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\DOI{10.5802/crgeos.338}
\datereceived{2025-11-21}
\daterevised{2026-03-12}
\dateaccepted{2026-04-20}
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\section*{Declaration of interests}
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\COI{The authors do not work for, advise, own shares in, or receive
funds from any organization that could benefit from this article, and
have declared no affiliations other than their research organizations.}
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\begin{document}

%\dateposted{2026-02-16}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\TopicFR{G\'eochimie, cosmochimie}
\TopicEN{Geochemistry, cosmochemistry}
\TopicFR{S\'edimentologie, stratigraphie, g\'eologie des bassins}
\TopicEN{Sedimentology, stratigraphy, basin geology}

\editornote{Article submitted by invitation}
\alteditornote{Article soumis sur invitation}

\title{Possibilities, challenges, and limitations of dinosaur eggshells
LA-ICP-MS U--Pb dating based on samples from Provence (Upper Cretaceous,
France)}

\alttitle{Possibilit\'{e}s, d\'{e}fis et limites de la datation U--Pb
par LA-ICP-MS des coquilles d'\oe{}ufs de dinosaures \`{a} partir
d'\'{e}chantillons provenant de Provence (Cr\'{e}tac\'{e}
sup\'{e}rieur, France)}

\author{\firstname{Abel} \lastname{Guihou}\CDRorcid{0000-0001-7347-378X}\IsCorresp\IsEqualContrib}
\address{Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France}
\email[A. Guihou]{guihou@cerege.fr} 

\author{\firstname{Baptiste} \lastname{Such\'{e}ras-Marx}\CDRorcid{0000-0002-8107-8242}\IsCorresp\IsEqualContrib}
\addressSameAs{1}{Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France}
\email[B. Such\'{e}ras-Marx]{sucheras-marx@cerege.fr} 

\author{\firstname{Thierry} \lastname{Tortosa}}
\address{R\'{e}serve Naturelle de Sainte-Victoire, DEGPR,
D\'{e}partement des Bouches-du-Rh\^{o}ne, Marseille, France}

\author{\firstname{Pierre}\nobreakauthor\lastname{Deschamps}\CDRorcid{0000-0003-1687-3765}}
\addressSameAs{1}{Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE,
Aix-en-Provence, France}

\author{\firstname{Yves} \lastname{Dutour}}
\address{Museum of Natural History of Aix-en-Provence, France}

\keywords{\kwd{U--Pb dating}\kwd{Dinosaur eggshell}\kwd{Provence}}

\altkeywords{\kwd{Datation U--Pb}\kwd{Coquille d'oeuf de
dinosaure}\kwd{Provence}}

\shortrunauthors

\begin{abstract}      
Obtaining accurate chronostratigraphic constraints on continental
deposits is challenging, necessitating innovative dating approaches.
Here, we investigate the feasibility of Laser Ablation Inductively
Coupled Plasma Mass Spectrometry (LA-ICP-MS) U--Pb dating of dinosaur
eggshell fragments from the Late Cretaceous of Provence, France.
Preliminary optical, Scanning Electron Microscopy (SEM), and
cathodoluminescence (CL) analyses were critical for identifying zones
of optimal preservation and mitigating potential diagenetic
contamination. Results from two samples attributed to
\textit{Megaloolithus mamillare} and \textit{Cairanoolithus dughii}
yielded ages of 67.4 ${\pm}$ 4.4 Ma (2s, $n=60$) and 69.5 ${\pm}$ 9.9 
(2s, $n=50$), respectively, broadly consistent with regional
stratigraphic markers. Element mapping reveals significant spatial
variation in U and Pb concentrations within individual eggshells, with
zones of high contamination contrasting with well-preserved cores. The
data highlight the crucial role of diagenesis and organic matter in
influencing U--Pb system behavior, although it appears to be limited to
early diagenesis. While LA-ICP-MS U--Pb dating of dinosaur eggshells
presents substantial challenges, this study demonstrates its potential
with careful sample selection and nuanced interpretation, paving the
way for further refinement and broader application.
\end{abstract}

\begin{altabstract} 
Il est parfois difficile d'obtenir des contraintes
chronostratigraphiques pr\'{e}cises sur les s\'{e}diments continentaux,
ce qui n\'{e}cessite des approches de datation innovantes. Nous
\'{e}tudions ici la faisabilit\'{e} de la datation U--Pb par
spectrom\'{e}trie de masse \`{a} plasma inductif avec ablation laser
(LA-ICP-MS) de fragments de coquilles d'\oe{}ufs de dinosaures
provenant du Cr\'{e}tac\'{e} sup\'{e}rieur de Provence, en France. Des
analyses pr\'{e}liminaires par microscopie optique, microscopie
\'{e}lectronique \`{a} balayage (MEB) et cathodoluminescence (CL) ont
\'{e}t\'{e} essentielles pour identifier les zones de conservation
optimale et att\'{e}nuer toute contamination diag\'{e}n\'{e}tique
potentielle. Sur la base d'un \'{e}chantillonnage de 10 fragments de
coquilles d'\oe{}ufs, les r\'{e}sultats de deux \'{e}chantillons
attribu\'{e}s \`{a} \textit{Megaloolithus mamillare} et
\textit{Cairanoolithus dughii} ont donn\'{e} des \^{a}ges de 67,4
${\pm}$ 4,4 Ma (2s, $n=60$) et 69,5 ${\pm}$ 9,9 (2s, $n=50$),
respectivement, globalement coh\'{e}rents avec les rep\`{e}res
stratigraphiques r\'{e}gionaux. La cartographie \'{e}l\'{e}mentaire
r\'{e}v\`{e}le une variation spatiale significative des concentrations
en U et Pb au sein des coquilles d'\oe{}ufs individuelles, avec des
zones de forte contamination contrastant avec des zones bien
pr\'{e}serv\'{e}s. Les donn\'{e}es soulignent le r\^{o}le crucial de la
diagen\`{e}se et de la mati\`{e}re organique dans le comportement du
syst\`{e}me U--Pb, bien que celui-ci semble se limiter \`{a} la
diagen\`{e}se pr\'{e}coce. Si la datation U--Pb par LA-ICP-MS des
coquilles d'\oe{}ufs de dinosaures pr\'{e}sente des d\'{e}fis
importants, cette \'{e}tude d\'{e}montre son potentiel gr\^{a}ce \`{a}
une s\'{e}lection rigoureuse des \'{e}chantillons et une
interpr\'{e}tation nuanc\'{e}e, ouvrant la voie \`{a} un affinement et
\`{a} une application plus large.
\end{altabstract} 

