# A morphometric dive into fish diversity

Florain Caillon, Vincent Bonhomme, Christian Möllmann, Romain Frelat

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Florain Caillon, Vincent Bonhomme, Christian Möllmann, Romain Frelat. A morphometric dive into fish diversity. Ecosphere, 2018, 9 (5), pp.e02220. 10.1002/ecs2.2220. hal-03142807

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# A morphometric dive into fish diversity

FLORIAN CAILLON,<fnref n="1" /> VINCENT BONHOMME,<fnref n="2" /> CHRISTIAN MÖLLMANN,<fnref n="1" /> AND ROMAIN FRELAT ID<fnref n="1" />,†

**Citation:** Caillon, F., V. Bonhomme, C. Möllmann, and R. Frelat. 2018. A morphometric dive into fish diversity. Ecosphere 9(5):e02220. 10.1002/ecs2.2220

**Abstract.** Trait-based approaches are increasingly popular in ecology to describe communities and their responses to natural or anthropogenic changes. Morphology is an integrative trait that combines functional and evolutionary information. However, the objective and quantitative description of the morphological diversity is quite challenging. Modern morphometrics encompass an array of mathematical approaches that turn shapes into quantitative variables. For models with no or only a few homologous points, outline analysis (e.g., elliptical Fourier transform) converts the outline geometry into quantitative variables, which can be used in the multivariate framework. The elliptical Fourier transform here describes the shape of 85 fish species found in the North Sea. This study shows that the main component of morphological diversity in the North sea is the elongation and development of dorsal, pelvic, and caudal fins. The spatial distribution of morphological diversity decreases along a latitudinal gradient, with higher diversity in the southern part of the study area. Compared to species diversity, our results indicate that environmental conditions filter morphological traits in the northern North Sea. Outline analysis is a powerful approach to provide an objective description of fish morphology and to improve our understanding of the diversity of large marine ecosystems.

**Key words:** elliptical Fourier transform; fish diversity; morphological traits; North Sea; outline analysis.

**Received** 23 March 2018; accepted 6 April 2018. Corresponding Editor: Tobias van Kooten.

**Copyright:** © 2018 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

† **E-mail:** romain.frelat@uni-hamburg.de

## INTRODUCTION

Trait-based approaches are increasingly popular in ecology to describe communities and their responses to natural or anthropogenic changes. Morphology is an integrative trait that combines functional and evolutionary information. However, the objective and quantitative description of the morphological diversity is quite challenging. Modern morphometrics encompass an array of mathematical approaches that turn shapes into quantitative variables. For models with no or only a few homologous points, outline analysis (e.g., elliptical Fourier transform) converts the outline geometry into quantitative variables, which can be used in the multivariate framework. The elliptical Fourier transform here describes the shape of 85 fish species found in the North Sea. This study shows that the main component of morphological diversity in the North sea is the elongation and development of dorsal, pelvic, and caudal fins. The spatial distribution of morphological diversity decreases along a latitudinal gradient, with higher diversity in the southern part of the study area. Compared to species diversity, our results indicate that environmental conditions filter morphological traits in the northern North Sea. Outline analysis is a powerful approach to provide an objective description of fish morphology and to improve our understanding of the diversity of large marine ecosystems.

information (Wainwright and Reilly 1994). The high inertial and viscous drag of water (e.g., compared to air) is a major selection pressure on the shape of marine organisms. However, the huge morphological diversity of fishes has often been described subjectively and qualitatively (Pecuchet et al. 2016, Froese and Pauly 2017). But trait-based approaches favor quantitative traits that are considered more practical, objective, and informative than their qualitative counterparts (McGill et al. 2006).

The quantitative description of shapes has long been challenging. Morphometrics, the statistical description of shapes, now distinguishes between traditional and modern morphometrics (Rohlf 1990). Traditional morphometrics rely

<footnote n="1">¹Institute for Marine Ecosystem and Fisheries Science, Center for Earth System Research and Sustainability (CEN), University of Hamburg, Große Elbstraße 133, 22767 Hamburg, Germany</footnote>

