# Morphological complexity promotes origination and extinction rates in ammonoids.

Luyi Miao, Xiaokang Liu, Arnaud Brayard, Dieter Korn, Xu Dai, Haijun Song

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Luyi Miao, Xiaokang Liu, Arnaud Brayard, Dieter Korn, Xu Dai, et al.. Morphological complexity promotes origination and extinction rates in ammonoids.. Current Biology, 2024, 34 (23), pp.5587-5594.e2. 10.1016/j.cub.2024.10.014. hal-04873080v2

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# Morphological complexity promotes origination and extinction rates in ammonoids

## Authors

Luyi Miao, Xiaokang Liu, Arnaud Brayard, Dieter Korn, Xu Dai, Haijun Song

## Correspondence

haijunsong@cug.edu.cn

## In brief

Miao et al. show that morphologically-complex ammonoid genera and species generally have shorter longevity and faster rates of turnover than morphologically-simple taxa. The diversification rate of taxa with complex morphology controls the apparent overall diversification fluctuations of ammonoids.

## Highlights

* A new method (“2D-OI”) has been developed to estimate quantitatively the ornamentation complexity in shelled animals.

* Morphologically-complex ammonoids generally exhibit shorter longevity than morphologically-simple taxa.

* Morphologically complex taxa have higher rates of origination and extinction than morphologically-simple taxa.

* Diversification rates of complex taxa drive overall fluctuations in ammonoid diversification rates.

## Graphical abstract
<figure><img src="image_2.png" /><figcaption>Morphologically-complex group</figcaption></figure>

<figure><img src="image_3.png" /></figure>
Morphological complexity promotes origination and
extinction rates in ammonoids

Luyi Miao¹,²,³, Xiaokang Liu¹, Arnaud Brayard², Dieter Korn³, Xu Dai¹,², Haijun Song¹*

¹ State Key Laboratory of Biogeology and Environmental Geology, School of Earth Sciences, China
University of Geosciences, Wuhan 430074, China.

² Biogéosciences, UMR 6282, CNRS, Université de Bourgogne, 21000 Dijon, France.

³ Museum für Naturkunde, Leibniz-Institut für Evolutions- und Biodiversitätsforschung, Invalidenstraße 43, 10115 Berlin, Germany

*Correspondence: haijunsong@cug.edu.cn

SUMMARY

The causes of heterogeneity in evolutionary rates are a key question in macroevolution.
Origination and extinction rates are intimately related to abiotic factors such as climate¹,² and
geography³,⁴, as well as biotic factors such as taxonomic richness⁵,⁶ and morphology⁷, are influenced
by phylogeny⁸,⁹. Studies of the relationship between morphology and macroevolution have focused
on morphological traits, including body size⁶,⁷,⁹, shape¹⁰, colour¹¹,¹², and complexity¹³⁻¹⁵, and have
proposed biological laws, such as the zero-force evolutionary law¹⁶ and Cope's rule¹⁷. However, the
relationship between morphological complexity and turnover rates remains poorly constrained due
to the lack of suitable measures for various subjects¹⁸,¹⁹. Here, we establish a new quantitative
method, the two-dimensional ornamentation index (2D-OI), which allows the description of the
ornamental complexity of ammonoids, to examine such a relationship at both genus and species
levels. This method is applied on two Mesozoic ammonoid datasets with different time resolution:
(i) early Pliensbachian (ca. 192.9–188.0 Ma) species at subzone timescale, (ii) Cretaceous (ca.
145.0–66.0 Ma) genera at substage resolution. Ammonoids (externally-shelled cephalopods) are one
of the most abundant and well-studied fossil groups with high turnover rates, and their conchs are
complex in structure²⁰. Ammonoids display some similarities with trilobites and mammals²¹,²² in
terms of high evolutionary rates, but underlying mechanisms remain elusive. Moreover, ammonoids
exhibit marked heterogeneities in turnover rates across spatio-temporal scales²³ and clades²³,²⁴,
making them a key clade for investigating the relationship between turnover rates and
morphological complexity. Results show that morphologically complex genera and species often
tend to have both higher origination and extinction rates than morphologically simple taxa, and
hence shorter longevity than simple taxa. Diversity fluctuations of taxa with complex ornamentation
generally overimprint and control the net diversification rates of overall ammonoids.
Morphologically complex taxa may have had greater plasticity, allowing for faster morphological
divergence and potentially making them more susceptible to speciation. This double-edged sword
of rapid evolution and increased extinction risk driven by complex morphologies have significant
implications for our understanding of how species survive over geological timescales.