\thanks{French Government, City of Aix-en-Provence (grant no. CIFRE
62/2008)}

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\defcitealias{VianeyLiaudetal1994}{ibid.}
\defcitealias{Tuckeretal2025}{ibid.}

\section{Introduction}\label{sec1}

Obtaining accurate chronostratigraphic constraints on continental
deposits is challenging, necessitating innovative dating approaches.
U--Pb dating applied to carbonate minerals has opened the possibility
to date calcium carbonate CaCO\tsub{3} either in the form of calcite or
aragonite \citep[e.g.][]{SmithFarquhar1989,RasburyCole2009}.
Dating based on isotopic dilution
offers an accurate and precise analysis but is limited in application
to relatively large samples (several mg) and requires a time consuming
clean chemical preparation to avoid any Pb contamination
\citep{WoodheadPetrus2019}. Last decade developments in LA-ICP-MS allow
sampling at high spatial resolution, down to ${\sim}$0.1 mm, and fast
data acquisition \citep{Robertsetal2017}. Several studies have
attempted to date calcite fossils using LA-ICP-MS by focusing on early
diagenesis mineral phases \citep[e.g.][]{Lietal2014,RochinBanagaetal2024}
showing the potential of U--Pb
dating on such materials. This method has also proven to be reliable on
less ideal fine grained carbonates \citep{Montanoetal2022} due to
relatively  high common Pb, and therefore relatively low
\tsup{238}U/\tsup{206}Pb which impacts age precision. This latter was
recently applied in palustrine/lacustrine deposits in the
Sainte-Victoire area allowing to refine the stratigraphy of those
deposits \citep{RoemersOliveiraetal2024}. Targeting biogenic carbonate
minerals such as eggshells comes with issues associated with the effect
of diagenesis on mobility of U and Pb. Ostrich eggshells U--Th dating
carried out on modern and quaternary samples have shown that the
eggshells behave as open systems for U and Th \citep{Sharpetal2019,
Loewyetal2020}. However, recent studies by \citet{Chenetal2025} and
\citet{Tuckeretal2025} proposed the first dinosaurs eggshells U--Pb
dating by LA-ICP-MS, suggesting that eggshells U and Pb systems could
close in early diagenetic stages and thus approximate the hatching age.
The present study is rooted in the same ongoing methodological
exploration.

The Provence in southern France is famous for dinosaur eggs and nest
outcrops. Philippe \citet{Matheron1869} made the first record in the
literature based on fragments collected in Rognac. The richness of
Sainte-Victoire mountain foothills was really highlighted in the first
half of the 20th century, with the first reports of
\citet{deLapparent1947} from Roques-Hautes and Rousset
(Bouches-du-Rh\^{o}ne), in addition of Fox-Amphoux (Var) areas. More
recently, very important nesting sites were excavated in the city
center of Aix-en-Provence \citep{Garciaetal2003} and in the R\'{e}serve
Naturelle de Sainte-Victoire, in the historic area of Roques-Hautes
\citep{Tortosa2014}. In this later, the nests lagerst\"{a}tte of
Beaurecueil-Grands Creux 2, for example, has yielded more than 500
eggs, spatially organized in cluster of 2--7 eggs (study in progress).
Those nests are observed in continental deposits, in reddish badlands
formed by fine sandstones to claystones cut by sandstones channels rich
in gravels corresponding to a fluvial plain environment. Those
continental environments are often difficult to date due to the lack of
biostratigraphical markers. Moreover, the sedimentation in these
environments is spatially and stratigraphically discontinuous.

In the present study, we combine imaging techniques and LA-ICP-MS to
identify zones with the best preservation in dinosaur eggshells
collected in Campanian-Maastrichtian (83.6 ${\pm}$ 0.2 to 66.0 Ma)
formations of Provence prior to U--Pb dating. This helps us to discuss
the reliability of U--Pb dating by LA-ICP-MS application on dinosaur
eggshells as well to better constrain continental deposit
chronostratigraphy in the specific Proven\c{c}al context. 

\section{Geological settings}\label{sec2}
\subsection{General context on Provence dinosaur eggs and nests}

As mentioned in Introduction, the Provence in southern France is famous
for dinosaur eggs and nests with first record from \citet{Matheron1869}
and more extensive observations---notably in the Sainte-Victoire
mountain surroundings---from \citet{deLapparent1947}. Since then, many
more nests have been discovered in the R\'{e}serve Naturelle de
Sainte-Victoire (RNSV), most of those housed in the Museum of Natural
History of Aix-en-Provence (MHNAix). Beyond these ``nests'', many more
isolated eggshells were also collected making the Provence eggshell
collection particularly rich. Most of those eggs---classified as
Megaloolithidae in the literature \citep{VianeyLiaudetal1994}---were
traditionally attributed to titanosaurian dinosaurs
\citep{Chiappeetal2003, Vilaetal2010} but recent Romanian discoveries
challenges this unique combination in associating it with basal
hadrosaurids \citep{Grigorescuetal2010}. So, it is more parsimonious to
envisage this oofamily associated with herbivorous dinosaurs,
especially since \textit{Rhabdodon} (Ornithopoda) was found as the most
abundant dinosaur in local layers rich in megaloolithid eggs (despite
the lack of non direct \textit{in embryo} nor \textit{in utero}
discoveries).

\begin{figure*}
\vspace*{2pt}
\includegraphics{fig01}
\vspace*{2pt}
\caption{\label{fig1}Geographical location of localities in this study
in the continental Upper Cretaceous of Aix-en-Provence Basin with
Beaurecueil---Grands Creux 2 (BGC2), Ch\^{a}teauneuf-le-Rouge---La Crau
(CRA) and---La Galini\`{e}re (GAL), Fox-Amphoux---M\'{e}tisson (FAM),
Puyloubier---Saint-Ser (PSS), Vitrolles---La Plaine (VLP).}
\vspace*{2pt}
\end{figure*}

In the Sainte-Victoire mountain foothills, the continental deposits
were not directly dated but inferred from magnetostratigraphic studies
combined with sedimentological analysis \citep{CojanMoreau2006} and
paleontological markers such as charophytes, ostracods, pollen, and
gastropods surrounding the interval rich in dinosaur eggshells
\citep{Babinotetal1983, Tortosa2014}. However, thanks to the richness in
eggshells, a local stratigraphy based on oospecies was proposed,
increasing the precision of the scale but remaining still poorly
anchored to the Geological Time Scale \citep{GarciaVianeyLiaud2001} and
highly dependent on the reliability and precision of determinations
\citep{Selles2012, Dhimanetal2019, vanderLindenetal2024}.

