of the snout in gavialoids, their supratemporal fenestrae are proportionally smaller—this suggests a phylogenetic constraint in crocodyloids regardless of snout length.

Realistic mappings of genes to morphology are inherently multivariate on both sides of the equation. The importance of coordinated gene effects on morphological phenotypes is clear from the intertwining of gene actions in signaling pathways, gene regulatory networks, and developmental processes underlying the development of shape and size. Yet, current approaches tend to focus on identifying and localizing the effects of individual genes and rarely leverage the information content of high dimensional phenotypes. Here, we explicitly model the joint effects of biologically coherent collections of genes on a multivariate trait-craniofacial shape - in a sample of n = 1,145 mice from the Diversity Outbred (DO) experimental line. We use biological process gene ontology (GO) annotations to select skeletal and facial development gene sets and solve for the axis of shape variation that maximally covaries with gene set marker variation. We use our process-centered, multivariate genotype-phenotype (process MGP) approach to determine the overall contributions to craniofacial variation of genes involved in relevant processes and how variation in different processes corresponds to multivariate axes of shape variation. Further, we compare the directions of effect in phenotype space of mutations to the primary axis of shape variation associated with broader pathways within which they are thought to function. Finally, we leverage the relationship between mutational and pathway-level effects to predict phenotypic effects beyond craniofacial shape in specific mutants. We also introduce an online application which provides users the means to customize their own process-centered craniofacial shape analyses in the DO. The process-centered approach is generally applicable to any continuously varying phenotype and thus has wide-reaching implications for complex-trait genetics.

Twenty years ago, Rohlf and Marcus proclaimed that a "revolution in morphometrics" was underway, where classic analyses based on sets of linear distances were being supplanted by geometric approaches making use of the coordinates of anatomical landmarks. Since that time the field of geometric morphometrics has matured into a rich and cohesive discipline for the study of shape variation and covariation. The development of the field is identified with the Procrustes paradigm, a methodological approach to shape analysis arising from the intersection of the statistical shape theory and analytical procedures for obtaining shape variables from landmark data. In this review we describe the Procrustes paradigm and the current methodological toolkit of geometric morphometrics. We highlight some of the theoretical advances that have occurred over the past ten years since our prior review (Adams et al., 2004), what types of anatomical structures are amenable to these approaches, and how they extend the reach of geometric morphometrics to more specialized applications for addressing particular biological hypotheses. We end with a discussion of some possible areas that are fertile ground for future development in the field.

Fred Bookstein

Morphometrics, a new branch of statistics, combines tools from geometry, computer graphics and biometrics in techniques for the multivariate analysis of biological shape variation. Although medical image analysts typically prefer to represent scenes by way of curving outlines or surfaces, the most recent developments in this associated statistical methodology have emphasized the domain of landmark data: size and shape of configurations of discrete, named points in two or three dimensions. This paper introduces a combination of Procrustes analysis and thin-plate splines, the two most powerful tools of landmark-based morphometrics, for multivariate analysis of curving outlines in samples of biomedical images. The thin-plate spline is used to assign point-to-point correspondences, called semi-landmarks, between curves of similar but variable shape, while the standard algorithm for Procrustes shape averages and shape coordinates is altered to accord with the ways in which semi-landmarks formally differ from more traditional landmark loci. Subsequent multivariate statistics and visualization proceed mainly as in the landmark-based methods. The combination provides a range of complementary filters, from high pass to low pass, for effects on outline shape in grouped studies. The low-pass version is based on the spectrum of the spline, the high pass, on a familiar special case of Procrustes analysis. This hybrid method is demonstrated in a comparison of the shape of the corpus callosum from mid-sagittal sections of MRI of 25 human brains, 12 normal and 13 with schizophrenia.

Geometric Morphometrics for Biologists is an introductory textbook for a course on geometric morphometrics, written for graduate students and upper division undergraduates, covering both theory of shape analysis and methods of multivariate analysis. It is designed for students with minimal math background; taking them from the process of data collection through basic and more advanced statistical analyses. Many examples are given, beginning with simple although realistic case-studies, through examples of complex analyses requiring several different kinds of methods. The book also includes URLâs for free software and step-by-step instructions for using the software.

Chris Klingenberg

Increasingly, data on shape are analysed in combination with molecular genetic or ecological information, so that tools for geometric morphometric analysis are required. Morphometric studies most often use the arrangements of morphological landmarks as the data source and extract shape information from them by Procrustes superimposition. The MorphoJ software combines this approach with a wide range of methods for shape analysis in different biological contexts. The program offers an integrated and user-friendly environment for standard multivariate analyses such as principal components, discriminant analysis and multivariate regression as well as specialized applications including phylogenetics, quantitative genetics and analyses of modularity in shape data. MorphoJ is written in Java and versions for the Windows, Macintosh and Unix/Linux platforms are freely available from http://www.flywings.org.uk/MorphoJ_page.htm.

Colin R Goodall

Two geometrical figures, X and Y, in R<sup>K</sup>, each consisting of N landmark points, have the same shape if they differ by at most a rotation, a translation and isotropic scaling. This paper presents a model-based Procrustes approach to analysing sets of shapes. With few exceptions, the metric geometry of shape spaces is quite complicated. We develop a basic understanding through the familiar QR and singular value decompositions of multivariate analysis. The strategy underlying the use of Procrustes methods is to work directly with the N × K co-ordinate matrix, while allowing for an arbitrary similarity transformation at all stages of model formulation, estimation and inference. A Gaussian model for landmark data is defined for a single population and generalized to two-sample, analysis-of-variance and regression models. Maximum likelihood estimation is by least squares superimposition of the figures; we describe generalizations of Procrustes techniques to allow non-isotropic errors at and between landmarks. Inference is based on an N × K linear multivariate Procrustes statistic that, in a double-rotated co-ordinate system, is a simple but singular linear transformation of the errors at landmarks. However, the superimposition metric used for fitting, and the model metric, or covariance, used for testing, may not coincide. Estimates of means are consistent for many reasonable choices of superimposition metric. The estimates are efficient (maximum likelihood estimates) when the metrics coincide. F-ratio and Hotelling's T<sup>2</sup>-tests for shape differences in one- and two-sample data are derived from the distribution of the Procrustes statistic. The techniques are applied to the shapes associated with hydrocephaly and nutritional differences in young rats.

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