RESULTS

The absence of an effective methodology for quantitatively assessing morphological
complexity hinders our understanding of its correlation with turnover rates. Typically, the
morphological "complexity" of a clade is defined as the diversity of types at a given hierarchical
level, such as cells, organs, or entire organisms<sup>14</sup>, which has varied across these different levels<sup>25</sup>.

Few of these hierarchical levels are generally preserved in fossils, thus measurements used for modern organisms such as 3D fractal dimensions<sup>19</sup> or counts of the number of organs<sup>26</sup>, are not readily applicable to deep-time studies. For main shelled organisms such as ammonoids, morphological complexity is often considered in terms of the type, density and strength of the shell ornamentation<sup>27,28</sup>, as well as suture lines<sup>17,29,30</sup>. Several methods have been proposed to approach ornamental complexity, but they either provide non-quantitative measurements<sup>27</sup>, or are limited to a single type of ornament, e.g. Fourier-related method<sup>31</sup>. The three-dimensional ornamentation index (3D-OI)<sup>18</sup> integrates ornament type, density, and intensity to yield a quantitative estimate of external shell complexity. However, 3D-OI relies heavily on the quality of fossil preservation and on a large number of scanned specimens, limiting its application to studies on large spatiotemporal scales. Here, we developed a new approach, the two-dimensional ornamentation index (2D-OI), which estimates the ornamentation complexity by measuring ammonoid diameters and associated width and height of ornamentation on fossil images (Figure 1, see details in Methods). A comparison of 3D-OI and 2D-OI on the same set of specimens shows that 2D-OI has a high similar accuracy in estimating ornamental complexity (Figure 1C).

To investigate the interplay between evolutionary rates and morphological complexity, we used the degree of shell ornamentation development in ammonoids as a case study. Ammonoids are one of the most abundant and well-studied fossil groups, exhibiting marked heterogeneities in turnover rates across spatio-temporal scales and clades<sup>24</sup>. For instance, some Triassic ammonoid families with species characterised by smooth compressed shells were empirically considered to be relatively long-ranging ('leiostraca'), whereas other families with more strongly ornamented species had
shorter life spans (‘trachyostraca’)³²,³³. Among Jurassic and Cretaceous ammonoids, some long-lived genera were also morphologically “simpler” (smooth or weakly ornamented) than those with shorter life spans³⁴. In summary, ammonoids are an appropriate clade for studying the relationship between turnover rates and morphological complexity. Therefore, we initiated a comprehensive study to investigate the relationship between the evolutionary dynamics and complexity of ammonoid across different temporal scales and taxonomic levels. Our study focused on two ammonoid datasets: (i) early Pliensbachian (Early Jurassic) species from the western Tethys, a dataset characterized by a high stratigraphic resolution and a well-defined phylogenetic framework³⁵, and (ii) Cretaceous genera, a dataset representing a longer time interval but at lower temporal and phylogenetic resolutions.

In the Pliensbachian dataset, longer lifespan species had a lower proportion of complex morphs (Figure 2A; Figure S1). The studied Pliensbachian species with strong ornamentation almost have a temporal range less than 3 million years (Myr). Conversely, species that spanned over 3 Myr have predominantly smooth or weakly ornamented shells. Similar results are found in the Cretaceous dataset, where genera with complex ornamentation also tend to have shorter life spans (Figure 2B; Figure S1). Cretaceous genera with the strongest ornamentation also exhibit shorter longevities. Taxa with complex ornamentation were therefore generally short-lived, while taxa with smooth or weakly ornamented shells included both long-lived and short-lived groups.