\subsection{Sampling sites}

The dinosaur eggshells were collected in several places in Provence
(Bouches-du-Rh\^{o}ne and Var departments), southern France
(Figure~\ref{fig1}).

\subsubsection{Beaurecueil---Grands Creux 2 (BGC2)}

Grands Creux 2 locality lies within the core restricted area of the
R\'{e}serve Naturelle Sainte-Victoire (Beaurecueil,
Bouches-du-Rh\^{o}ne department), at the foothill of the Montagne
Sainte-Victoire, about 7~km east of Aix-en-Provence
(Figure~\ref{fig1}). This historical site, also known as Roques-Hautes,
was discovered by  \citet{deLapparent1947} and subsequently received
considerable attention during the following decades for studies on
dinosaur eggs \citep[see][]{TortosaVianeyLiaud2021}. It is
located in the central part of the Aix-en-Provence Basin and belongs to
the continental deposits historically referred to as the lower
``\textit{Argiles et Gr\`{e}s \`{a} Reptiles}'' or lower ``\textit{Argiles
Rutilantes}'' Formation, dated to the upper Campanian (lower Rognacian
local facies; Figure~\ref{fig2}). In this area, the eggs---organized in
nests---occur in floodplain fluvial deposits consisting of reddish
siltstones to fine sandstones forming badland\break morphologies.

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig2}Chronostratigraphic position of the studied
localities within a synthetic log of the continental Upper Cretaceous
of Provence with time scale showing standard ages ($a$,$p$),
geomagnetic polarity ($b$,$o$), polarity zones ($c$,$n$), stages
($d$,$m$), local continental facies ($e$,$g$,$l$), synthetic log of
the Aix-en-Provence Basin and succession of formations ($f$,$h$),
ootaxa stratigraphic distribution ($i$) and synthetic log of
Fox-Amphoux syncline with succession of formations ($j$,$k$). Modified
after \citet{GarciaVianeyLiaud2001}, 
\citet{CojanMoreau2006}, \citet{Tortosa2014},
\citet{Philipetal2017}, \citet{Gradsteinetal2020} and
\citet{TortosaLeleu2021}. Abbreviations:  Beg.\ ${=}$\ Begudian, D.\ 
${=}$\  Danian, Sant.\ ${=}$\ Santonian, V.\ ${=}$\ Valdonnian, Vit.\ 
${=}$\ Vitrollian.}
\end{figure*}

\subsubsection{Ch\^{a}teauneuf-le-Rouge---La Crau Autoroute (CRA)}

La Crau Autoroute locality (Ch\^{a}teauneuf-le-Rouge,
Bouches-du-Rh\^{o}ne department) is located about 12 km southeast of
Aix-en-Provence (Figure~\ref{fig1}). This site was discovered in 2009
by the MHNAix during highway works for the widening of the A8 
\citep{Tabuceetal2013, Tortosaetal2014, Tongetal2022}. The site is
located in the central part of the Aix-en-Provence Basin and belongs to
the continental deposits historically referred to as the lower
``\textit{Argiles et Gr\`{e}s \`{a} Reptiles}'' or lower
``\textit{Argiles Rutilantes}'' Formation, dated to the upper Campanian
(lower Rognacian local facies; Figure~\ref{fig2}). The locality lies
within floodplain deposits consisting of red clays interbedded with
fluvial beds rich in bioclastic elements. 

\subsubsection{Ch\^{a}teauneuf-le-Rouge---La Galini\`{e}re (GAL)}

La Galini\`{e}re locality (Ch\^{a}teauneuf-le-Rouge,
Bouches-du-Rh\^{o}ne department) is located about 13~km southeast of
Aix-en-Provence (Figure~\ref{fig1}). The presence of dinosaur eggs was
officially recorded by a bailiff in 1977, which prevented the
urbanization of the parcel. This locality was excavated in 2008 during
a valorization campaign of paleontological localities carried out by
the MHNAix within the Grand Site Sainte-Victoire labeled area. The
outcrop is located in the central part of the Aix-en-Provence Basin and
belongs to the continental deposits historically referred to as the
upper ``\textit{Argiles et Gr\`{e}s \`{a} Reptiles}'' or upper
``\textit{Argiles Rutilantes}'' Formation, above the Calcaires de
Rousset Formation and dated to the lower Maastrichtian (see middle part
of Rognacian local facies; Figure~\ref{fig2}). It consists of typical
floodplain fluvial environments deposits, with reddish fine-grained
sandstones, and contains several dinosaur egg clutches (interpreted
here as nests). 

\subsubsection{Fox-Amphoux---M\'{e}tisson (FAM)}

M\'{e}tisson locality (Fox-Amphoux, Var department) is located about
53~km east of Aix-en-Provence (Figure~\ref{fig1}). It is a renowned
locality for vertebrate discoveries \citep[][for historical
overview]{deLapparent1947, Tortosa2014}. The site is
located within the Fox-Amphoux syncline and belongs to the continental
deposits historically referred to as the ``\textit{Gr\`{e}s et Argiles
\`{a} Reptiles}'' Formation, dated to the upper Campanian (lower
Rognacian local facies; Figure~\ref{fig2}) \citep{deLapparent1947,
GarciaVianeyLiaud2001, CojanMoreau2006, Tortosa2014}. This formation is
represented by approximately 300~m of alternating coarse sandstones,
often conglomeratic, purple to pink marls, and marly limestones with
pisoliths. The sandstones, with cross-bedding structures, are
interpreted as fluvial channel fills, whereas the marls correspond to
floodplain deposits. 