<footnote n="2">²UMR 5554, Institut des Sciences de l'Evolution, Équipe Dynamique de la Biodiversité, Anthropo-Écologie, CNRS, IRD, EPHE, Université de Montpellier, Place Eugène Bataillon, 34095 Montpellier Cedex 05, France</footnote>
upon the measurements of shape indicators such
as lengths, areas, angles, and their ratios (Gatz
1979, Wainwright 1988, Wikramanayake 1990),
hence focusing on selected aspects of shape only
(subjectively chosen and/or technically con-
strained). Consequently, the original shape can-
not be unequivocally reconstructed from the
measured indicators. Modern morphometrics, in
contrast, consider the entire shape, and two main
approaches are currently used: configuration of
landmarks and outline analysis (Rohlf 1990,
Claude 2008, Bonhomme et al. 2014). The first
approach uses homologous points between
shapes, known as landmarks, and studies their
relative position. The technique has been used
extensively in the last decades to study intra-
species fish morphology (Loy et al. 2000, Klin-
genberg et al. 2003, Costa and Cataudella 2007,
Elmer et al. 2010). However, homologous points
are often hard to define between various shapes
—for example, between species from different
families, and the number and position of homol-
ogous landmarks vary between studies and
organisms (Farré et al. 2016). In contrast, outline
analyses consider the whole outline. The most
popular outline analysis approach is elliptical
Fourier transform (EFT), and it has been used in
marine biology to describe otolith shapes (Tracey
et al. 2006, Mérigot et al. 2007), shells (Costa et
al. 2008), and fish species morphologies (Loy et
al. 2000, Ventura et al. 2017). To our knowledge,
these studies considered very similar biological
objects only and the technique was never
extended to explore the diversity patterns in
species assemblages.

Using the North Sea as a case study, this
study demonstrates the use of EFT to quantita-
tively describe the morphological variability in a
highly diverse marine fish species assemblage
(Daan et al. 1990). The North Sea fish commu-
nity is structured along a strong latitudinal gra-
dient, mainly associated with differences in
depth and primary production (Emeis et al.
2015, Frelat et al. 2017). The many commercially
important fish populations provide highly val-
ued ecosystem services. Our new quantitative
description of morphological variability can
improve our understanding of the community
diversity and identify environmental processes
structuring the fish community of this large
marine ecosystem.

MATERIALS AND METHODS

Sample collection

Images of bony fishes from the North Sea were
collected in January 2017 from nine online image
databases (Appendix S1). Four criteria were used
to only retain comparable images: (1) lateral views
of (2) male individuals (to cope with any sexual
dimorphism) (3) with all their fins well represented
(i.e., spread and not eaten), and (4) no eel-shaped
species (discarded because of their recurrent ser-
pentine representation). We considered images of
all species recorded regularly during bottom trawl
survey in the North Sea and fitting the four criteria
previously cited. When available, several images
of the same species were included to evaluate the
robustness of the approach. A total of 218 images
(48 photographs and 170 drawings) from 85 bony
fish species of the North Sea were included in this
study (Appendix S1).

Before performing the outline analysis, we
transformed the images into black silhouettes
(Fig. 1b). Numerous studies have defined land-
marks on fish to study their morphology. We
used five commonly used landmarks (Loy et al.
2000, Elmer et al. 2010, Farré et al. 2016) that are
located on the outline, easily recognizable, and
present on all species: (1) snout tip; (2) anterior
insertion of the dorsal fin; (3) dorsal and (4) ven-
tral insertion of the caudal fin; and (5) insertion
of the pelvic fin (Fig. 1b). The silhouettes were
then converted into (x; y) coordinates.

Elliptical Fourier transform

Elliptical Fourier transform is a popular method
of outline analysis, fitting separately the *x* and *y*
coordinates of an outline projected on a plane
(Rohlf 1990, Bonhomme et al. 2014). Before con-
ducting such analysis, outlines must be aligned to
remove differences in rotation, translation, or size.
We used five landmarks to align the outlines using
a full Procrustes superimposition. This superimpo-
sition optimally rotates, translates, and scales these
five landmarks to minimize Procrustes distances
between them. The first landmark (position of the
mouth) was defined as the starting point of every
outline. Outlines are closed curves than can be
described as periodic functions. The EFT describes
the outline geometry as two periodic functions—
the difference between the abscissa/ordinate of the
first and all successive points (Fig. 1c). The Fourier
<figure><img src="image_3.png" /><figcaption>Fig. 1. Illustration of outline analysis using elliptical Fourier transform (EFT). From original image (a), to black silhouette with five landmarks (b), on which the outline (c), can be described with EFT (d). The species in the figure is Gadus morhua, image from FAO.</figcaption></figure>

transform then decomposes them into a harmonic sum of trigonometric functions, weighted with coefficients known as harmonic coefficients. The original signal f can then be expressed as follows:

$$f(t) = \frac{a_0}{2} + \sum_{n=1}^{+\infty} \left[ a_n \cos \left( n \frac{2\pi}{T} t \right) + b_n \sin \left( n \frac{2\pi}{T} t \right) \right] \quad (1)$$

with T as the perimeter of a given closed outline and t as the curvilinear abscissa that varies from 0 to T. The harmonic coefficients a_n and b_n can be expressed as follows:

$$\begin{align}
a_n &= \frac{2}{T} + \int_{0}^{T} f(t) \cos(n \frac{2\pi}{T} t) dt \tag{2} \\
b_n &= \frac{2}{T} + \int_{0}^{T} f(t) \sin(n \frac{2\pi}{T} t) dt.
\end{align}$$

