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\begin{document}

\title{Assessing the patterns and drivers of shape complexity in the amblypygid
pedipalp using elliptical Fourier analysis}



\author[1]{Callum McLean}%
\author[2]{Russell Garwood}%
\author[1]{Charlotte Brassey}%
\affil[1]{Manchester Metropolitan University}%
\affil[2]{The University of Manchester}%


\vspace{-1em}



  
  \date{June 02, 2024}


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\selectlanguage{english}
\begin{abstract}
Amblypygids are an arachnid order possessing a unique pair of spined
pedipalps: appendages that perform in prey capture, courtship and
contest. Pedipalp length, hypothesised to be under sexual selection,
varies markedly across amblypygid species, and pedipalp spination,
thought to reflect selection for function in prey capture, also differs
interspecifically. Differences in pedipalp shape between species may
indicate that the relative strength of selection for prey capture and
sexual selection vary across the group. However, interspecific
differences in pedipalp shape have not been quantified, due to
difficulties in identifying homologous features. For the first time, we
quantify trends in amblypygid pedipalp shape complexity. We use
elliptical Fourier analysis to quantify 2D complexity in pedipalp
outlines across eleven species and six genera. We find that complexity
significantly decreases as pedipalp length increases. This appears to be
driven by relative spine length, suggesting that a trade-off exists
between pedipalp length and spination. Furthermore, significant
female-biased sexual dimorphism in shape complexity is present in the
tibial segment of the amblypygid pedipalp. Our results provide novel
insights into the drivers of amblypygid pedipalp evolution, and suggest
that a functional trade-off between performance in prey capture and
other functions under sexual selection exist in this enigmatic
structure.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Amblypygids are a group of predatory arachnids bearing a unique pair of
raptorial pedipalps. The order comprises ca. 220 modern species
(McArthur et al., 2018). The raptorial appendages in amblypygids are
homologous to the claw-bearing limbs of scorpions and thelyphonids that
are used for prey capture in those groups, and to the limb bearing the
palpal bulb in male spiders which is used as a means of transferring
spermatophores. In common with other arachnids, the amblypygid pedipalp
performs multiple functions, most notably prey capture (Weygoldt, 2000;
Santer \& Hebets, 2009). However, recent work has also highlighted the
importance of the pedipalps in display (Chapin \& Reed-Guy, 2017),
courtship (Weygoldt, 2000; Chapin \& Hebets, 2016) and in the build-up
to contest (Fowler-Finn \& Hebets, 2006; Santer \& Hebets, 2011; Chapin,
2015). Indeed, the majority of territorial disputes are also decided via
display-based contest (Chapin \& Reed-Guy, 2017). Pedipalps are also
used in physical contest (Alexander, 1962; Weygoldt, 2000), and for
drinking and grooming (Shultz, 1999; Weygoldt, 2000).

Amblypygid pedipalp morphology is markedly different from other arachnid
orders, with palpal tibiae and femora taking an elongate and spinose
form. Pedipalps also display a high level of interspecific morphological
variation (Weygoldt, 2000). Across the group, they vary greatly in both
absolute length, and in length relative to body size. For example, adult
members of the genus \emph{Sarax} and \emph{Charinus} are characterised
by pedipalps with a combined femur and tibia length equal to
approximately one body length (Rahmadi, Harvey \& Kojima, 2010; Jocque
\& Giupponi, 2012), whilst members of \emph{Euphrynichus}
and\emph{Phrynichus} possess palps with combined femur and tibia lengths
four times that of their body length (Simon \& Fage, 1936; Weygoldt,
2000). Shape is also known to vary considerably across the group, with
the position, number, relative length and curvature of the pedipalp
spines differing markedly amongst species (Weygoldt, 2000). However,
shape diversity in the amblypygid pedipalp has been poorly quantified:
most information on shape diversity is limited to qualitative data or
simple ratios (McArthur et al., 2018; McLean et al., 2018; Weygoldt,
2000).

This historic focus on gross pedipalp size has likely restricted our
understanding of the functional ecology of these unusual limbs.
Amblypygid pedipalps, like those of many other arachnid orders, are
sexually dimorphic (Weygoldt, 2000; McArthur et al., 2018; McLean,
Garwood \& Brassey, 2018). Yet most studies of sexual dimorphism in
amblypygids have focused solely on dimorphism in pedipalp \emph{length}
, with the limited work previously directed at \emph{shape} dimorphism
being qualitative (McLean, Garwood \& Brassey, 2018). However, modern
morphometric techniques can be used to elucidate previously undocumented
shape dimorphism. For the first time, McLean et al. (2020) quantified
shape variation within the pedipalps of a single amblypygid species
using 2D geometric morphometric (GMM) analysis, and identified
significant sexual dimorphism within the spines, and relative width of
the central shaft. That study discussed the potential importance of
display-based conflict and divergent reproductive roles in driving
pedipalp sexual dimorphism (McLean et al., 2020), and highlighted the
need to quantify shape variation across the order more broadly.