The early Pliensbachian phylogenetic chronogram combined with 2D-OI values (Figure S2) shows that the Lytoceratoidea and Phylloceratida species are rather long-ranging; almost all species in these two clades are smooth or possess a weak ornamentation. The family Liparoceratidae has the largest number of species with a complex ornamentation. Especially in the *Davoei* chronozone,
the richness of highly complex species in the family Liparoceratidae increased, and their life span
decreased. Based on the phylogeny (Figure S1), only taxa with a complex morphology show a short
longevity, which might represent a faster turnover rate. Observed shorter longevities correspond to
higher extinction rates³⁶,³⁷.

The results of both Bayesian framework and per capita diversification analyses (Figure 3;
Figure S3) show that groups with complex morphology generally have higher turnover rates than
groups with simple morphology of the same period. In this work, the distinction between “complex”
and “simple” taxa is bounded by the median 2D-OI of the database. The results show that species
with high ornamental complexity have higher origination and extinction rates during most intervals
of the early Pliensbachian (Figure 3A and 3C; Figure S3). A similar pattern is observed for
Cretaceous genera (Figure 3B and 3D; Figure S3). The difference between origination and
extinction rates is more obvious during certain intervals of marked diversity fluctuations, e.g., the
*Davoei* chronozone for the early Pliensbachian and the Albian-Cenomanian boundary for the
Cretaceous. We also used the PyRate software/package (reference) to calculate turnover rates at the
genus level for the early Pliensbachian dataset (Figure S4). Origination rates and extinction rates of
“simple” taxa are generally lower than that of “complex” taxa. In order to verify the difference of
turnover rates between the “complex” and “simple” groups, paired t-tests were conducted on the
average evolutionary rates in units of 1 Myr for the Cretaceous dataset and in units of 0.2 Myr years
for the Pliensbachian dataset. The extinction rates difference between “complex” and “simple”
groups is significant in both the Pliensbachian (n = 25, t = -3.385, P < 0.05, Cohen d = 0.682, paired
samples t-test) and Cretaceous (n = 78, t = -3.904, P < 0.05, Cohen d = 0.192, paired samples t-test).
The difference in origination rates between “complex” and “simple” taxa is significant for the early
Pliensbachian species (n = 25, t = -6.640, P < 0.05, Cohen d = 0.322, paired samples t-test), but not for the Cretaceous genera (n = 78, t = -1.083, P < 0.05, Cohen d = 0.177, paired samples t-test).

Based on the extinction/origination rate curves (Figures S5 and S6), net diversification rates (origination-extinction) of “complex” taxa appear as a controlling factor of the total ammonoid net diversification rates. During both the ealy Pliensbachian and Cretaceous, the turnover rates of “simple” morphotypes exhibited less variation than those of “complex” morphotypes. There is a significant positive correlation between the total net diversification rates of Pliensbachian species and the net diversification rates of complex morphs only (n = 25, ρ = 0.921, P < 0.001, Spearman’s rank correlations; Figure 4; Table S1), but not with simple morphs. Similarly, the net diversification rates for all and complex Cretaceous genera also display a significant positive correlation (n = 78, ρ = 0.508, P < 0.001, Spearman’s rank correlations).