\subsubsection{Puyloubier---Saint-Ser (PSS)}

Saint-Ser locality (Puyloubier, Bouches-du-Rh\^{o}ne department) is
located at the foothill of the Sainte-Victoire mountain, about 16~km
east of \mbox{Aix-en-Provence} (Figure~\ref{fig1}). The outcrop was sampled in
2008 during a valorization campaign of paleontological localities
carried out by the MHNAix within the Grand Site Sainte-Victoire labeled
area, following initial reports from the 1980s. It is located in the
eastern part of the Aix-en-Provence Basin and belongs to the
continental deposits referred to as the lower ``\textit{Argiles et
Gr\`{e}s \`{a} Reptiles}'' or lower ``\textit{Argiles Rutilantes}''
formations \citep[][Figure~\ref{fig2}]{CojanMoreau2006}. The
overlying limestone formation was recently distinguished from deposits
observed in the western part of the Aix-en-Provence Basin
\citep{GarciaVianeyLiaud2001, Tabuceetal2013}, and is here referred to
the ``\textit{Calcaires de Rousset}'' Formation, dated to the upper
Campanian (Figure~\ref{fig2}). The outcrop consists of a sandstone
slab, lying a few meters below the limestone formation, on which
several dinosaur egg sections are visible. 

\subsubsection{Vitrolles---La Plaine (VLP)}

La Plaine locality (Vitrolles, Bouches-du-Rh\^{o}ne department) is
located about 17~km southeast of Aix-en-Provence (Figure~\ref{fig1}).
The site is located in the western part of the Aix-en-Provence Basin
and belongs to the continental deposits historically referred to as the
lower ``\textit{Argiles et Gr\`{e}s \`{a} Reptiles}'' or lower
``\textit{Argiles Rutilantes}'' Formation \citep{Tabuceetal2004, 
Valentinetal2012}. The outcrop consists of a succession of clays and
mottled marls with interbedded sandstone lenses, overlain by the
``\textit{Calcaires de Rognac}'' Formation. 

Based on the stratigraphic distribution of ootaxa,
\citet{GarciaVianeyLiaud2001} demonstrated that this unit, also
referred to as the ``middle Rognacian'' facies, is diachronous across
the basin. In its western occurrences, the top of lower
``\textit{Argiles et Gr\`{e}s \`{a} Reptiles}'' facies corresponds to
the lower Maastrichtian whereas in its eastern counterparts, the base
of the upper ``\textit{Argiles et Gr\`{e}s \`{a} Reptiles}'' facies is
of the same age (see the middle Rognacian local facies;
Figure~\ref{fig2}). The so-called ``middle Rognacian'' interval
therefore represents a lacustrine carbonate facies developed between
the base of the Calcaires de Rousset formation and the top of the
``\textit{Calcaires de Rognac}'' formation \citep{Tortosa2014,
Turin2017}.

\section{Material and methods}
\subsection{Sample collection}

A total of 10 eggshell samples were examined in this study. These
specimens are curated in two public institutional collections: the
Bouches-du-Rh\^{o}ne Departmental Collection (CD13) and the Mus\'{e}um
d'Histoire Naturelle d'Aix-en-Provence (MHNAix), France. Five eggshell
samples originated from Beaurecueil---Grands Creux 2 (BGC2;
Figure~\ref{fig1}). Those eggshells were collected in 2017 during
planned excavations conducted by the RNSV and MHNAix teams. The BGC2
series is housed in the CD13 collections, those also have a national
collection number: BGC2.1A.2017.16 (collection number
CD13-PV.2025.01.001), BGC2.1A.2017.32 (CD13-PV.2025.01.002),
BGC2.1A.2017.49 (CD13-PV.2025.01.003), BGC2.1A.2017.51
(CD13-PV.2025.01.004) and BGC2.1A.2017.52 (CD13-PV.2025.01.005). The
remaining specimens are curated in the MHNAix collections: one eggshell
named hereafter CRA from Ch\^{a}teauneuf-le-Rouge---La Crau Autoroute
(CRA in Figure~\ref{fig1}) was collected from a complete egg
(collection number MHNAIX.PV.2025.1.2). One eggshell named hereafter
GAL is from Ch\^{a}teauneuf-le-Rouge---La Galini\`{e}re (GAL in
Figure~\ref{fig1}), sampled from a complete egg (MHNAIX.PV.2025.10.1).
One eggshell sample hereafter named FAM (collection number
MHNA-PV.2005.24.18) is a subsample of eggs collected during excavation
campaigns conducted by the MHNAix between 1997 and 2001 at 
Fox-Amphoux---M\'{e}tisson (FAM; Figure~\ref{fig1}). One eggshell named
hereafter PSS (collection number MHNAIX.PV.2025.9.1) was collected from
a sandstone slab from Puyloubier---Saint-Ser (PSS in
Figure~\ref{fig1}). Finally, the eggshell sample named hereafter VLP
(collection number MHNA-PV.1999.13) is from Vitrolles---La Plaine (VLP
in Figure~\ref{fig1}) and was collected in 1999. 

\subsection{Eggshells preparation}

To perform microscopic observations and geochemical analysis by
LA-ICP-MS, the samples were mounted in radial section in a 1-inch resin
epoxy plug---araldite 2020 produced by ESCIL. Once prepared, the radial
section was polished in order to abrade any residual resin on the
eggshell. The resin used is depleted in Pb and U, thus preventing any
contamination of the sample. 

\subsection{Eggshells optical microscopy, cathodoluminescence and
numerical microscopy}

Eggshells were observed in optical microscopy with a binocular lens
Leica M125 with a magnification from ${\times}$8 up to ${\times}$100 scale
of observation commonly used for the parataxonomic assignment of
dinosaur eggshells \citep{Mikhailov1997}. However, this scale and
methodology was not adequate to fully explore the degree of
preservation of the eggshell structures.