Four coefficients are obtained for each harmonic calculated. The number of harmonics was chosen to retain 99% of the cumulative harmonic power. The harmonic coefficients can be considered as

quantitative variables and analyzed within a multi-variate framework. More details can be found in Bonhomme et al. (2014). A principal component analysis (PCA) was calculated on the matrix of coefficients. Each principal component (PC) captured an independent and synthetic aspect of shape variability. Morphospaces, theoretical shapes regularly drawn on the factorial plane, helped to interpret the results. The first three PCs were compared to commonly used morphological traits by categorizing the caudal and body shapes (Pecuchet et al. 2016, Dencker et al. 2017; Appendix S2: Text S1). Finally, we compared the morphological distance (Euclidean pairwise distances of images calculated from coordinates on the first three PCs) with the taxonomical distance calculated with five taxonomic levels (Appendix S3: Text S1).

## Morphological diversity in the North Sea

Abundance data of the North Sea fish community has been collected by the North Sea International Bottom Trawl Survey (ICES 2015), an international effort to monitor demersal fish
populations. The sampling procedure monitored
the North Sea on a regular grid of 1° longi-
tude × 0.5° latitude, known as the ICES rectan-
gles. Each contributing research vessel applies a
standard otter trawl net which is hauled over the
seabed for 30 min. The data for the first quarter
of the period 2006–2015 were downloaded from
http://datras.ices.dk/. To avoid any bias that may
arise due to different sampling efforts (i.e., differ-
ent number of hauls per ICES rectangles), 10
hauls per ICES rectangles were randomly
selected, and we assessed their species and mor-
phological richness. We repeated the random
selection 100 times to estimate the variability of
species occurrence (i.e., the presence or absence
of species). ICES rectangles with <10 hauls in the
10-yr period were removed from the analysis. In
total, 172 ICES rectangles were included in the
analysis.

Two indicators of morphological diversity
were calculated for each ICES rectangle from
occurrence data and the mean scores of species
on the three PCs defining the morphospace
(Villéger et al. 2008). Morphological richness is
the volume of the morphospace occupied by the
convex hull of the community. Morphological
dispersion is the mean distance to the barycenter
of each community (Laliberté and Legendre
2010). The morphological diversity was then
compared to species (i.e., taxonomic) richness
obtained from the occurrence data. We expected
that the morphological richness increases with
taxonomic richness. A null model for the rela-
tionship between species and morphological
richness was estimated by randomly selecting a
given number of species from the entire species
pool (with specific probabilities in accordance
with their occurrence in the North Sea) and by
calculating the morphological diversity indica-
tors with a random assemblage of species. We
repeated the randomization process 1000 times
and computed it for species richness ranging
from 10 to 50.

Software and tutorial

All statistical analyses were conducted in the
programming environment R 3.3 (R Core team
2017). Morphometric analyses were done with
the package Momocs 1.2.3 (Bonhomme et al.
2014), while morphological diversity indicators
were calculated with the FD package. The

geographic distribution of species and morpho-
logical richness was visualized with the mapdata
and rgdal packages. A tutorial explaining the
EFT on fish communities is available on GitHub:
https://rfrelat.github.io/FishMorpho.html (https://
doi.org/10.5281/zenodo.1108518).

RESULTS

Outline analysis and morphological space

Fourteen harmonics were enough to gather
99% of the total harmonic power (Fig. 2). The
PCA on the 56 resulting coefficients yielded three
PCs, accounting for 78% of the variance (Fig. 3).
The first principal component (PC1), accounting
for 42% of the total variance, highlighted the gen-
eral rounding or elongation of the shapes
(Fig 3b). Shapes presenting the lowest scores on
this PC belonged to elongated fish species such
as the smooth sandeel (Gymnammodytes semisqua-
matus) and the great sandeel (Hyperoplus lanceola-
tus). On the other hand, shapes presenting the
highest values on this component belonged to
flat fish species such as the turbot (Scophthalmus
maximus) or the European plaice (Pleuronectes pla-
tessa).