That such an interspecific study of amblypygid pedipalp morphology has
not been previously undertaken is perhaps surprising. Pedipalp
morphology has long been considered diagnostic at a species level
(Weygoldt, 2000) and pedipalp-based characters have been used
extensively in the construction of morphological amblypygid phylogenies
(Garwood et al., 2017; Prendini et al., 2005; Weygoldt, 1996).
Furthermore, documented amblypygid behaviour is complex and varies
markedly across the order, incorporating diverse social dynamics,
varying degrees of territorially, differing mating strategies and
disparate feeding behaviours (Chapin and Reed-Guy, 2017). Such factors
have the potential to heavily influence the evolution of pedipalp shape.

This lack of multispecies comparisons may in part be attributed to
difficulties in defining pedipalp spine homology. Common shape analysis
methods such as GMM require the manual/semi-automatic placement of
`landmarks' upon homologous features that are readily identifiable
across all individuals in a sample. \emph{Within} a given amblypygid
taxon, spination is remarkably consistent in terms of gross pattern, and
McLean et al. (2020) therefore proceeded with manual landmarking on the
most prominent four spines. \emph{Between} species however, spination is
highly irregular, homology is difficult to determine by visual
inspection, and the toolkit of evolutionary developmental biology has
yet to be brought to bear on the genetic basis of pedipalp morphology.
Thus, any comparison of shape across the amblypygid pedipalp must avoid
assumptions of spine homology and employ non-landmark-based methods.

Recently developed tools for quantifying shape \emph{complexity} offer a
potential solution, as they do not rely on the placement of homologous
landmarks. Shape complexity is distinct from the metrics of shape
variation calculated by GMM, and can broadly be defined as the number of
`simple shapes' required to create a more complex shape, and the
self-similarity of those composite parts (Chambers et al., 2018;
Gardiner, Behnsen \& Brassey, 2018).

Recent research has deployed shape complexity metrics to investigate a
number of biological systems. For instance, tooth complexity has been
related to dietary differences in primates and reptiles (Prufrock, Boyer
\& Silcox, 2016; Melstrom, 2017). Shape complexity has also been used on
a number of invertebrate systems including genitalia of water striders
(Rowe \& Arnqvist, 2012), and \emph{Drosophila} wings (Ray et al.,
2016). Furthermore, complexity has been linked with a number of
important biological concepts. For example, status badge size has been
correlated with territory shape complexity in birds, suggesting it can
be a good measure of territorial quality (Roberts \& King, 2019), and
diversity within spider habitats also correlates with shape complexity
(Baldissera, Rodrigues \& Hartz, 2012).

Here we apply a suite of tools, including elliptical Fourier analysis,
to estimate the shape complexity of the amblypygid pedipalp. This
facilitates, for the first time, a quantitative comparison of
interspecific pedipalp shape across this important order.

\textbf{Aims and Hypotheses}

We aim to establish a methodology for quantifying amblypygid pedipalp
complexity in the absence of homologous landmarks, and to characterise
the patterns in gross shape complexity across the group. Our goal is to
understand its evolutionary drivers. Specifically, we hypothesise:

H\textsubscript{1} - Given the pedipalps' previous roles as taxonomic
characters, we expect that species can be statistically differentiated
from one another on the basis of pedipalp outline shape.

H\textsubscript{2} - Across species, shape complexity will decrease with
relative pedipalp length (normalised to body size), trading off shape
complexity for segment elongation. Previous GMM analysis
within\emph{Damon variegatus} found relative spine length to decrease
with increasing pedipalp length (McLean et al., 2020), yet the degree to
which this \emph{intraspecific} pattern in static allometry holds true
across the order is unclear.

H\textsubscript{3} - Females will possess higher palpal complexity than
males. This is likewise informed by McLean et al. (2020), in which
relative spine length was found to be significantly higher in
female\emph{Damon variegatus} than males.

\textbf{Methods}

\textbf{Data collection and preparation}

We used a sample of individuals from 11 species to investigate shape
complexity in the amblypygid pedipalp. This incorporated 82 individuals
in the tibia analysis, and 77 in the femur analysis. Disparity in the
number of specimens between analyses resulted from the exclusion of
individuals with damaged pedipalp segments. Species were chosen to
represent a diversity of pedipalp lengths and morphotypes, and cover a
large taxonomic range, spanning two of the five amblypygid families and
encompassing six out of seventeen amblypygid genera. Specimens were
placed in to species by taxonomists based on morphology. The species
chosen also span a wide geographic range, originating from South and
Central America, Africa and Asia. Multiple replicates of males and
females were collected for each species to facilitate comparisons
between the sexes (see Supplementary Material S1). All specimens were
held in spirit at the Royal Central African Museum (Tervuren, Belgium),
the Natural History Museum (London, England), The American Museum of
Natural History (New York, USA) or the Natural History Museum in Vienna,
Austria.

Photographs were taken with a Canon EOS D750 attached to a copy stand to
ensure the camera remained perpendicular to the specimens. Photographs
of smaller specimens were taken with a 60 mm macro lens. Pedipalps were
not detached from specimens, but pedipalps were orientated in a standard
position parallel to the camera lens. The pedipalps occupied as much of
the camera field of view as possible in order to minimise differences in
relative image resolution between species. Binarised outlines were
subsequently obtained from photographs by manually tracing the contour
of the dorsal surface of the femur and tibia segments in Inkscape.
Outlines were then converted to JPEG images in preparation for
morphometric analysis.