%tab1
\begin{table*}
\caption{\label{tab1}Sample list classified based on U--Pb screening,
analyses and ages calculation\vspace*{-3pt}}
\fontsize{9.5}{11}\selectfont\tabcolsep3pt
\begin{tabular}{cccccc}
\thead
Sample name & Localization & Oospecies & 
\parbox[t]{6pc}{\centering U--Pb screening (\tsup{238}U/\tsup{206}Pb {$>$} 5)}\vspace*{2pt} & 
U--Pb analyses & 
U--Pb age \\
\endthead
\parbox[t]{10pc}{\centering BGC.1A.2017.32 (CD13-PV.2025.01.002)}\vspace*{2pt} & BGC2 & \textit{Megaloolithus} sp. & Not analyzed & - & - \\ 
\parbox[t]{10pc}{\centering BGC.1A.2017.49 (CD13-PV.2025.01.003)}\vspace*{2pt} & BGC2 & \textit{M.~petralta} & Not analyzed & - & - \\ 
\parbox[t]{10pc}{\centering BGC.1A.2017.51 (CD13-PV.2025.01.004)}\vspace*{2pt} & BGC2 & \textit{M.~petralta} & Not analyzed & - & - \\ 
\parbox[t]{10pc}{\centering BGC.1A.2017.16 (CD13-PV.2025.01.001)}\vspace*{2pt} & BGC2 & \textit{M.~petralta} & Not ok & - & - \\ 
\parbox[t]{10pc}{\centering BGC.1A.2017.52 (CD13-PV.2025.01.005)}\vspace*{2pt} & BGC2 & \textit{M.~petralta} & Not ok & - & - \\ 
GAL (MHN AIX.PV.2025.10.1) & GAL & \textit{M.~mamillare} & Not ok & - & - \\ 
FAM (MHNA-PV.2005.24.18) & FAM & \textit{C.~dughii} & Not ok & - & - \\ 
PSS (MHN AIX.PV.2025.9.1) & PSS & \textit{M.~siruguei} & Ok & \tsup{238}U/\tsup{206}Pb {${<}$} 10 & No \\ 
CRA (MHN AIX.PV.2025.1.2) & CRA & \textit{C.~dughii} & Ok & \tsup{238}U/\tsup{206}Pb  {${<}$} 30 & Yes \\ 
VLP (MHNA-PV.1999.13) & VLP & \textit{M.~mamillare} & Ok & \tsup{238}U/\tsup{206}Pb  {${<}$} 30 & Yes 
\botline
\end{tabular}
\vspace*{-3pt}
\end{table*}

All samples were studied with a cathodoluminescence installed on an
optical microscope with ${\times}$4 and ${\times}$10 objectives and 
${\times}$10 oculars. The microscope used was an Olympus BH-2, the
cathodoluminescence a NewTec Scientific Cathodyne connected with an iDS
camera. Depending on the luminescence of the eggshells, the electric
potential was set between 12~kV and 18~kV, the intensity between
100~$\upmu$A and 200~$\upmu$A and 3~s photo acquisition time by
default. Set of pictures after LA-ICP-MS analyses were performed using
a Keyence VHX-7000 with magnification from ${\times}$30 up to ${\times}$300
under coaxial light.\vspace*{-3pt}

\subsection{Eggshells SEM and EDS}

Before the preparation in plugs, BGC2.1A.2017.32, BGC2.1A.2017.51, CRA,
GAL and FAM were observed with a SEM Hitachi S-3000N. Few uncalibrated
EDS (Bruker Nano 129~eV XFlash Detector 5010) analyses were also
performed on those samples with a range of spot analysis about few
micrometers. These devices were used to identify minute structures and
to observe possible chemical contamination or traces of diagenetic
overprints. Sample VLP SEM images were taken after the U--Pb
analyses.\vspace*{-3pt}

\subsection{U--Pb analyses}

U--Pb analyses were carried out at CEREGE, Envitop Analytical facility,
Aix-en-Provence, France, using an ESI 193~nm excimer laser ablation
system coupled to an Element XR SF-ICP-MS (more detailed methodology
and the U--Pb dataset are presented in supplementary material). At
least 30 spots of 150~$\upmu$m diameter were placed manually in zones
showing the best preservation on cathodoluminescence images and having
the highest U/Pb using quick laser ablation prescreening of Pb, U and
Th signals. During prescreening, an empirical cut-off value for the
\tsup{238}U/\tsup{206}Pb of 5 is applied (Table~\ref{tab1}). This
value, although not very radiogenic for samples {${<}$}100~Ma, allowed to
quickly preselect zones with the best chance of providing spread in the
\tsup{238}U/\tsup{206}Pb ratios and hence U--Pb ages after data
reduction.

After data acquisition, processing was done using Iolite
\citep{Patonetal2011} and an in-house excel spreadsheet to derive ages
from Tera-Wasserburg diagrams using IsoplotR software
\citep{Vermeesch2018}. WC1 was used as a primary standard to correct
\tsup{238}U/\tsup{206}Pb fractionation \citep{Robertsetal2017} and
AUG-B6 as a secondary standard to check for accuracy, yielding an age
of 43 ${\pm}$ 2 Ma in agreement with \citet{Pageletal2018}. Ages are
quoted at a 2s, including the propagation of systematic uncertainty of
the standards following \citep{Horstwoodetal2016}.

\begin{figure*}
\includegraphics{fig03}
\caption{\label{fig3}Radial section observation of calcite structure of
(A) sample BGC2.1A.2017.51 \textit{M.~petralta} and (B) sample PSS
\textit{M.~siruguei}. CL---continuous layer and ML---mammillary layer.}
\end{figure*}

For LA-ICP-MS elemental mapping, a square spot size of 100~$\upmu$m,
raster speed, and MS cycling time were synchronized to provide
low-resolution images with 100~$\upmu$m\tsup{2} pixels, sufficient to
correlate these mappings to other imagery techniques used in this
study. A JCp$^{*}$-1-NP pellet from myStandards GmbH was used as a
reference.

\section{Results}
\subsection{Egg shells oospecies identification, microstructure,
preservation and contamination}