The second principal component (PC2), explain-
ing 24% of the variability, highlighted the

<figure><img src="image_4.png" /><figcaption>Fig. 2. Progressive reconstruction of shapes. Four-
teen harmonics gathered 99% of the total harmonic
power.</figcaption></figure>
<figure><img src="image_5.png" /></figure>

Fig. 3. Principal component (PC) analysis calculated on the matrix of Fourier coefficients. (a) Scatterplot of the scores on the first two PCs, accounting for 66% of the total variance; the morphospace in the background presents theoretical shapes reconstructed from the PCs. (b) Illustration of the synthetic components of shape captured by the first three PCs. Raw outlines of the species projected near PCs extrema are displayed as example.

development of the pelvic fin and the underside. Shapes presenting the lowest values on this component belonged to species with strong and developed pelvic fins such as the tub gurnard (*Chelidonichthys lucerna*) and the golden redfish (*Sebastes norvegicus*). On the contrary, shapes presenting the highest values on this component belonged to species with smooth ventral sides and short pelvic fins such as the Norway pout (*Trisopterus luscus*) and the sand sole (*Pegusa lascaris*).

Finally, the third principal component (PC3), explaining 12% of the variability, was related to the shape of the dorsal and caudal fins. Shapes that presented the lowest values on this component belonged to species with strong, short, and developed dorsal fins and fork-shaped caudal fins such as the Clupeidae family like the allis shad (*Alosa alosa*), sardine (*Sardina pilchardus*), and herring (*Clupea harengus*).

On the other hand, shapes presenting the highest values on this component belonged to species with a continuous body, long dorsal fins, and round-shaped caudal fins such as the striped seasnail (*Liparis liparis*) and the checker eelpout (*Lycodes vahlii*). Body and caudal shape traits described by Pecuchet et al. (2016) were significantly linked with PC1 and PC3, respectively (Appendix S2: Fig. S1). The morphological distance between individuals increased with the taxonomic distance (Appendix S3: Fig. S1). We found no significant difference in the distances within species if calculated only with the same type of images, or with one drawings and one photograph (*P*-value of the Student's *t* test = 0.26). This result indicated that the type of images does not
influence our analysis. The average scores for each
species on the three components are provided in
Appendix S4.

*Morphological diversity in the North Sea fish assemblages*

Morphological diversity, expressed as richness or dispersion, decreased along a latitudinal gradient with highest values in the southern North Sea (Fig. 4a, b). The maximum morphological diversity was observed in the Kattegat, at the Elbe river mouth, and at the connection to the English Channel. The Kattegat also presented the maximum species richness of all ICES rectangles (39 species recorded). As expected, a positive correlation was found between the species richness and the morphological richness in the null model (Fig. 4c). We compared the observed morphological diversity indicators of each ICES rectangle with their expected values in the null model (Fig. 4c, d). As expected, the null model predicted that morphological richness increased with the number of species (Fig. 4c). Morphological dispersion was not linked with species richness, but the variance of the predictions of the null model decreased with the number of species (Fig. 4d). Most of the area in the northern North Sea had lower morphological richness than predicted by the null model, and nine ICES rectangles had significantly (P value < 0.05) lower morphological richness than expected by the 1000 randomizations in the null model (Fig. 4e). In the southern North Sea, most of the rectangles had morphological richness falling within the range or slightly higher than the predicted level, but none was significantly different those in the null model. Similar patterns were found with morphological dispersion. Eight ICES rectangles in the southern North Sea had significantly higher morphological dispersion than expected, and 12 ICES rectangles located in the northern North Sea had significantly lower morphological dispersion than expected (Fig. 4f).

DISCUSSION

Outline analysis appeared to be effective at
describing the morphological diversity of fish
species in the North Sea. Elliptical Fourier trans-
form revealed three main components of mor-
phological diversity in marine fish species. The

most important component was related to elon-
gation of the main body; the second to the devel-
opment of the pelvic fin; and the third to the
shape of the dorsal and caudal fins. These three
integrative and quantitative variables are good
candidates for new morphological traits in accor-
dance with the criteria stated by McGill et al.
(2006): "To be useful to community ecology, traits
should vary more between than within species
and preferably be measured on continuous
scales."