Linear metrics of pedipalp length and overall body length (taken as a
proxy for overall body size) were taken using digital callipers with a
measurement precision of 0.01 mm. Relative pedipalp length was defined
as pedipalp tibia length divided by body length. Blind repeated measures
were taken on a set of \emph{Damon variegatus} of varying size, the mean
measurement error was 2.80\% (SD--1.46\%, 10 specimens). All specimens
were sexed by lifting the genital operculum in order to determine the
presence/absence of the spermatophore organ. Any individual listed as
juvenile or immature was excluded from the analysis. Wherever possible,
linear measurements and photographs were collected from the right
pedipalp. However, in instances where the right pedipalp was damaged,
the left pedipalp was mirrored and used instead.

\textbf{Morphometric analyses}

Due to the current lack of data regarding pedipalp spine homology across
amblypygid species, here we set out to quantify geometric complexity
using non-landmark based morphometric methods. We thus use elliptical
Fourier analysis on binarised outlines of amblypygid pedipalps. All
methods of measuring 2D shape complexity were implemented using the R
package `Momocs' (Bonhomme et al., 2014).

\textbf{Elliptical Fourier Analysis}

Pedipalp outlines were analysed using elliptical Fourier analysis (EFA).
EFA uses the principle of conventional Fourier analysis, which states
that the \emph{xy} coordinates of a circle or simple ellipse can be
described by a set of sine and cosine waves referred to as harmonics.
During the analysis, complex shapes are described by a series of
`epicycles', where a point moves around an ellipse of harmonic
\emph{n}which in turn moves around the perimeter of a larger ellipse of
harmonic\emph{n} -1 and so on, creating a series of moving ellipses
which `draw' out the prospective shape. A shape traced by a number of
moving ellipses can thus be described by a series of sine and cosine
waves, which are themselves described by a series of harmonic
coefficients. Each harmonic is essentially layered on top of each other,
with each harmonic describing a further level of shape complexity. As
further harmonics are added to the model, the harmonics produce an
outline that is closer to the original shape and captures more of its
complexity, with a hypothetical harmonic model containing infinite
harmonics drawing out an exact replica of the original shape.

Binarised pedipalp images were imported as JPEGs into R, and were
subsequently converted into a series of 10000 equally spaced
\emph{xy}coordinates representing each outline. Outlines were rotated
such that their principal axes aligned with the global x-axis, and then
centred with their centroid at the global origin (0,0). The effect of
scale was also removed from the analysis by normalising all outlines to
centroid size, the square root of the sum of squared distances of all
the outline points f an object from their centroid or central point. A
Procrustes fit was also required to align shapes. This method of
alignment is often employed in studies that use elliptical Fourier
analysis to quantify shapes with few major protrusions such as orca
fins, human crania and posterior lobes of \emph{Drosophila} (Friess \&
Baylac, 2003; Takahara \& Takahashi, 2015; Emmons et al., 2019). Despite
a workflow intended to avoid alignment via landmarks (due the problems
of homology), pedipalps with few large spines or protrusions aligned
solely through principal axes often appeared flipped about their long
axis relative to other pedipalps, this is phenomenon has been previously
documented for shape with high aspect ratio shapes (Bonhomme et al.,
2014). To overcome this issue, three landmarks were assigned to the
femoral segments, and four to the tibia on the proximal and distal end
points of the pedipalp. These landmark points did not include pedipalp
spines and thus did not encounter the issue of homology (see
Supplementary Material S3 for location of landmarks). The Procrustes fit
between these numbered landmarks prevented pedipalps from flipping.

EFA was carried out using 32 harmonics, as this number was found to
describe 99.9\% of shape complexity of the original outline across the
sample, in both tibia and femur segments. From the resulting harmonic
fits, we calculated shape complexity. This was achieved by comparing
perimeters, either between EFA shapes of contrasting harmonics.
Comparing boundary measures, such as perimeter, is a tenet of many
methods of estimating shape complexity (Chambers et al., 2018). The
first metric calculated is a low perimeter ratio that here we term
`gross complexity'. This is calculated by dividing the perimeter of the
outline created by fitting a complex 20\textsuperscript{th} harmonic
model, by the perimeter of a simple 4\textsuperscript{th} harmonic model
(see Figure 1), such that high values indicate high levels of gross
complexity. Comparing 4\textsuperscript{th} and
20\textsuperscript{th}harmonic fit models has previously been used to
quantify overall shape complexity in studies of other biological
structures (Rowe \& Arnqvist, 2012).

\textbf{Data Analysis}

All data analysis was carried out in R. A principal component analysis
was conducted on all harmonic coefficients derived from the Fourier
analysis, in order to characterise intraspecific and interspecific
variation in pedipalp shape complexity. The resulting PC scores were
subject to clustering analysis in order to determine the degree to which
species may be correctly identified on the basis of Fourier outlines. PC
scores were scaled to have the same mean and standard deviation before
being fed into the clustering algorithm. An unsupervised k-means
clustering was applied; k-means was instructed to split the dataset into
11 clusters, the same as the number of species, in order to determine if
clustering would split down species lines. A pairwise MANOVA was also
conducted in `Momocs'.

