Two morphometric methods are applied and compared for the analysis of suture lines in Early Carboniferous ammonoids of the superfamilies Pericycloidea, Girtyoceratoidea and Goniatitoidea. We analysed (1) classic metric data (proportions of the width and depths or heights of lobes and saddles) using multivariate statistic methods and (2) outline data of the external lobe and the ventrolateral saddle of the same ammonoid taxa using the elliptic Fourier analysis. Both methods lead to similar results and simultaneously demonstrate ontogenetic and phylogenetic trends of these ammonoids. Our results are consistent with three previously suggested evolutionary patterns: (1) a general decrease of the amplitude of lobes and saddles, (2) a proportional widening of the external lobe and (3) a heightening of the median saddle.

The scientific branch of morphometrics, i.e. the quantitative investigation of biological shape variation (Bookstein, 1996), has a long history. The description of the organisms by means of their shape and proportions allowed for a classification of biological objects; the study and evaluation of morphological characters enabled the development of a taxonomic hierarchy. Newly found organisms could easily be attributed into the zoological nomenclature introduced by von Linné (1758). However, with the increasing number of described taxa it became clear that a strict separation between the species and their intraspecific variation became somewhat problematic (e.g. De Baets et al., 2015). Additional to the qualitative approaches, quantitative analyses are becoming increasingly important.

The classic investigations of shape variation in organisms were mainly based
on metric parameters. Francis Galton (Galton, 1883) proposed an approach towards a
quantitative differentiation between human faces, later known as two-point
shape coordinates or Bookstein shape coordinates (BCs). An approach towards
the analysis of geometric shape differences was developed by the
mathematician D'Arcy W. Thompson (Thompson, 1917) in his seminal book

With the availability of powerful computers at the end of the 20th century, the development of the “statistical theory of shape” has been driven forward (e.g. Lazarus, 1986). This allowed for the application of new methods in the generation of large multi-dimensional data sets and the use of statistical tests based on resampling procedures (Mitteroecker and Gunz, 2009). This new branch of morphometrics has been named “geometric morphometrics” (Corti, 1993; Adams et al., 2013; Gerber, 2017).

Geometric morphometrics is mainly based on the analysis of coordinates and their relationships. Frequently used methods are the landmark analysis and the outline analysis (Bookstein, 1991). Landmarks are distinct places in the shape of the investigated specimen (such as meeting points of sutures between bones) or points of maximal extension (such as tip of the nose or the point of a fin). Such points have to be homologous, if possible. They can be acquired using digitization tools such as tps-Dig (Rohlf, 2011) or the package Geomroph in R (Adams and Otárola-Castillo, 2013). If a statistically sufficient number of homologous landmarks are not available, semi-landmarks (“sliding landmarks”) can be used for a Procrustes analysis, first performed by Bookstein (1991). These are points along an outline of a form, which are determined by distinct mathematic procedures; they can be used for the analysis of objects with a smooth outline, where homologous landmarks cannot be determined. The number of semi-landmarks has to be the same in all analysed objects and some geometric similarity of the objects must be given.

Another important morphometric method is the study of the outline of an object (outline analysis, contour analysis) with the application of Fourier analysis. Closed outlines without homologous landmarks can be quantified by using this method. Objects with a simple or primitive outline, in which the radii beginning from the centre meet the outline only once, can easily be studied with the application of the classical Fourier analysis. Elliptic Fourier analysis (EFA; Kuhl and Giardinia, 1982) enables the study of complex outlines, i.e. those in which the radii meet the outline more than once.

Methods of morphometrics have become increasingly important for palaeontology within the last few decades. The change of the purely descriptive, conservative morphology towards the quantitative science at the beginning of the 20th century has been named the “quantification revolution” (Bookstein, 1998). Shape variations within or between organism groups can be described with the more completed arsenal of multivariate, statistical methods (Adams et al., 2004). For this, distance measurements, angles and proportions between distances can be used for the analysis. After the establishment of the geometric morphometrics at the end of the 20th century, the use of these methods was extended; landmark and outline analyses have been used in a number of research projects (for an overview, see MacLeod, 2002). These can now also be easily acquired from three-dimensional objects (e.g. Polly and Motz, 2016).

Another research topic that is at the centre of interest is the application of quantitative morphometric methods in phylogenetic and evolutionary studies, also in ammonoids (e.g. Monnet et al., 2011; Bookstein and Ward, 2013; see review in Monnet et al., 2015). MacLeod (2002) and Adams et al. (2004) pointed out the various difficulties associated with this method, but they also stated that it could be used to supplement other phylogenetic or evolutionary approaches (see also Monnet et al., 2011; Collyer and Adams, 2013; Adams, 2014). Polly (2008) discussed the role of morphometrics in the study of evolutionary novelties, which can appear almost suddenly (Klingenberg, 2008). Therefore, Polly (2008) proposed the application of homology-free methods such as outline analyses for the quantification of morphological change.