# DISCUSSION

## Taxonomic bias

Ammonoid species are defined based on the morphology of their shells. Thus, changes in species identitification through time, which are used here to calculate speciation and extinction rates, may instead reflect morphological changes (i.e. pseudospeciation or pseudoextinction). Such a bias could affect ammonoids, for which substantial intraspecific morphological variations is documented³²,³⁸⁻⁴⁰. Consequently, smoother morphs may be classified within the same taxonomic groups, whereas more ornamented morphs are more likely to be separated⁴⁰. These taxonomic discrepancies may artificially increase the number of complex taxa, and lead to apparent shorter life spans and higher evolutionary rates⁸. The problem in taxonomic assignments of ammonoids is
partly circumvented by using the ontogenetic development of additional complementary shell
features such as the suture line and conch shape. Both can help in resolving taxonomic bias and are
somewhat less dependent on ornamentation and intraspecific variation. The early Pliensbachian
dataset provides an up-to-date and well-constrained case study that includes recently revised
taxonomic, phylogenetic, and geographic data³⁵,⁴¹,⁴². Additionally, this dataset takes into account
the known species dimorphism (microconch *vs*. macroconch), intraspecific variation and ontogeny
for these ammonoids³⁵, which minimises the impact of taxonomic bias on this dataset. It can also
be noted that for the early Pliensbachian ammonoids, the overall ornamental complexity does not
appear to be coupled to species richness (Figure S7). For the Cretaceous dataset, we used the genus
taxonomic level, which is less susceptible to be influenced by sexual dimorphism, ontogeny, or
intraspecific variation. Furthermore, many Cretaceous ammonoid experts have accounted for the
intraspecific variability⁴³,⁴⁴, and some Cretaceous genera contain both ornamentally-simple and
complex species³⁸. In summary, a taxonomic bias is likely to be minimal for the used datasets when
interpreting the observed patterns between morphological complexity and longevity.

Hypothetical influence of shell construction costs

The positive correlation between ornamental complexity and turnover rates can be tentatively
explained by the energy requirements for shell construction. Increased complexity in shell
ornamentation may indeed have required a greater energy expense for shell construction, and based
on the energy budget theory⁴⁵, these high energy-consuming organisms are unsuitable for living in
resource-poor habitats. The environmental stress might cause the appearance of simple, “primitive-
looking” forms of ammonoid⁴⁶. For example, during the Permian–Triassic mass extinction, the
morphospace of ammonoids displays significant morphological selection on ornamentation, favouring species with smooth or weakly ornamented shells, while those with strongly ornamented shells went extinct47,48 and rediversified later during the Early Triassic49. Consequently, energy limitations on shell construction associated with extreme environmental events have potentially contributed to the predominance of smooth or weakly ornamented shells in surviving ammonoid taxa.

Factors such as shell material economy, compactness, and hydrodynamics also potentially influenced the evolution of ammonoids and their morphospace50, as shell ornamentation is thought to have putative roles such as anti-predation27,51 and hydrodynamic efficiency52. Thus, ammonoid shells with a complex ornamentation may have required more energy to be built, are often thought to be more adapted against predators and to high-energy waters, and therefore more likely to have favored shallow-water habitats40,53. This aligns with the mechanisms behind the observed pattern of ornamentation in brachiopods across latitudinal gradients54,55. Complex ornamented taxa in brachiopods would be biased towards lower latitudes, whereas smooth taxa are more abundant at higher latitudes. Smooth taxa thus might be more adapted to high-latitude low-richness habitats with lower energetic demands, whereas complex taxa favoured low-latitude, high-richness habitats putatively being more adapted at defending against predators55. High species richness may also intensify competition and lead to increased structural complexity of communities and consequently potentially driving speciation5,56.

## Morphological plasticity

Another hypothesis is that taxa with complex morphology have a greater morphological
plasticity, potentially leading to a higher rate of biological speciation. Smooth-shelled species can
only evolve in one direction, i.e. becoming more complex, whereas complex ornamented species
may have possessed the flexibility to either simplify or further complicate to intensify their
ornamentation. Therefore, compared with weakly ornamented shell taxa, those with a strong
ornamentation may have possess additional dimensions of variation, theoretically expanding their
potential morphological space. Such kind of ‘left wall effect’ is also oberved in suture line
complexity and conch involution of ammonoids²⁹,⁵⁷, analogous to the lower limit in body size that
has been proposed for evolutionary trends⁵⁷⁻⁶⁰.

Chirat *et al.*<sup>61</sup> developed a mathematical model illustrating that the diverse structures of spines
can arise from minor variations in the control parameters of the underlying mechanical processes.
From these mechanical perspective on shell construction, smooth-shelled ammonites may faced
greater plasticity constraints as some of the smooth-shelled, laterally compressed ammonites were
hardly able to produce coarse and dense ribs<sup>62</sup>.