To test the relationship between pedipalp shape complexity and length,
species-average values of `gross complexity' were calculated. Due to
uncertainty in amblypgyid phylogeny, ordinary least squares regression
was then carried out between measures of complexity and pedipalp length
for each segment individually. Pedipalp tibia length is considered a
standard metric of pedipalp length and is used in multiple studies
(Weygoldt, 2000; Prendini, Weygoldt \& Wheeler, 2005; McArthur et al.,
2018). As such, this was the measure of pedipalp length used herein. A
Shapiro-Wilk test confirmed that shape complexity metrics for both
segments followed a normal distribution.

Tests for sexual dimorphism in shape complexity were carried out using a
nested ANOVA between measures of complexity and sex, with species
included as a random effect. Shapiro-Wilk tests confirmed shape
complexity in both metrics was normally distributed within species, and
species standard deviations were very similar in all species.

A paired Wilcoxon rank-sum test was used to investigate differences in
shape complexity between segments, as data were non-normally
distributed. Specimens that did not appear in both the tibia and femur
dataset were excluded from this analysis, resulting in a total sample
size of 75.

\textbf{Results}

\textbf{Evaluation of Shape Complexity Metrics}

Our first task was to assess what component of shape was driving
increased complexity scores across the dataset. We define `complexity'
as the difference between the 4\textsuperscript{th} and
20\textsuperscript{th} harmonic model. On average across all taxa, the
4\textsuperscript{th} harmonic model describes 87.9\% of the complexity
of the original femur shape and 85.5\% in the tibia, while the
20\textsuperscript{th} harmonic model describes around 99.7\% of the
complexity of the original segment shape both segments. Thus, gross
complexity comprises approximately 14\% of the total shape complexity.

On a qualitative level, the main visual difference between the
4\textsuperscript{th} and the 20\textsuperscript{th} harmonic outlines
appears to be the presence of large spines in the
20\textsuperscript{th}harmonic outline. This would suggest that gross
complexity is heavily influenced by these `major' spines. Indeed,
initial inspection of boxplots suggests that species that are
characterised by larger spines relative to the central pedipalp shaft
have high gross complexity scores (see Figure 2). Observationally, the
total number of large spines also appears to influence gross complexity.
This is best illustrated in the tibial segment, in which species with
relatively long but few large spines, such as \emph{H.longicornis} and
\emph{P.whitei} , have lower gross complexity scores than other species
with a larger number of `major' spines. The tibia segment was found to
have a statically higher complexity (Wilcoxon, p = \textless{}0.001, v =
2849) than the femur.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1 -- Outlines created by fitting Fourier models of varying
harmonic order in the femur segment of \emph{D.diadema}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2 -- Plot of gross complexity against species in the tibia
segment. Species arranged in order of absolute pedipalp length (mm):
short pedipalps, left; long pedipalps, right. Notably, species with
longer spines relative to the central pedipalp shaft have higher gross
complexity scores. The graph also shows that gross complexity decreases
with increasing pedipalp length.

\textbf{Species clustering}

A PCA of harmonic coefficients was carried out in order to visualise
intra- and interspecific shape variation and generate PC scores to be
used in species clustering (Figure 4). The PCA appears to show a higher
degree of intraspecific than interspecific differences in both segments.
Furthermore, there was marked overlap between species in both segments,
this was particular marked in the femur where species within the same
family often overlapped. In both segments, PC1 appears to correlate to
pedipalp elongation, where PC2 seems to be related to the relative
position of the longest spines and the length of those spines in the
tibia and femur. PC1 accounted for just over half of observed variation
in both segments (femur = 56\%, tibia = 59.2\%) and mainly separated
Phrynichidae species (\emph{D.diadema} , \emph{D.medius}
and\emph{Ph.exophamus} ) from other species. PC2 contributed roughly
15\% of variation in both the femur and tibia. PC's 1 through 10
accounted for just over 95\% of total observed variation in both
segments, thus PC1-PC10 were carried forward into the species clustering
analysis.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3 - PCA of harmonic coefficients, black outlines visualise
outlines of representative pedipalps, grey outline are hypothetical
morphs (calculated at the 20\textsuperscript{th} harmonic) from extreme
position on the PC axes, convex hulls represent the intraspecific
variation within species. Exo = \emph{Phrynichus exophalmus} , dia
=\emph{Damon diadema} , med = \emph{Damon medius} , lon
=\emph{Heterophrynus longicornis} , whi = \emph{Phrynus whitei} , cor
=\emph{Acanthophrynus coronatus} , ger = \emph{Phyrnus gervasii} , vir
=\emph{Paraphrynus viridiceps} , lop = \emph{Phrynus longipies} , azt
=\emph{Paraphrynus aztecus} , wil = \emph{Paraphrynus williamsi}