Because of their high value for phylogeny and taxonomy, suture lines have frequently been chosen for detailed investigations of Palaeozoic ammonoids (Kullmann and Wiedmann, 1970; Wiedmann and Kullmann, 1981; Saunders and Work, 1996, 1997; Korn, 1997; Korn and Klug, 2002) and have also been used for development of quantitative methods to study these structures through time (Boyajian and Lutz, 1992; Pérez-Claros et al., 2002; Allen, 2006, 2007; Saunders et al., 2008; Ubukata et al., 2010, 2014; Yacobucci and Manship, 2011). Many additional quantitative studies have focused on Post-Paleozoic ammonoids (Olóriz et al., 1997, 1999; Pérez-Claros et al., 2007; Yacobucci and Manship, 2011; Pérez-Claros and Bengtson, 2018).

Various methods for the analyses of suture lines have been applied, including the study of the fractal geometry (e.g. Boyajian and Lutz, 1992; Lutz and Boyajian, 1995; Olóriz et al., 1997, 1999; Pérez-Claros et al., 2002). These studies focused mainly on the Mesozoic ammonoid suture lines and followed mathematical analyses to describe complex sutural elements (e.g. Canfield and Anstey, 1981; Long, 1985; Damiani, 1990; Manship, 2004). In the future, the emerging importance of 3-D techniques will receive increasing attention for the study of ammonoid sutures (e.g. Hoffmann et al., 2018), which is of interest as the complexity of suture lines must to some degree be related to the complexity of the septa and soft tissues. However, it will take some time to have a representative data set for these purposes. Furthermore, due to insufficient preservation and lack of material, such data will be impossible to obtain for some taxa only.

The quantitative illustration of morphological differences with the aid of Fourier analysis methods between suture lines (Gildner, 2003; Allen, 2006, 2007), ribs (Dommergues et al., 2007) or other structures like cephalopod hooks (Hoffmann et al., 2017) has been of great scientific interest within the last few decades. Their application on suture lines, however, has only been shown as reliable and reproducible within certain limits, particularly if the investigated suture lines are very complex and brought the Fourier methods close to their limits (Allen, 2006).

Stratigraphic distribution of the genera in the superfamily Goniatitoidea analysed in this study. Relative lengths of the ammonoid zones after Korn and Kaufmann (2009), conodont stratigraphy after Meischner and Nemyrovska (1999) and Wang et al. (2018).

In this study, we quantitatively analyse suture lines of Early Carboniferous ammonoids; a morphospace for these suture lines will be outlined. We apply two methods of morphometric analysis for the purpose of a comparison of the results by studying Early Carboniferous ammonoids: (1) the analysis using distances between semi-landmarks (analysis of metric data) and (2) the outline analysis using the EFA.

The focus of this study is the Early Carboniferous superfamily Goniatitoidea de Haan, 1825 for a number of reasons: (1) it is a very diverse superfamily with many genera and species, (2) it shows high evolutionary rates with short-ranging taxa, (3) it is represented by large material, (4) it shows, despite the rather simple “goniatitic” suture line, numerous characteristic features that allow for a detailed morphometric analysis (e.g. Ruzhencev and Bogoslovskaya, 1971; Korn, 1988) and (5) all analysed species share a similar conch morphology so that differences in the suture lines due to covariation with conch geometry can largely be ruled out.

Suture lines of representatives of Early Carboniferous suborder
Goniatitina (

This superfamily emerged with several representatives in the early Late
Tournaisian (Korn et al., 2003, 2010). Early and Middle
Viséan representatives are unknown, but it is widely distributed in the
Late Viséan (Korn et al., 2005). During the early Late Viséan
(Asbian of the British chronostratigraphic scheme), the typical genus

The superfamily Goniatitoidea contains the families Goniatitidae,
Agathiceratidae and Delepinoceratidae with a total of about 25 genera. The
numerous species are characterized by distinct features in the suture line
as well as conch geometry and ornament. All species possess a V-shaped or
Y-shaped external lobe and a narrowly rounded to acute ventrolateral saddle
(Fig. 2). According to the suture line terminology proposed by Wedekind
(1918), it has the formula (E

The suture lines of 55 species out of Goniatitoidea were
analysed and compared with some representatives of the superfamilies
Pericycloidea and Girtyoceratoidea (Early Carboniferous Goniatitida;
Supplement). The suture lines used in this study were obtained from various
monographs on Carboniferous ammonoids (Ruzhencev and Bogoslovskaya, 1971;
Korn, 1988, 2017; Korn et al., 2005, 2010; Klug et al., 2006; Korn and Ebbighausen,
2008; Bockwinkel et al., 2010; Ebbighausen et al., 2010;
Korn and Titus, 2011). For comparability, suture lines of
specimens between 20 and 30

Separation of the external lobe and ventrolateral saddle for the outline analysis.