Typical structures of eggshells were observed in optical microscopy
based on radial sections and complementary information were made based
on the sculpture of the outer surface. Shell units were
discretispherulitic (or tubospherulitic) with ovoid mammilla and
radial-tabular columns \citep[][Figure~\ref{fig3}A]{Mikhailov1997}. 
The spaces between the mammila were filled with
sediments with a different color and texture than the shell itself. The
discretispherulitic structure confirmed the attribution to
Megaloolithidae oofamily. Pore canals were not easily observed in most
samples, with the exception of FAM and PSS which had tubocanaliculate
pore canals (Figure~\ref{fig3}B). In many samples---when visible---the
outer face of the egg was covered by nodes. The proximal face was
smooth---when not encrusted. More precisely, BGC2.1A.2017.16
(Supplementary Figure~1), BGC2.1A.2017.49, BGC2.1A.2017.51
(Figure~\ref{fig3}A) and BGC2.1A.2017.52 (Supplementary Figure~2) were
attributed to the oospecies \textit{Megaloolithus petralta}
\citep{VianeyLiaudetal1994} based on the node diameter (0.4--0.6~mm),
its slightly arched growth lines, and partially fused, narrow
fan-shaped shell units. The sample BGC2.1A.2017.32 was tentatively
attributed to \textit{Megaloolithus} sp. Although historically
attributed to \textit{Megaloolithus aureliensis}
\citepalias{VianeyLiaudetal1994} and later to \textit{Megaloolithus} cf.\ 
\textit{aureliensis} \citep{VianeyLiaudGarcia1999}, it is now regarded
as a distinct oospecies with a smaller general size, thinner shell
thickness, arched growth lines, and partially fused fan-shaped shell
units. So far, \textit{Megaloolithus} sp.\ was exclusively reported from
BGC2 locality. The sample GAL (Supplementary Figure~3) from
Ch\^{a}teauneuf-le-Rouge---La Galini\`{e}re and the sample VLP from
Vitrolles---La Plaine were attributed to the oospecies
\textit{Megaloolithus mamillare} \citep{VianeyLiaudetal1994} based on
arched growth lines following the surface and unfused short and broadly
fan-shaped shell units. The sample PSS (Supplementary Figure~4) from
Puyloubier---Saint-Ser was attributed to the oospecies
\textit{Megaloolithus siruguei}
\citepalias[][Figure~\ref{fig3}B]{VianeyLiaudetal1994}, with strongly arched
growth lines, unfused fan-shaped shell units, and a reticulate canal
pore system. Finally, the samples CRA (Ch\^{a}teauneuf-le-Rouge---La
Crau Autoroute) and FAM (from Fox-Amphoux---M\'{e}tisson; Supplementary
Figure~5) were attributed to the oospecies \textit{Cairanoolithus
dughii} \citepalias{VianeyLiaudetal1994} based on horizontal growth lines in
the interlocking shell units and more arched single units as well as
the presence of very smooth nodes on the external surface. The
Supplementary Figure~6 summarizes the oospecies identifications. 

\begin{figure*}
\includegraphics{fig04}
\caption{\label{fig4}(A,B) SEM picture of sample CRA \textit{C.~dughii}
(CRA). (C) EDS spectrum of sample CRA \textit{C.~dughii} calcite. (D,E)
SEM pictures of sample VLP \textit{M.~mamillare}.}
\end{figure*}

\begin{figure*}
\vspace*{2pt}
\includegraphics{fig05}
\caption{\label{fig5}Sample CRA \textit{C.~dughii} pictures (A) in
natural light (${\times}$30 magnification); (B) natural light high
magnification panorama (${\times}$150 magnification); (C)
cathodoluminescence. CL---continuous layer and ML---mammillary layer.}
\vspace*{2pt}
\end{figure*}

SEM pictures of sample CRA \textit{C.~dughii}, sample GAL
\textit{M.~mamillare}, sample FAM \textit{C.~dughii}, sample
BGC2.1A.2017.32 \textit{Megaloolithus} sp.\ and sample BGC2.1A.2017.51
\textit{M.~petralta} showed that the \mbox{prismatic} structure of the thick
CaCO\tsub{3} layer was preserved (Figure~\ref{fig4} and Supplementary
Figures 7--10). The cathodoluminescence showed that recrystallisation
and secondary crust were luminating (Figures~\ref{fig5}, \ref{fig6} and
Supplementary Figures 7--10). Those were concentrated in the inner and
outer faces of eggshells, probably due to the contribution of clays. In
most case, luminescence was observed between two shell units, within
radial thin structures. If some of those structures may correspond to
pore canals (Supplementary Figure~4), in most case those seemed too
narrow to correspond to tubocanals and thus may correspond to fractures
and/or interface between two shell units (Figure~\ref{fig5} and
Supplementary Figure~1). In PSS (Supplementary Figure~4), the pore
canals displayed circularly banded luminescence interpreted as
recrystallisation within the pores. 

\begin{figure*}
\vspace*{-4pt}
\includegraphics{fig06}
\vspace*{-4pt}
\caption{\label{fig6}Sample VLP \textit{M.~mamillare} pictures (A,B) in
coaxial light high magnification panorama (${\times}$150 magnification);
(C,D) in natural light (${\times}$30 magnification); (E,F)
cathodoluminescence. Circles on the sample are the trace of the laser
ablation. CL---continuous layer and ML---mammillary layer.}
\vspace*{-4pt}
\end{figure*}

Most of the prismatic calcite forming the majority of the eggshell was
depleted in transition metals (Figure~\ref{fig4} and Supplementary
Figures 7--10) and did not present any luminescence
(Figures~\ref{fig5}, \ref{fig6} and Supplementary Figures~1, 2, 5). To
conclude, the faces, thin fractures, transversal canal pores, and
longitudinal pores were encrusted with clays and/or CaCO\tsub{3}
enriched in transition metals testifying secondary crystallization. The
rest of the prismatic layer showed comparatively a better preservation
and was targeted for laser ablation analyses.

\subsection{U--Pb--Th concentrations}

Elemental mapping (LA-ICP-MS) of sample VLP showed distinct spatial
distributions of Mn (not shown), Pb, Th, U. Concentrations ranged from
0 to 150 ppm, 50 ppm, 1.5 ppm, 10~ppm respectively (Figure~\ref{fig7}).
The highest values for all elements occurred near sutures and in the
inner and outer layers, which were interpreted as zones enriched in
clays and/or affected by diagenetic processes. In contrast, the
prismatic calcite outside these areas exhibited significantly lower
concentrations (Th ${\ll}$ 0.5 ppm, Pb ${\ll}$ 1 ppm, U ${\ll}$ 1 ppm),
suggesting minimal contamination and secondary alteration---consistent
with observations from cathodoluminescence imaging.
\tsup{238}U/\tsup{206}Pb varied from 0 to ${\sim}$25 with the most
radiogenic values (highest ratios) found in areas with the lowest Pb
and U concentrations. Age calculation from the elemental mapping could
not be applied due the overall low Pb content in the best-preserved
zones that prevented the use of \tsup{207}Pb measurements, as the
signal on the 207 mass was too low to be reliable.

\begin{figure*}[p!]
\includegraphics{fig07}
\caption{\label{fig7}Low resolution (1 pixel ${=}$\ 100~$\upmu$m\tsup{2})
elemental and \tsup{238}U/\tsup{206}Pb mapping of sample VLP
\textit{M.~mamillare} showing low concentration of detrital elements
such as \tsup{232}Th in the prismatic calcite zones. Circles on the
sample are the trace of the laser ablation.} 
\end{figure*}

\begin{figure*}
\includegraphics{fig08}
\caption{\label{fig8}Tera-Wasserburg diagram of the U--Pb data of
sample VLP (A) and CRA (B). The uncertainty on the age includes the
propagation of systematic uncertainties of the standards as specified
in the supplementary material.} 
\end{figure*}