Species clustering using k-means and MANOVA methods provided markedly
different results. In the femur, unsupervised k-means clustering could
only classify \emph{Ph. exophalmus} with 100\% accuracy, placing all
specimens of this species within the same cluster alongside no
additional species. K-means also placed the two \emph{Damon} species
together within a discrete genus cluster which contained no other
species, but was unable to differentiate between the two species.
K-means performed poorly at correctly identifying all other species (see
Table 1). In contrast, MANOVA found statistically significant
differences in the pairwise comparisons between most species in the
femur (see Table 2). However, like k-means clustering, MANOVA was unable
to delimitate between species within the genera \emph{Paraphrynus} and

\emph{Damon.}\selectlanguage{english}
\begin{longtable}[]{@{}llllllllllll@{}}
\toprule
~Cluster & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11\tabularnewline
\emph{Pa. aztecus} & \emph{} & \emph{28.6\%} & \emph{} & \emph{} &
\emph{14.3\%} & \emph{42.9\%} & \emph{} & \emph{} & \emph{} &
\emph{14.3\%} & \emph{}\tabularnewline
\emph{A. coronauts} & \emph{} & \emph{} & \emph{85.7\%} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{14.3\%} &
\emph{}\tabularnewline
\emph{D. diadema} & \emph{100\%} & \emph{} & \emph{} & \emph{} & \emph{}
& \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\emph{Ph. exophalmus} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{}
& \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{100\%}\tabularnewline
\emph{P. gervasii} & \emph{} & \emph{} & \emph{} & \emph{16.7\%} &
\emph{16.7\%} & \emph{} & \emph{} & \emph{16.7\%} & \emph{50.0\%} &
\emph{} & \emph{}\tabularnewline
\emph{H. longicornis} & \emph{} & \emph{} & \emph{} & \emph{50.0\%} &
\emph{12.5\%} & \emph{} & \emph{25.0\%} & \emph{12.5\%} & \emph{} &
\emph{} & \emph{}\tabularnewline
\emph{P. longipies} & \emph{} & \emph{} & \emph{57.1\%} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{42.9\%} &
\emph{}\tabularnewline
\emph{D. medius} & \emph{100\%} & \emph{} & \emph{} & \emph{} & \emph{}
& \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\emph{Pa. viridiceps} & \emph{} & \emph{20.0\%} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} & \emph{80.0\%} & \emph{} &
\emph{}\tabularnewline
\emph{P. whitei} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{100\%} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\emph{Pa. williamsi} & \emph{} & \emph{57.1\%} & \emph{} & \emph{} &
\emph{14.3\%} & \emph{28.6\%} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\bottomrule
\end{longtable}

Table 1 - Results of k-means clustering applied to femoral segment.
K-means tables contain the percentage of specimens that fall into each
cluster. Columns represent cluster defined by k-means, rows represent
species.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllll@{}}
\toprule
& \emph{A.coronauts} & \emph{D.diadema} & \emph{Ph.exophalmus} &
\emph{P.gervasii} & \emph{H.longicornis} & \emph{P.longipies} &
\emph{D.medius} & \emph{Pa.viridiceps} & \emph{P.whitei} &
\emph{Pa.williamsi}\tabularnewline
\emph{Pa.aztecus} & \emph{\textless{}0.05} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & N.S. & \emph{\textless{}0.001} &
N.S.\tabularnewline
\emph{A.coronauts} & \emph{} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & \emph{\textless{}0.01}\tabularnewline
\emph{D.diadema} & \emph{} & \emph{} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & N.S. & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001}\tabularnewline
\emph{Ph.exophalmus} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001}\tabularnewline
\emph{P.gervasii} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.05} &
\emph{\textless{}0.001} & \emph{\textless{}0.01}\tabularnewline
\emph{H.longicornis} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001}\tabularnewline
\emph{P.longipies} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & \emph{\textless{}0.05}\tabularnewline
\emph{D.medius} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001}\tabularnewline
\emph{Pa.viridiceps} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{\textless{}0.001} &
N.S.\tabularnewline
\emph{P.whitei} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001}\tabularnewline
\bottomrule
\end{longtable}

Table 2 --Results of pairwise MANOVA tests between species applied to
the femoral segment. MANOVA tables contain the magnitude p-values for
pairwise comparison, species comparisons that show no significant
differences are highlighted in bold.

K-means performed similarly poorly in the tibial segment (Supplementary
Material S2). Only \emph{P. gervasii} was correctly classified by
k-means, and the majority of clusters contained multiple species. MANOVA
again identified many statistically significant differences in the
pairwise comparison between species. However, no differences were found
between \emph{Pa. viridiceps} vs. \emph{Pa. aztecus} , and \emph{D.
diadema} vs. \emph{D. medius} .

\textbf{Relationship between shape complexity and absolute pedipalp
length}

Statistically significant negative relationships between pedipalp length
and size-independent shape complexity were identified in both tibial and
femoral segments (Table 3).\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Segment & a & b & R\textsuperscript{2} & F-statistic & P\tabularnewline
\midrule
\endhead
Tibia & 1.991 & -0.668 & 0.667 & 21.03 & 0.001\tabularnewline
Femur & 1.484 & -0.316 & 0.544 & 12.95 & 0.006\tabularnewline
\bottomrule
\end{longtable}

Table 3 -- Results of OLS analysis comparing pedipalp length to species
mean complexity.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4 -- Relationship between measure of shape complexity and
pedipalp length, in the tibia and femur segments. Points represent
species means, error bars show standard error around the mean.