Therefore, based on the above views, complex species might have had greater phenotypic
plasticity. In addition, studies have shown that the rate of phenotypic differentiation is positively
correlated with the rate of speciation<sup>22,63-65</sup>. Species undergoing rapid morphological differentiation
may have faster turnover rates. This pattern has been shown in trilobites, where species with longer
lifespans often exhibit reduced intraspecific variation, whereas taxa with higher turnover rates are
often recorded in the fossil record as being relatively short-lived but more morphologically
variable<sup>22,66</sup>. However, this hypothesis is controversial, because it is hard to separate heritable
phenotypic variation from variation resulting from a plastic response to the environment<sup>40,67</sup>,
especially in extinct groups.
Environmental changes, including sea level fluctuations, global warming and hypoxic events, have often been assumed to cause enhanced or suppressed intraspecific morphological variability in ammonoid species⁵³,⁶⁸. This could also explain the observed minimal difference in evolutionary rates between “complex” and “simple” groups during intervals of background extinction, and why complex-type ammonoid genera tend to have higher extinction rates than simple-type genera at the boundaries between geological stages (Figures 3; Figure S2). Several large-scale oceanic anoxic events (OAEs) occurred in the Cretaceous⁶⁹,⁷⁰, while fluctuations in origination and extinction rates occurred during these periods. Complex taxa especially showed three peaks in extinction rates at the Aptian-Albian (OAE 1b), Albian-Cenomanian (OAE 1d), and Cenomanian-Turonian boundaries (OAE 2, Figures 3D and 4D), while simple morphotypes showed no significant fluctuations in extinction rates. The simple morphs have more stable origination rates, except for a peak at the Aptian-Albian boundary and fluctuations during the Cenomanian-Coniacian. Origination rate of the complex taxa showed three peaks in the OAEs from the late Barremian to Cenomanian periods (Figure 3B). In addition, at the Berriasian-Valanginian boundary, only complex morphs show a peak in origination rate, which may be related to the potential effect of a greenhouse climate and an OAE⁷¹. The complex group seem to be more prone to peaks in origination and extinction rates during several OAEs, which might be associated to an increased morphological plasticity caused by environmental changes further leading to higher turnover rates.

## Implications for macroevolution

The correlations between overall and different morphological complexity groups in diversification rates (Figure 4) indicate that the turnover rates of the simpler taxa are relatively stable,
whereas those of more complex morphotypes are subject to greater fluctuations, thereby influencing
broader patterns of diversification. This pattern may further elucidate the existence of morphological
selection under environmental stresses⁴⁶,⁴⁷, where complex morphologies are more likely to go
extinct, while those with simpler morphologies may have been more prone to survive.

This study represents a first attempt to quantitatively document a correlation between shell
morphological complexity and turnover rates in ammonoids. Although previous studies have
investigated the association between suture complexity and longevity in ammonoids³⁰, the
relationship between evolutionary rates and suture complexity remain to be clarified. The existence
of this phenomenon in other time intervals and marine clades is also still elusive. However, evidence
from certain clades suggests a positive correlation between body size and diversification rates, as
observed in bivalves and vertebrates²⁴,⁶³,⁷²,⁷³. This correlation is similar to that observed between
morphological complexity and diversification rates in our datasets. This suggests that the observed
positive correlation between morphological complexity and turnover rates may represent a more
widespread pattern. Marshall³⁷ noted that the average species' longevity is inversely related to the
extinction rate and that the average extinction rate is approximately equal to the average origination
rate. Our study suggests that the quantitative relationship between morphological complexity,
diversification rate, and species lifespan is likely to be much more complex and that the underlying
mechanisms remain to be elucidated.
# ACKNOWLEDGEMENTS

We thank Jérôme Thomas, Pascal Neige, David Ware and Christian Meister for their help with data collection and fossil scanning. This study was supported by the National Natural Science Foundation of China (42325202), State Key R&D Project of China (2023YFF0804000), Natural Science Foundation of Hubei (2023AFA006), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan). Sample management and valorisation at Université de Bourgogne, Dijon, benefited from ANR-11-INBS-0004-RECOLNAT. L. Miao would like to acknowledge the funding from the China Scholarship Council scholarship (No. 202206410074).