\subsection{U--Pb ages}

Only two samples, CRA and VLP, yielded reliable U--Pb isochrons
(Figure~\ref{fig8}). Some other samples were tested (see
Table~\ref{tab1}), but did not yield reliable isochrons mainly due to
unfavorable \tsup{238}U/\tsup{206}Pb ratios---below the cut-off value
of  5---and excluded to the exception of sample PSS presented in
Supplementary Figure~11. The age of sample VLP attributed to
\textit{Megaloolithus mamillare} was calculated to 67.4 ${\pm}$ 4.4 Ma
(2s, $n=60$) (Figure~\ref{fig8}A). The age of sample CRA attributed to
\textit{Cairanoolithus dughii} was calculated to 69.5 ${\pm}$ 9.9 (2s,
$n=50$) (Figure~\ref{fig8}B). \mbox{Considering} the uncertainties, sample VLP
was dated within the Maastrichtian-Danian (Paleocene) time interval and
sample CRA within the Campanian-Selandian (Paleocene) time interval.
Since these eggshells coming from dinosaur species cannot be younger
than the Cretaceous--Paleogene (K--Pg) boundary, VLP age's was
considered Maastrichtian and CRA Campanian to Maastrichtian. For both
samples, the \tsup{238}U/\tsup{206}Pb were relatively low ({${<}$}35)
compared to the \tsup{238}U/\tsup{206}Pb radiogenic concordia intercept
of ${\sim}$100 for ages ${\sim}$68~Ma, leading to moderate uncertainties
(6.5\% and 15\%, respectively). Based on LA-ICP-MS, CRA had lower Pb
concentrations and lower U concentrations ({${<}$}100~ppb in average for
both Pb and U) compared to VLP (${\sim}$500~ppb in average for both Pb
and U) which explain its greater uncertainty despite showing a similar
\tsup{238}U/\tsup{206}Pb range. For each sample, the initial
\tsup{207}Pb/\tsup{206}Pb ${\sim}$0.84 was consistent with the expected
value of less than 100~Ma formations \citep{StaceyKramers1975}. The
\tsup{232}Th concentrations were well below 0.5 ppm (Figure~\ref{fig7})
limiting the possible contamination from secondary phases (see previous
section).

\section{Discussion}

\subsection{U--Pb system in eggshells and diagenesis}

Previous U--Th analyses of Quaternary ostrich eggs showed that the
prismatic calcite forming the shell behaved as an open U-series system,
requiring advection--diffusion models to account for U mobility during
diagenesis and to derive \tsup{230}Th--U ages estimates 
\citep{Sharpetal2019}. On U--Pb timescales, it can be expected that the
U-series system was subject to several post-depositional processes,
including contamination from soil-derived detrital particles filling in
the intercrystalline microporosity of the eggshell
\citep{Loewyetal2020} and/or mobility of U and Pb, potentially driven
by meteoric or sediment derived fluids circulation along pores or
microfractures of the shells \citep{Tuckeretal2025}. The time scale for
which the U-series system in prismatic calcite remains open is still an
open question and hence U--Pb ages must be considered as minimum ages.
\citetalias{Tuckeretal2025}  demonstrated that U--Pb ages obtained from
dinosaur eggshells in the Western Interior Basin of the USA---where
preservation was rigorously controlled through both optical and
geochemical  analyses---agree within a 5\% margin with Maximum
Deposition Ages derived from detrital zircons. In the samples studied
here, elemental mapping (Figure~\ref{fig7}) defined two zones with
distinct spatial distribution of U and \tsup{238}U/\tsup{206}Pb. The
first one, corresponding to the inner and outer layers as well as the
fractures and pores, was characterized by variable and high U and Th
contents, along with high Mn and Pb and low \tsup{238}U/\tsup{206}Pb.
This zone showed evidence of contamination with detrital material in
both optical and cathodoluminescence images. The second zone, located
in the core of the prismatic calcite, exhibited lower U ({${<}$}1~ppm),
Th, Mn and Pb and relatively high and variable
\tsup{238}U/\tsup{206}Pb ratios. Optical and cathodoluminescence
imaging indicated that this zone was well preserved.

\begin{figure*}
\includegraphics{fig09}
\vspace*{2pt}
\caption{\label{fig9}Stratigraphic position of the studied localities
(H) in time scale showing standard ages (A), geomagnetic polarity (B),
polarity zones (C), stages (D), local continental facies (E),
succession of continental formations withing Aix-en-Provence Basin (F)
and ootaxa stratigraphic distribution (G), modified after
\citet{GarciaVianeyLiaud2001}, \citet{CojanMoreau2006}, 
\citet{Tortosa2014}, \citet{Philipetal2017}, \citet{Gradsteinetal2020} and
\citet{TortosaLeleu2021}. Radiometric U--Pb ages (blue boxes) and the
repositioning of localities based on the biostratigraphic synthesis
(red boxes). Abbreviations: Beg. ${=}$\ Begudian, D. ${=}$\ Danian, Sant.
${=}$\ Santonian, Sel. ${=}$\ Selandian, Than. ${=}$\  Thanetian, V. ${=}$\
 Valdonnian, Vit. ${=}$\ Vitrollian.}
\end{figure*}

U--Pb spot analyses in the well-preserved prismatic calcite of samples
VLP and CRA define Tera-Wasserburg diagrams with robust linear
alignment and consistent intercept ages (Figure~\ref{fig8}). These
results demonstrate that the U--Pb system remained closed for
approximately 68~Ma in both samples. Notably, both samples exhibit
limited radiogenic ingrowth, as evidenced by \tsup{238}U/\tsup{206}Pb
below 30---significantly lower than the expected radiogenic intercept
of around 100 for 68~Ma Tera-Wasseburg isochron (Supplementary
Figure~12). Similar \tsup{238}U/\tsup{206}Pb ranges were reported by
\citet{Chenetal2025} and \citet{Tuckeretal2025} for samples aged
between 95 and 66~Ma from diverse continental \mbox{settings.} These
consistencies in \tsup{238}U/\tsup{206}Pb are interpreted as indicative
of a shared mechanism of U incorporation during early diagenesis in the
prismatic calcite of dinosaur eggshells.