\textbf{Sexual differences in shape complexity}

Complexity was statistically higher in the female tibia (ANOVA, p =
0.037, F = 13.89). However, no statistically significant differences
were found in the femur.

\textbf{Discussion}

The comparative analysis presented here documents both intra- and
interspecific differences in shape complexity within the amblypygid
pedipalp. A principal component analysis of Fourier harmonics shows
frequent overlap between species, with intraspecific shape variation
often exceeding shape differences between species, even in the
relatively low numbers of individuals representing each taxon in this
study. MANOVA does identify statistically significant pairwise shape
differences between most species. However, unsupervised k-means
struggles to define species clusters accurately. Of note, the
two\emph{Damon} species, \emph{D. diadema} and \emph{D. medius} , could
not be separated on the basis of MANOVA, k-means or within the PCA
morphospace in either segment. Likewise, some species
of\emph{Paraphrynus} could not be differentiated on the basis of shape
complexity in either segment. As such, our results do not support
Hypothesis 1.

This result has potential implications for species recognition using
pedipalp characters. MANOVA, a `supervised' method which knows which
specimens belong to each species \emph{a priori} , could define
differences between species. However, the unsupervised k-means methods,
which has no prior knowledge of which species specimens belong to, could
not. K-means is arguably a better analogue for the placement of a
specimen within a species, as a taxonomist, like the k-means algorithm,
would have no prior knowledge of specimen's placement within a species.
Notably, previous studies have identified species of \emph{Damon}
and\emph{Paraphyrnus} partially on the basis of the relative length of
spines on the femur and tibia pedipalp segments (Weygoldt, 2000;
Prendini, Weygoldt \& Wheeler, 2005; Joya \& de Armas, 2012). Although
our results do not invalidate the use of any specific pedipalp tibia and
femur characters to define species (as our analysis investigates overall
pedipalp shape), we do urge caution when differentiating between closely
related species using pedipalp traits.

In support of Hypothesis 2, a significant negative relationship between
complexity and pedipalp length was identified in both segments. Visual
inspection of Fourier outlines suggests that complexity predominantly
reflects the relative length of major pedipalp spines (Figure 2).
Interestingly, a similar pattern was revealed using GMM in \emph{D.
variegatus} , with longer pedipalps having shorter spines. Longer
amblypygid pedipalps are therefore found to have relatively shorter
`major' spines once normalised to centroid size. Previous work has
demonstrated the importance of display in the evolution of pedipalp
morphology. Roughly, 80\% of conflicts in \emph{P. longipes} are decided
via display in the favour of the individual with longer pedipalps
(Chapin \& Reed-Guy, 2017). Pedipalp display has also been observed in
territorial contests in a number of amblypygid species (Fowler-Finn \&
Hebets, 2006; Porto \& Peixoto, 2013; Chapin \& Hill-Lindsay, 2016) and
during the first stages of courtship across the group (Weygoldt, 2000;
Chapin \& Hebets, 2016). This suggests that amblypygid pedipalps are
likely under the influence of sexual selection via mate choice, and that
resource holding potential may be correlated with pedipalp length.

It may therefore be possible that a trade-off between pedipalp length
and complexity exists, with some species taking a less complex form,
with relatively shorter spines, allowing for increased pedipalp length,
developing under the pressures of sexual selection and contest, to be
achieved at lower developmental cost. Hypothetically, a less complex
form with shorter spines may be less energetically costly to produce per
unit length, which may allow individuals to achieve longer pedipalps at
lower energetic cost, though as yet we know nothing of genetics of
development in amblypygids, and such inferences are therefore
limited\textbf{.}

There is some evidence for structures becoming less complex with
increasing size within arachnids, although little is known about
interspecific trends of shape complexity in arachnids. For example,
cheliceral dentition is known to be more pronounced in juveniles and
relatively decreased in the large chelicerae of adults (Solifugae),
though this may in part be a function of cheliceral wear (Bird, 2015).
Some pedipalp spines also appear reduced in male thelyphonids with large
pedipalps (Rajashekhar \& Bali, 1982). However, it is often the case
that structures under the influence of sexual selection are larger and
more complex in arachnids. For example, male spider legs that are used
in courtship display are longer than female conspecifics and often
possess elaborations such as ridges of setae (Peckham \& Peckham, 1889;
Kronestedt, 1990; Girard \& Endler, 2014). Furthermore, the fourth legs
of male opiliones, used in male-male contest, are also longer and have
larger elaborated coxal apophyses not seen in females (Willemart et al.,
2009; da Silva Fernandes \& Willemart, 2014). Thus, though a trade-off
may be possible, evidence from other arachnids provides mixed support.
However, it must be stressed that these examples are all intraspecific
and thus may not be a good analogue for the interspecific trends we
report in this work.