# AUTHOR CONTRIBUTIONS

L.M. and H.S. conceived and designed the study, and analysed the data. L.M., A.B., D.K., D.X. and X.L. collected data. L.M., X.L., A.B., D.K., D.X. and H.S. wrote the paper.

# COMPETING INTERESTS

The authors declare no competing interests.

Correspondence and requests for materials should be addressed to H.S.

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KEY RESOURCES TABLE

<table><thead><tr><th>REAGENT OR SOURCE</th><th>IDENTIFIER</th></tr></thead><tbody><tr><td><strong>RESOURCE</strong></td><td></td></tr><tr><td>Deposited data</td><td></td></tr><tr><td>Fossil dataset</td><td>This study</td></tr><tr><td>Early Pliensbachian dataset</td><td>Dommergues, et al. <sup>35</sup></td></tr><tr><td>Cretaceous dataset</td><td>Wright, et al. <sup>74</sup></td></tr><tr><td>Software and algorithms</td><td></td></tr><tr><td>R package divDyn V 0.8.2</td><td>https://cran.r-project.org/web/packages/divDyn/index.html</td></tr><tr><td>R package dplyr V 1.1.14</td><td>https://cran.r-project.org/web/packages/dplyr/index.html</td></tr><tr><td>R package ggpubr V 0.6.0</td><td>https://cran.r-project.org/web/packages/ggpubr/index.html</td></tr><tr><td>PyRate</td><td>Silvestro, et al. <sup>75</sup></td></tr><tr><td>Per capita rate</td><td>Foote <sup>76</sup></td></tr><tr><td>Per-taxon rate</td><td>Foote <sup>76</sup></td></tr><tr><td>Van Valen metric</td><td>Van Valen <sup>77</sup></td></tr><tr><td>Van Valen metric without singletons</td><td>Alroy <sup>78</sup></td></tr></tbody></table>

RESOURCE AVAILABILITY

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, H. Song (haijunsong@cug.edu.cn).

Material availability

This study did not generate new unique materials.

Data and code availability

All data used in the study are sourced from publicly accessible sources. Any supplementary data, three-dimensional models, and statements of data and code availability are available at https://doi.org/10.5281/zenodo.10954303.
# EXPERIMENTAL MODEL AND SUBJECT DETAILS

## Fossil dataset

In order to test the 2D-OI new method, we measured and scanned 146 specimens, including 88 specimens from the Université de Bourgogne, Dijon, France (UBGD), 46 specimens from the Museum für Naturkunde, Berlin, Germany (MB. C), 8 specimens from the Yifu Museum at the China University of Geosciences, Wuhan, China (YFMCUG), and 4 three dimensions models from the Digital Atlas of Ancient Life database (https://www.digitalatlasofancientlife.org). These 3D specimens were thus scanned and also used to calculate the 2D-OI value.

## Early Jurassic species dataset

To examine the evolutionary dynamics of ammonoid complexity across different temporal scales and taxonomic levels, the study focused on the Pliensbachian and Cretaceous ammonoid datasets. The Pliensbachian dataset includes 211 early Pliensbachian ammonoid species from the western Tethys and adjacent areas³⁵, with species-level ammonoid data and a high-precision stratigraphic resolution. Furthermore, this dataset includes a comprehensive phylogenetic tree⁴¹,⁴², which enables tests for phylogenetic conservatism of ornamentation complexity and longevity among lineages and allows us to account for the effects of diverse taxonomic scales and temporal resolutions. We calculated the temporal distribution of each species according to their respective spanned chronozones and subchronozones⁷⁹,⁸⁰ (Table S2). The dataset was then split according to the species-level phylogenetic tree published by Hardy et al.⁴¹,⁴². Consequently, the 2D-OI of species can be analysed within each phylogenetic clade, maintaining a high stratigraphic resolution.
In addition, we used the mean value of the 2D-OI of species to subdivide the ornamentation complexity of early Pliensbachian genera.