All suture lines were digitized and thereafter precisely aligned and scaled for a standard procedure (e.g. Furnish and Unklesbay, 1940). The vast majority of the analysed suture lines were drawn by one of us (Dieter Korn) and published in various articles; additionally, suture drawings provided by Ruzhencev and Bogoslovskaya (1971) were digitized (Fig. 3).

Two sutural elements were used in the quantitative analysis, (1) the
external lobe (E lobe) and (2) the ventrolateral saddle (VL saddle). These
two regions possess a convenient number of distinct characters and are not
too complex for a Fourier analysis. The use of these two sutural elements
allows for a quantification of various aspects of the superficially rather
similar suture lines:

the width ratio of the external lobe, ventrolateral saddle and adventive lobe

the width

the height of the median saddle

the degree of divergence of the E lobe flanks

the curvature of the E lobe flanks

the width

the general shape of the VL saddle.

The E lobe, however, is a rather complex structure and hence the EFA (Kuhl and Giardinia, 1982) was used. In the EFA the primary data (

Fitting of outline tracing in suture lines using 30 harmonics to represent the outline of the external lobe.

In our study, we used the comparatively high number of 30 harmonics to reach a convenient degree of precision, particularly for a sufficient representation of the prongs of the external lobe (Fig. 4). The coefficients of the suture lines were gained by the EFA using the program PAST (version 3.11; Hammer et al., 2001). Before this, we rescaled the coordinate data by Procrustes superimposition (standard size), then aligned (standard position) and finally rotated (standard orientation) them. We gained independent data sets Fourier coefficients for the external and the ventrolateral saddle, but for later processing, these two data sets were subsumed. A principal component analysis (PCA) using the correlation mode further processed this data set.

Terminology of measurements in the suture lines used in this article.

For a comparison of the results gained by the outline analysis, we
achieved an analysis of the metric data, using suture lines of 55
representatives of the Goniatitoidea. The following measurements of sutural
elements were obtained (Fig. 5):

external lobe (EL): the depth (EL

median saddle height (MS

ventrolateral saddle: its height (which is the same measurement as the
depth of the external lobe; EL

adventive lobe width (AL

We performed two types of analyses with respect to early Carboniferous ammonoid suture lines; a Fourier outline analysis was performed with two different data sets (one analysing various superfamilies and one focusing on Goniatitoidea) and one additional analysis was using metric data. For the latter, we also applied an analysis producing a ternary diagram.

We analysed 62 Early Carboniferous ammonoid species of the superfamilies Pericycloidea, Girtyoceratoidea, Neoglyphioceratoidea and Goniatitoidea (Supplement).

Result of outline analysis 1, based on 111 suture lines of
representatives of the superfamilies Goniatitoidea, Pericycloidea and
Girtyoceratoidea.

Fourier outline analysis 1, which was done for overview purposes, was
realized with the analysis of 109 suture lines (mostly of specimens with
phragmocone diameters of 20–30

Eigenvalue and percentages of variance for the first three principal components.

The distribution of data points within the PC1–PC2 morphospace diagram can
be translated in terms of suture morphology (Fig. 6a):

shape of the external lobe: suture lines with a parallel E lobe are preferably positioned at the lower margin of the PC1–PC2 plot (low values of principal component 2); V-shaped external lobes show high values of PC2.

width of the external lobe (relative to its depth): suture lines with the narrowest E lobe are located at the lower right margin (high PC1 and low PC2 values) and sutures with a wide E lobe occupy the upper left region.

height of the median saddle (relative to ventrolateral saddle): the lower left area (low PC1 and low PC2 values) is represented by individuals with a low M saddle, while the upper right area is dominated by suture lines with high M saddles.

shape of the ventrolateral saddle: nearly concordant with the median saddle height, suture lines with a rounded VL saddle are concentrated at the lower left margin of the scatter plot.

The distribution of the ammonoid species within the morphospace clearly
reflects similarities and dissimilarities between the suture lines. All
included genera of the superfamily Goniatitoidea (

The analysed genera of the superfamily Goniatitoidea (

The early Brigantian genera

The late Brigantian to Serpukhovian genera

The latest Brigantian to Serpukhovian genus

These results show that the proposed phylogenetic lineage from

The representatives of the superfamily Pericycloidea possess a position at the lower left margin of the scatter plot because of their low median saddle, the rounded ventrolateral saddle and the external lobe with parallel to slightly divergent flanks.

Analysis of representatives of the superfamily Goniatitoidea.

Result of outline analysis 2, based on 55 suture lines of
representatives of the superfamily Goniatitoidea.