Another possibility is that that spine length is constrained by
selective regimes or developmental factors, meaning spines have simply
remained at a similar absolute size across species. In this case,
species with longer pedipalps would have relatively shorter spines. For
example, spine length could be limited by developmental constraints
relative to pedipalp length. Additionally, it is possible that
absolutely longer spines may provide limited additional functional
benefits to prey capture, and are not important in display-based
contest, meaning there is little advantage to spine length increasing
with isometry relative to pedipalp length. Pedipalp spines are thought
to primarily function in prey capture, with a number of species forming
pedipalp `catching baskets', which are hypothesised to help capture and
secure prey items. Little is known about amblypygid diets, but they are
thought to be largely composed of primary consumer arthropods,
especially of the orders Orthoptera and Blattodea (Chapin \& Hebets,
2016). If the primary function of spines is indeed in prey capture,
spine size may scale more closely with prey size than pedipalp size.
Therefore, should prey size remain similar or equal across the group,
spine size may also remain similar across species leading to relatively
smaller spines in species that have attained longer pedipalps due to
pressures of sexual selection and contest. However, this hypothesis can
only be properly investigated by addressing the current paucity in data
related to diet in amblypygids.

An analogue to the palpal form in Amblypygi is found in scorpion
pedipalp chelae, which increase in size at rates much lower than
isometry with relation to body size (Van der Meijden, Herrel \& Summers,
2010). This may be because species with vastly different body sizes feed
on similarly sized prey (Polis \& McCormick, 1986), suggesting there is
little added benefit to larger species producing equivalently sized
chelae. If a similar overlap in prey size exists across amblypygid
species, spines (which are hypothetically under the most direct
selection for prey capture) may also scale at rates lower than isometry
relative to pedipalp length. More work is needed into amblypygid life
history and social dynamics to determine the relative importance of
sexual selection, selection via territorial contest, and natural
selection via prey capture.

As part of this study, sexual shape dimorphism was quantified across
amblypygids for the first time. Significant sexual dimorphism in shape
complexity is identified in the amblypygid pedipalp tibia, with female
tibiae found to be characterised by greater complexity than their male
counterparts. As previously discussed, complexity appears to be
influenced by the length of the major spines, which are relatively
larger in the female tibia. This may be due to the increased length of
the male pedipalp, which develops under the pressure of sexual
selection. A similar pattern has already been identified using GMM
analysis of the pedipalps of \emph{D. variegatus} , with the observed
sexual shape dimorphism being thought to arise due to female optimising
for prey capture while males optimise for pedipalp display (McLean,
Garwood \& Brassey, 2020). The occurrence of this form of dimorphism in
numerous species across the group may suggest that these driving forces
behind sexual dimorphism in size and complexity are pervasive across the
group. Interestingly, contest and courtship both involve display and are
very similar in behaviour across amblypygid species, suggesting this
could be a common selection pressure (Weygoldt, 2000). However, more
work into amblypygid life history is needed to fully understand the
drivers of pedipalp morphology.

\textbf{Conclusion}

In conclusion, our results highlight the importance of considering
intra- and interspecific variation in terms of shape, by highlighting a
number of previously undocumented shape relationships across amblypygid
pedipalps. Here we find that within-species shape complexity variation
in pedipalps can occasionally exceed differences between species, and
thus caution needs to be taken when defining species on the basis of
pedipalp characters. We also find that gross complexity decreases with
increasing pedipalp length, potentially uncovering a trade-off between
investment in pedipalp total length (for use in sexual selection and
territorial contest) and pedipalp spine length (primarily for use in
prey capture). Sexual dimorphism in gross complexity is also present in
the tibia and follows similar patterns seen intraspecifically in other
studies, once again highlighting the pressures of display based contest
and courtship, and trophic niche partitioning. Future studies that look
to address the paucity of data on amblypygid life history, ecology and
social dynamics will be valuable in further understanding the functional
morphology in this unique system.

\textbf{Acknowledgements}

We would like to thank the staff of the Royal Central African Museum,
Tervuren, Belgium; The Natural History Museum, London, United Kingdom;
The American Musuem of Natural History, New York, USA; The Natural
History Museum in Vienna, Austria. Specifically, we thank Didier van der
Spiegel, Christoph Allard, Rudy Jocque, Jan Beccaloni, Pio Colmenares,
Lorenzo Prendini, Christoph Horweg and Michael Seiter.

\textbf{Funding}

This work was supported by the American Arachnological Society

\textbf{Data statement}

Pedipalp photographs, raw binarized outlines and body and pedipalp
lengths of all specimens used in this study will be made available via
Figshare at 10.6084/m9.figshare.c.5289733

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\textbf{Supplementary Material 1}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
& Femur (n) & Femur (n) & Tibia (n) & Tibia (n)\tabularnewline
Species & F & M & F & M\tabularnewline
\emph{A. coronatus} & 4 & 3 & 4 & 3\tabularnewline
\emph{D. diadmea} & 4 & 4 & 4 & 4\tabularnewline
\emph{D. medius} & 4 & 4 & 4 & 4\tabularnewline
\emph{H. longicornis} & 4 & 4 & 4 & 4\tabularnewline
\emph{Pa. aztecus} & 4 & 3 & 4 & 3\tabularnewline
\emph{Pa. viridiceps} & 3 & 2 & 3 & 3\tabularnewline
\emph{Pa. williamsi} & 3 & 4 & 4 & 4\tabularnewline
\emph{P. gervasii} & 3 & 3 & 3 & 3\tabularnewline
\emph{P. longipies} & 4 & 3 & 4 & 4\tabularnewline
\emph{P. whitei} & 4 & 4 & 4 & 4\tabularnewline
\emph{Ph. exophalmus} & 2 & 4 & 4 & 4\tabularnewline
\bottomrule
\end{longtable}

S1 -- Sample sizes of the number of male and female individuals used in
the analysis of the femur and tibia segments.