## Cretaceous genera dataset

A second dataset focuses on the Cretaceous; 462 genera/subgenera were selected from 775 Cretaceous ammonoid genera/subgenera listed in the Treatise on Invertebrate Paleontology⁷⁴. The selected taxa have well-preserved type species and coiled planispiral shells. We checked and updated the stratigraphic data, and measured 2D-OI from images of the type species. For highly-speciose genera, especially those with multiple type species, we measured several type species and calculated the average 2D-OI to represent the “average” ornamentation complexity of the genus. Considering Buckman's laws of covariations³²,³⁸, we also selected images of type species that approximated an "intermediate" morphology or measured multiple fossil images and calculated the average 2D-OI, to represent species exhibiting significant intraspecific variation, whenever possible.

In addition, to mitigate a potential ontogenetic bias, we tried to select only adult specimens. The selection of a single specimen per species for measurement could have introduced a sampling bias.

However, the limited number of well-preserved and illustrated specimens of the different species and genera presently prevents to apply the 2D-OI method to a large dataset. Overall, manually selecting specimens with adult and intermediate morphologies represented an optimal simplified approach under current constraints.
# METHOD DETAILS

## 2D ornamentation index (2D-OI)

The 3D-OI method for comparing ornamentation complexity among taxa, is only appropriate for well-preserved specimens and necessitates the use of 3D-scanned fossil models. This approach uses areas of the original 3D model and the simplified smooth model retaining the initial 3D shape of fossil, to estimate the proportion of the area covered by its ornamentation. To analyse ammonoid datasets on large spatial and temporal scales, we developed a novel approach, here called two-dimensional ornamentation index (2D-OI), based on measurements taken from ammonoid pictures (including ventral and lateral views). This approach quantifies the shell ornamentation complexity by measuring density and geometric shape of the ornamentation. Only best illustrated and most complete specimens were retained for analyses. The 2D-OI is expressed as follows:

$$2D\tilde{O}I = \frac{\sqrt{4h^2 + w^2} - w}{\pi D} \times n$$

where *h* is the maximum height of one morphological feature (rib, tubercle, spine) on 1/4 to 1/2 of the outer whorl from the aperture, and *w* is the width of the same feature, visible in both frontal and ventral views (Figure 1A). The measured ornamentation is here generally taken from the 1/4 to 1/2 position of the outer whorls of most complete and well-preserved specimens to reduce the potential influence of ontogeny during first growth stages. *D* is the conch diameter, and *n* is the number of features (rib, tubercle, spine) on the outer whorl. Ornamentation patterns are often made of wide valleys and sharp ridges, their measurements on photographs are here considered to be approximated as triangular prismatic bulges. We simplify such ribbing wave to the appearance of regular triangular prismatic bulges on a rectangle (Figure 1B). The ratio of the area where
ornamentation occurs to the projected area is obtained by measuring the length, width, height, and
number of raised folds, the lengths of the rectangle, and finally substituting them into the equation.
2D-OI measurements may be influenced by various parameters such as the ontogenetic stage, fossil
illumination angle, photographic perspective, and measurement errors. To evaluate the impact of
these factors on the obtained 2D-OI values, we compared them to 3D-OI values for the very same
specimens (Figure 1C). Results show a robust and significant correlation between 2D- and 3D-OI
values (n = 146, r = 0.934, P < 0.001, Pearson's correlation). Thus, the 2D-OI approach can be a
simplified method to estimate the ammonoid ornamentation complexity. This method can also be
applied to the analysis of ornamentation complexity of shelly fossils such as foraminifera or
gastropods. The 2D-OI approach might also be helpful to study changes in the ornamentation of
shelled organisms during environmental events, such as the potential reduction of ornament in
gastropods⁸¹ and foraminifera⁸² during ocean acidification. 2D-OI requires time-consuming manual
measurements, but we expect that the combination of this approach with and AI image analyses can
accelerate its process and enlarge the number of analysed specimens.