U sensitivity to redox conditions influences its geochemical behavior
and mobility during diagenesis \citep{Langmuir1978}, in contrast to Pb.
Modern avian eggs incorporate negligible U during calcification (U
{${<}$}1 ppt) \citep{Loewyetal2020}, and arguably this can be speculated
to apply to non-avian dinosaur eggs. Post-depositional incorporation of
U in CaCO\tsub{3} (as $\mathrm{UO}_{2}^{2+}$) would require calcite
dissolution-precipitation \citep{Reederetal2001}, which is inconsistent
with the pristine mineralogical preservation observed in optical, SEM,
and cathodoluminescence images of the well-preserved zones. Avian
eggshells also contain significant amounts of organic matter, such as
proteins, that impregnate the calcite matrix \citep{SmithHayward2010}.
Given that tetravalent U(IV) has a known affinity for organic matter
\citep{Boneetal2017}, the presence and spatial distribution of the
organic phase---though not analyzed during this study---could explain
both the observed heterogeneity in U distribution and the long-term
stability of the U--Pb system. If U uptake within the eggshell is
controlled by the early diagenesis of organic matter intertwined with
calcite, U uptake would be inherently linked to the bio-mineralogical
composition of the shell and its \mbox{interaction} with external factors such
as meteoritic or sediment-driven fluid circulation. U uptake would not
need dissolution--reprecipitation to take place. This mechanism could
greatly expand the applicability of U--Pb dating of dinosaur eggshells
in other \mbox{continental} deposits, as also demonstrated by the successful
results published by \citet{Chenetal2025} and \citet{Tuckeretal2025}.

\subsection{Consistency of the U--Pb ages with stratigraphy of the
sampling sites}

The two U--Pb ages are consistent with each other, with a combined age
of 67.7 ${\pm}$ 4.2 Ma (2s, $n=110$) (see also Supplementary
Figure~13), and both align with the stratigraphic age derived from
independent markers (Figure~\ref{fig9}). However, while these U--Pb
ages are broadly consistent with the expected ca.\ 70~Ma range, their
uncertainties, reaching up to 15\% due to relatively low
\tsup{238}U/\tsup{206}Pb and low U and Pb contents, remain too large to
resolve detailed stratigraphic relationships. The U--Pb ages obtained
are less precise than the local stratigraphy. Although stratigraphy in
continental deposits are often less precise than in marine deposits,
the Provence region gathered almost 80 years of litho-, bio- and
magnetostratigraphy literature limiting the input of calcite U--Pb
ages. Together with the limited range in \tsup{238}U/\tsup{206}Pb and
the low success rate discussed in the previous section, these results
highlight both the promise and current limitations of the method. In
cases where dinosaur eggshells are the only available biostratigraphic
markers, U--Pb analyses could provide a valuable complementary approach
to microstructural studies and possible age anchors in the regional
stratigraphy. Nevertheless, such analyses require thorough assessment
of sample preservation before conducting {in~situ} U--Pb
measurements, similarly to results of \citetalias{Tuckeretal2025}.

\section{Conclusion}

U--Pb dating by LA-ICP-MS was tested on Provence dinosaur eggshells.
Prior to chemical analyses, a combination of optical, SEM and
cathodoluminescence observations allowed to identify potential
contamination from detrital and secondary mineralogical phases in
borders, fractures, pores, and even within the calcite for some
samples. Over the whole set tested (seven samples), only two yielded
statically robust ages, although with elevated uncertainty (up to
16\%). These ages, nevertheless, are broadly consistent with the
independent stratigraphic framework for the study sites. The results
produced in this study showed that U--Pb dating can be applied to
non-avian dinosaur eggshells---similarly to very recent publications.
It also highlights that it is critical to conduct a thorough
determination of preservation of the eggshells with optical, SEM and
cathodoluminescence microscopy prior to conducting U--Pb analyses.

Altogether, this study shows that, despite a low success rate, U--Pb
dating of dinosaur eggshells holds significant potential. When combined
with microstructural, paleontological, and stratigraphic markers, it
provides a complementary approach for constraining the temporal
framework of continental successions that otherwise remain poorly
anchored to the global time scale. Without any other stratigraphic
markers, the application of this method is even more attractive to
estimate the age of the eggshells and the surrounding sediment. These
results pave the way for further applications on other Upper Cretaceous
localities in Europe and beyond.

\section*{CRediT authorship contribution statement}

\textbf{Abel Guihou:} Conceptualization, Formal analysis,
Investigation, Methodology, Resources, Validation, Visualization,
Writing---original draft, Writing---review \& editing. 

\noindent
\textbf{Baptiste Such\'{e}ras-Marx:} Conceptualization, Investigation,
Project administration, Validation, Visualization, Writing---original
draft, Writing---review \& editing. 

\noindent
\textbf{Thierry Tortosa:} Investigation, Resources, Visualization,
Writing---original draft, Writing--review \& editing. 

\noindent
\textbf{Pierre Deschamps:} Resources. 

\noindent
\textbf{Yves Dutour:} Resources.

\section*{Acknowledgments}

We warmly thanks Julien Longerey for the preparation of the plugs and
help with the SEM. U--Pb analyses were performed at CEREGE by equipment
acquired in the frame of the Initiative d'Excellence of Aix-Marseille
University---A$^{*}$Midex, DatCarb project. We gratefully acknowledge
the D\'{e}partement des Bouches-du-Rh\^{o}ne and J.-M. Perrin, its
elected representative for the promotion of Provence's paleontological
and archaeological heritage, for their continuous support, excavation
authorization, and administrative assistance. We are also indebted to
the Direction de l'Environnement, des Grands Projets et de la Recherche
(E. Mangion, H. Souan, M. Bourrelly) and and numerous volunteers during
the field campaigns on the R\'{e}serve Naturelle de Sainte-Victoire for
their help in the field and logistical coordination since 2015. We
further thank the staff of the Mus\'{e}um d'Histoire Naturelle
d'Aix-en-Provence (S. Berton, M. Desparoir, Nicolas Vialle, Eric
Turini). Part of TT's work was supported by a PhD CIFRE 62/2008
grant from the French government and the city of Aix-en-Provence.
Finally, we thanks the two anonymous reviewers and the editorial team
for their comments that greatly improved the manuscript.

\CDRGrant[French government]{CIFRE 62/2008}

\printCOI

\section*{Supplementary materials}

Supporting information for this article is available on the journal's
website under \printDOI\ or from the author.

\CDRsupplementaryTwotypes[application/zip]{supplementary-material}{\cdrattach{crgeos-338-suppl.zip}}

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