The suture lines of 55 individuals from the superfamily Goniatitoidea were used for this analysis (Supplement).

Eigenvalue and percentages of variance for the first three principal components.

The percentage of variance that is explained by the first principal
component is clearly higher here; the first two principal components explain
about 72 % of the total variance (Table 2). The PC1–PC2 diagram (Fig. 7)
shows the following patterns:

The width of the external lobe (relative to its depth) increases from
the left (low PC1) to the right (high PC1) in the scatter plot. Therefore,

The height of the median saddle (relative to the ventrolateral saddle)
increases from the upper left area to the lower right area.

Suture lines with strongly diverging flanks of the external lobe are located at the upper margin (high PC2 value), while more parallel-sided or Y-shaped external lobes are at the bottom of the morphospace (low PC2 values).

Suture lines with a rounded ventrolateral saddle are located in the lower left area; suture lines with acute ventrolateral saddles are mainly located in the upper right area.

Suture lines with tectiform ventrolateral saddles (i.e. with constricted flanks and a pointed top) occur in the lower right area while those with a simple triangular shape occupy the upper left area.

By characterizing morphological aspects, the outline analysis can be a useful supporting tool to determine phylogenetic relationships. However, the consideration of other characteristics, like those of the conch shape, conch ontogeny and shell ornament, is necessary to test the results gained by the analysis of the suture line.

Result of the morphometric analysis, based on 55 suture lines of
representatives of the superfamily Goniatitoidea (same data set as for
outline analysis 1).

For a methodological comparison with outline analysis 2, a morphometric approach based only on metric data was made. For this, the same 55 individual suture lines of the Goniatitoidea from outline analysis 2 were examined (Supplement); 72.5 % of the total variance within the data set is explained by the first two principal components (Table 3).

Eigenvalue and percentages of variance for the first three principal components.

The morphospace plot (Fig. 8) shows the following characteristic features:

A widening of the external lobe from the lower right area (genera

A similar distribution can be seen with the increase in the height of the median saddle. Parallel to the widening of the E lobe the median saddle becomes wider.

The PC1–PC2 diagrams of the metric data analysis and outline analysis 2,
which represent the same material, reveal a very similar distribution
pattern. In both analyses,

Ternary diagram based on the proportions the three sutural
elements external lobe (measurement EL

Within the morphometric analysis of 55 individual suture lines of representatives of the family Goniatitoidea, we obtained width measurements of the external lobe, ventrolateral saddle and adventive lobe. These measurements were obtained in a straight line at half the height of the suture line. We summed up the relative percentages of E lobe, VL saddle and A lobe and plotted them in ternary diagrams.

The phylogenetic tendencies of external lobe widening during the late Early
Carboniferous are visible in the ternary diagrams (Fig. 9); particularly the
genus

The two methods used in the present study – (1) the outline analysis and (2) the quantitative metric analysis of goniatitid suture lines – yielded results that are testable and reproducible. The distribution patterns of the analysed taxa in the morphospace, calculated by using the two independent methods, are strikingly similar (e.g. with species with widened external lobe at the margin of the morphospace); this demonstrates that morphologically similar suture lines cluster together in the morphospace diagrams.

Patterns in the distribution within the morphospace in both methods can be correlated with phylogenetic aspects. Fourier outline analysis 1 demonstrates that the superfamilies Pericycloidea and Goniatitoidea are separated within the occupied morphospace. This result is promising for future analyses with a wider scope of taxa.

The reliability and reproducibility of the analyses described in the present study is dependent on a number of factors. The first of these factors is the precision in the reproduction of the suture line and its digitization. Furthermore, the precision of the metric data and the precision of the outline tracing are important preconditions.

An attempt to study complete suture lines in an outline analysis and EFA was not successful. Probably the complex outline of the suture lines precluded a correct representation. Therefore, distinct regions of the suture lines (E lobe and VL saddle separately) were analysed by the EFA in our study. The essential dimension reduction of the Fourier metadata, done by PCA, enabled the illustration of the results. The different genera occupy separated positions within the total morphospace. The complex and non-stationary pattern of ammonoid suture lines will foster the development of new methods for morphological analysis in the future. In this context, multivariate methods appear to be a suitable tool to encounter the information content of suture lines when taking into account their potential limitations.

The data utilized in this article can be found in the Supplement.

The supplement related to this article is available online at:

MW performed the project in the framework of his diploma thesis (Martin-Luther-Universität Halle-Wittenberg) and performed the analyses. DK collected the suture line data and provided the determinations of the analysed species. MW, KDB, and DK discussed the results and wrote the paper.

The authors declare that they have no conflict of interest.

We are indebted to Sonny A. Walton (Potsdam) for proofreading an earlier version of the manuscript. Edited by: Christian Klug Reviewed by: Rene Hoffmann and one anonymous referee