## Methods for calculating evolutionary rates

We used the Bayesian framework implemented within the program PyRate<sup>75</sup>, the per capita
boundary-crosser rate<sup>76</sup>, the per-taxon rate<sup>83</sup>, and the Van Valen metric<sup>77,84</sup> to calculate extinction
and origination rates for the Pliensbachian species and Cretaceous genera datasets. We performed
the reversible-jump MCMC (RJMCMC) algorithm (-A 4 option) to estimate the speciation and
extinction rates and their temporal variation by PyRate. After comparing (-PPmodeltest option)
different preservation models, all analyses were set with the best-fit preservation process, the time-
variable Poisson process (-q option). As the Cretaceous dataset only records reported periods for
genera and does not include data on the occurrence time of fossils with reported profiles, which
cannot be calculated by the Bayesian framework, we used occurrence data of 340 Cretaceous genera
from the Paleobiology Database (PBDB; https://paleobiodb.org/) to calculate evolutionary rates.
Besides, we applied the per capita rate, per-taxon rate and Van Valen metric to calculate the
origination and extinction rates for the Pliensbachian and Cretaceous datasets. We further divided
species and genera of each dataset into complex and simple groups taking as a reference boundary
the 2D-OI median values, and used PyRate to compare the extinction and origination rates between
the two groups.

QUANTIFICATION AND STATISTICAL ANALYSIS

See 'Method Details' for specific information. Evolutionary rate calculation and correlation analysis
using Python 3.6.8 and R 4.2.3. Building 3D models using Autodesk 3ds Max 2023 25.3.0.3640.
Figure legends

<figure><img src="image_4.png" /><figcaption>Figure 1. Measurements and reliability of 2D-OI values compared to the 3D-OI approach. (A) Examples of 2D-OI taken on a digital image of *Deroceras dudressieri* (MB.C.16367.1). Measured feature from 1/4 to 1/2 of the outer whorls from the aperture. (B) Schematic diagram of 2D-OI formula measurement. (C) Plot of 3D-OI vs. 2D-OI results for 146 specimens, with trendline associated Pearson's correlations coefficient (n = 146, r = 0.934, ***P < 0.001).</figcaption></figure>
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Figure 2. Relationships between longevity and 2D-OI for (A) Pliensbachian and (B) Cretaceous ammonoids. The colours represent different classes of 2D-OI values (higher the value, stronger is the morphological complexity).</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 3. Variations in Bayesian estimates of origination and extinction rates for Pliensbachian species and Cretaceous genera. All parameter estimates are inferred as posterior mean values (solid lines) and associated 95% confidence intervals (shaded areas). Subdivision between complex and simple morphological types is based on median 2D-OI values for the Pliensbachian (0.09) and the Cretaceous (0.10) datasets. The absolute ages of Early Jurassic (sub)zones are referred to the Geological Time Scale 2020⁷⁹,⁸⁰.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 4. Relationships between net diversification rate of all ammonites and diversification rate of different complexity morphs. (A) Diversification rates of all species and simple types are not significantly correlated through the early Pliensbachian (n = 25, ρ = 0.390, P = 0.054, Spearman's rank correlation). (B) The diversification rate of all genera and simple types are not significantly correlated through the Cretaceous (n = 78, ρ = 0.031, P = 0.790, Spearman's rank correlation). (C) Positive correlation between diversification rates of all species and complex types through the early Pliensbachian (n = 25, ρ = 0.921, ***P < 0.001, Spearman's rank correlation). (D) Positive correlation between diversification rates of genera and complex types through the Cretaceous (n = 78, ρ = 0.508, ***P < 0.001, Spearman's rank correlation). The average diversification rates are measured in units of 1 Myr for the Cretaceous and in units of 0.2 Myr for the Pliensbachian,</figcaption></figure>
removing anomalously negative biased outlier points due to the end-Cretaceous mass extinction. *n*,
number of time intervals; NS, not significant.