Morphological traits found in this study had already been described by previous subjective and qualitative descriptions (Pecuchet et al. 2016). Furthermore, we found elongation to be the major source of variability in shape, in accordance with numerous studies on fish morphology (Elmer et al. 2010, Claverie and Wainwright 2014, Ventura et al. 2017) and, more generally, on vertebrate morphology (Collar et al. 2013). These similarities suggest that EFT can describe both quantitatively and objectively the known morphological features and reveal more subtle components of morphological diversity. Additional studies should link these morphological traits with specific functions of fish, such as swimming performance and feeding behavior (Norton et al. 1995, Bejarano et al. 2017).

Morphological diversity decreased along a lati-
tudinal gradient with highest values in the south-
ern North Sea. This shallow area is known to host
a different species assemblage than the northern
part due to different environmental pressures—
for example, higher temperature and primary pro-
duction (Daan et al. 1990, Frelat et al. 2017) and
different epibenthic invertebrate community
(Callaway et al. 2002). One of the main differences
in species assemblages is the numerous small flat-
fish species that inhabits only the southern North
Sea (Callaway et al. 2002). Adding quantitative
morphological traits will help researchers to deter-
mine the community assembly rules, the relation-
ship between taxonomic and functional diversity
(Bellwood et al. 2002, Dencker et al. 2017). As
expected, we observed that areas with high spe-
cies richness were more likely to present a higher
morphological richness. However, areas with low
species richness in the northern North Sea
presented significantly lower morphological
diversity than expected, if the species were cho-
sen randomly. This result suggests that the
<figure><img src="image_6.png" /><figcaption>Fig. 4. (a, b) Spatial patterns of fish morphological diversity in the North Sea. (c, d) Relationship between the observed morphological diversity and species richness. The bold black line represents the mean morphological diversity of 1000 random samplings for a given number of species; the shaded areas in dark and light gray represent the standard deviation and 95th percentile, respectively. (e, f) The map of the residuals between observed and predicted morphological diversity. Black dots indicate communities significantly different from the null model. The left column (a, c, e) represents morphological richness, and the right column (b, d, f) represents morphological dispersion.</figcaption></figure>

environmental conditions filter species lacking a
specific combination of morphological traits
(Keddy 1992, Mouillot et al. 2007). This observa-
tion was confirmed by morphological dispersion
which showed a strong latitudinal gradient
and suggests two opposing mechanisms:

environmental filtering in the north and limiting
similarity in the south. The border between the
two mechanisms matches the boundary between
the thermally stratified waters of the northern
North Sea and the permanently vertically mixed
waters of the southern North Sea (Callaway et al.
2002). The high seasonal fluctuations in bottom water temperature in the south may be a factor limiting the morphological similarities between species, while the more stable conditions in the northern North Sea seem to filter morphologically similar species. This interpretation remains to be confirmed and tested in other large marine ecosystems.

Elliptical Fourier transform is known to be sensitive to the choice of the alignment method but our analysis consistently found the same three main components (Appendix S5). Naturally, fishes are 3D objects whose morphological descriptions could be refined, for example, with EFT on 2D orthogonal views to characterize the cross-section body shape (Terral et al. 2004, Bonhomme et al. 2015, Bouby et al. 2016). It would require a collection of images of the cross-section data for numerous fish species that are not available online yet. Our study focused on only the shape, which is the form minus size, and the latter would probably be an informative covariate. Moreover, the outline analysis produced here only considers the information included in the outline, missing, for example, the shape and the position of the pectoral fin, the operculum, and the eye, features known to have a functional role (Klingenberg et al. 2003, Mouillot et al. 2007, Farré et al. 2016). However, a comparison of landmark-based approach and outline analysis showed no significant differences (Loy et al. 2000) and a recent study shows that most of the morphological variability in reef fishes was found in body elongation (Claverie and Wainwright 2014). The outline analysis of the shape of the single lateral view proved to bring important insights into the diversity of fish morphology. The outcome of the outline analysis can be of great interest for further morphological studies and trait-based approaches in ecology and biogeography. Extending such an approach to the species from other large marine or freshwater ecosystems would characterize the global spectrum of fish morphology.

## ACKNOWLEDGMENTS

We thank the two anonymous referees for their useful comments that helped improve this manuscript. RF has received funding from the European Union's Horizon 2020 research and innovation program under the

Marie Skłodowska-Curie Grant Agreement No. 675997 (ITN MARmaED). The results of this publication reflect only the author's view, and the Commission is not responsible for any use that may be made of the information it contains. The study is a contribution to the University of Hamburg Center of Excellence on "Integrated Climate System Analysis and Prediction" (ClimSAP) funded by the German Science Foundation.

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## SUPPORTING INFORMATION

Additional Supporting Information may be found online at: http://onlinelibrary.wiley.com/doi/10.1002/ecs2.2220/full