\textbf{Supplementary Material 2 -- Manova and K-means results for tibia
segment}\selectlanguage{english}
\begin{longtable}[]{@{}llllllllllll@{}}
\toprule
Cluster & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11\tabularnewline
\emph{Pa.aztecus} & \emph{} & \emph{} & \emph{} & \emph{42.9\%} &
\emph{42.9\%} & \emph{14.3\%} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\emph{A.coronauts} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{85.7\%} & \emph{} & \emph{14.3\%} & \emph{} &
\emph{}\tabularnewline
\emph{D.diadema} & \emph{} & \emph{50.0\%} & \emph{} & \emph{} & \emph{}
& \emph{} & \emph{} & \emph{} & \emph{50.0\%} & \emph{} &
\emph{}\tabularnewline
\emph{Ph.exophalmus} & \emph{} & \emph{100\%} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\emph{P.gervasii} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{100\%} & \emph{} & \emph{} &
\emph{}\tabularnewline
\emph{H.longicornis} & \emph{62.5\%} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{37.5\%} &
\emph{}\tabularnewline
\emph{P.longipies} & \emph{} & \emph{} & \emph{25.0\%} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{50.0\%} &
\emph{25.0\%}\tabularnewline
\emph{D.medius} & \emph{} & \emph{87.5\%} & \emph{} & \emph{} & \emph{}
& \emph{} & \emph{} & \emph{} & \emph{12.5\%} & \emph{} &
\emph{}\tabularnewline
\emph{Pa.viridiceps} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{33.3\%} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{66.7\%}\tabularnewline
\emph{P.whitei} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{100\%} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\emph{Pa.williamsi} & \emph{} & \emph{} & \emph{} & \emph{75.0\%} &
\emph{25.0\%} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{}\tabularnewline
\bottomrule
\end{longtable}

S2a - Results of k-means clustering applied to tibial segment. K-means
tables contain the percentage of specimens that fall into each cluster.
Columns represent clusters defined by K-means, rows represent species.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllll@{}}
\toprule
& \emph{A.coronauts} & \emph{D.diadema} & \emph{Ph.exophalmus} &
\emph{P.gervasii} & \emph{H.longicornis} & \emph{P.longipies} &
\emph{D.medius} & \emph{Pa.viridiceps} & \emph{P.whitei} &
\emph{Pa.williamsi}\tabularnewline
\emph{Pa.aztecus} & \emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.05} &
\emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & N.S. & \emph{\textless{}0.001} &
\emph{\textless{}0.001}\tabularnewline
\emph{A.coronauts} & \emph{} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001}\tabularnewline
\emph{D.diadema} & \emph{} & \emph{} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & N.S. & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001}\tabularnewline
\emph{Ph.exophalmus} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001}\tabularnewline
\emph{P.gervasii} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & \emph{\textless{}0.01} &
\emph{\textless{}0.001} & \emph{\textless{}0.001}\tabularnewline
\emph{H.longicornis} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001}\tabularnewline
\emph{P.longipies} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001} & \emph{\textless{}0.001}\tabularnewline
\emph{D.medius} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{\textless{}0.001} & \emph{\textless{}0.001} &
\emph{\textless{}0.001}\tabularnewline
\emph{Pa.viridiceps} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{\textless{}0.01} &
\emph{\textless{}0.01}\tabularnewline
\emph{P.whitei} & \emph{} & \emph{} & \emph{} & \emph{} & \emph{} &
\emph{} & \emph{} & \emph{} & \emph{} &
\emph{\textless{}0.001}\tabularnewline
\bottomrule
\end{longtable}

S2b- Results of pairwise MANOVA tests between species applied to tibial
segment. MANOVA tables contain the magnitude p-values for pairwise
comparison, species comparisons that show no significant differences are
highlighted in bold.

Supplementary Material 3 -- Landmark positions for tibia and femur
segment\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

S3a -- Positions of tibia landmarks. Landmarks were placed in 3
positions to aid alignment. Landmarks were placed in the following
locations 1.) Articulation point between femur and tibia, 2.)
Articulation point between tibia and tarsus, 3.) Inflection point at end
of pedipalp central shaft. Specimen photographs were consulted to aid
landmark placement where necessary.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

S3b -- Positions of femur landmarks. Landmarks were placed in 4
positions to aid alignment. Landmarks were placed in the following
locations 1.) Proximal femur end inflection point, 2.) Distal femur end
inflection point, 3.) Articulation point between femur and tibia, 4.)
Articulation between femur and trochanter. Specimen photographs were
consulted to aid landmark placement where necessary.

\selectlanguage{english}
\FloatBarrier
\end{document}

