# Triple oxygen isotopes in eggshell carbonate as a proxy of late Cenozoic CO2 and primary productivity

Vincent J. Hare, Drake A. Yarian, J. Tyler Faith, Chris Harris, Julia A. Lee-Thorp, Benjamin H. Passey, Kathryn G. Sokolowski, Loïc Segalen

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## To cite this version:

Vincent J. Hare, Drake A. Yarian, J. Tyler Faith, Chris Harris, Julia A. Lee-Thorp, et al., Triple oxygen isotopes in eggshell carbonate as a proxy of late Cenozoic CO2 and primary productivity. Geochimica et Cosmochimica Acta, 2025, 399, pp.48-63. 10.1016/j.gca.2025.04.002. hal-05267610

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# Triple oxygen isotopes in eggshell carbonate as a proxy of late Cenozoic CO₂ and primary productivity

Vincent J. Hare<sup>a,b,D</sup>,*, Drake A. Yarian<sup>a,b,c</sup>, J. Tyler Faith<sup>d,e,a ID</sup>, Chris Harris<sup>i ID</sup>, Julia A. Lee-Thorp<sup>f ID</sup>, Benjamin H. Passey<sup>g</sup>, Kathryn G. Sokolowski<sup>e</sup>, Loïc Ségalen<sup>h ID</sup>

## ARTICLE INFO

Associate editor: Stefano M. Bernasconi

Dataset link: (https://github.com/vinhare/MC-MC-17O)

**Keywords:**

Triple oxygen isotopes

Animal body water

Paleoclimate

Ostrich eggshell

Global primary productivity

Biomineral carbonate

## ABSTRACT

The triple oxygen isotope composition of biominerals is a promising recorder of changes in global primary productivity (GPP), as well as environment and animal physiology. However, application is largely unexplored, particularly in many regions of the world where eggshell is a common component of paleontological/archeological sites of the late Cenozoic. Ratites (ostriches and their relatives), as nonobligate drinkers, gain most of their oxygen from atmospheric O₂ and leaves, meaning that their eggshell should carry a strong imprint of anomalous ¹⁷O in atmospheric O₂ - which is ultimately related to GPP and CO₂ levels. In this study, we analyzed fossil eggshells from different climate states of the late Cenozoic, notably the Middle Miocene, Late Miocene, and Last Glacial Maximum (LGM), as well as modern eggshell from the same region, southern Africa. We interpret our results using an existing animal body water model, which we modify for parameter estimation using Bayesian inverse methods. Our results show that the predominant signal in the triple isotopic composition of biomineral carbonate is that of global carbon cycling (i.e. the ratio of GPP:CO₂), meaning that with further refinement, a relatively common material can be used to reconstruct changes in planetary primary productivity for periods beyond the ice core record. During the Middle Miocene, we find that GPP was significantly lower than today, at 95% confidence. Comparison with box-model output of the atmospheric O₂ budget shows that Middle Miocene GPP levels dropped to below 60% of modern values, assuming that Middle Miocene CO₂ levels were between 441 and 472 ppm (95% confidence). The result is discussed, with potentially important implications for future climate change.

## 1. Introduction

Historically, variations in the ¹⁸O/¹⁶O ratio of biominerals have been widely used to study a variety of processes including animal physiology, diet, and climate (Longinelli, 1984; Kohn et al., 1996; Fricke et al., 1998; Levin et al., 2006). Natural variations in the third, least abundant stable isotope of oxygen, ¹⁷O (abundance range 0.037 – 0.040%), are presently less widely used. However, variations in both the ¹⁸O/¹⁶O and ¹⁷O/¹⁶O ratios of biominerals (“triple oxygen isotopes”) are increasingly the focus of study (Pack et al., 2013; Passey et al., 2014; Lehmann et al., 2022; Feng et al., 2022). Triple oxygen

isotopes provide a nuanced understanding of isotopic variations in natural systems; offering insights into processes that are often masked when only ¹⁸O/¹⁶O ratios are employed (Sharp et al., 2018; Miller and Pack, 2021). In nature, the δ¹⁷O value tends to be around half that of the δ¹⁸O value, for any given oxygen-containing material. This relationship exists because different processes such as exchange or diffusion fractionate ¹⁷O roughly half as much as they fractionate ¹⁸O: for instance; the fractionation exponent, θeq = ln(¹⁷α)/ln(¹⁸α), for equilibrium exchange between water vapor and liquid water is 0.529 (Barkan and Luz, 2005). In general, small deviations from such

<footnote><sup>a</sup> Stable Light Isotope Laboratory, Department of Archaeology, University of Cape Town, South Africa</footnote>

<footnote><sup>b</sup> Node for Isotope Biogeochemistry, BIOGRIP, University of Cape Town, South Africa</footnote>

<footnote><sup>c</sup> Department of Earth and Planetary Sciences, Yale University, New Haven, CT, USA</footnote>

<footnote><sup>d</sup> Natural History Museum of Utah, Salt Lake City, UT, 84108, USA</footnote>

<footnote><sup>e</sup> Department of Anthropology, University of Utah, Salt Lake City, UT, 84112, USA</footnote>

<footnote><sup>f</sup> School of Archaeology, University of Oxford, Oxford, UK</footnote>

<footnote><sup>g</sup> Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109, USA</footnote>

<footnote><sup>h</sup> Univ Rouen Normandie, Université Caen Normandie, CNRS, Normandie Univ, M2C UMR 6143, F-76000 Rouen, France</footnote>

<footnote><sup>i</sup> Department of Geological Sciences, University of Cape Town, South Africa</footnote>

<footnote>* Corresponding author.
E-mail address: vincent.hare@uct.ac.za (V.J. Hare).</footnote>
mass-dependent relationships between δ¹⁷O and δ¹⁸O are represented by

$$ \Delta^{\prime 17}O = \delta^{\prime 17}O - \theta \delta^{\prime 18}O, \qquad (1) $$

where the prime notation δ'¹⁷O is used for the logarithmic form of the δ-value, e.g.

$$ \delta^{\prime 17}O = 1000 \ln(\delta^{\prime 17}O/1000 + 1), \qquad (2) $$

and a similar expression exists for δ'¹⁸O. For Earth surface processes, the variation in Δ'¹⁷O values is small; typically, on the order of 10 – 100 per meg (or equivalently, ppm). For meteoric water experiencing Rayleigh distillation, θ = 0.528 (Blunier et al., 2002; Luz and Barkan, 2010). By convention, this value of θ is used to calculate Δ'¹⁷O values for all terrestrial systems that are strongly influenced by meteoric waters (Bao et al., 2016; Miller and Pack, 2021), such as biominerals. In the present study, we adopt the same value.

Although most materials are expected to fall on a line in δ'¹⁷O – δ'¹⁸O space with a slope of θ (or very close to this slope), significant deviations from such mass-dependent relationships can sometimes be found in nature. Of particular interest is stratospheric O₂, which undergoes mass-independent fractionation, with θ ≈ 1 (Heidenreich and Thiemens, 1983; Young et al., 2014). The resulting ¹⁷O anomaly is transported down to the troposphere, where O₂ is significantly depleted in ¹⁷O relative to other gases bearing oxygen. Measurements of the present-day tropospheric Δ'¹⁷O (O₂) anomaly vary according to different standardization schemes and analytical techniques (Miller and Pack, 2021), but range between –451 per meg (Barkan and Luz, 2005) and –422 per meg (Pack et al., 2017) with respect to the conventional slope of θ = 0.528, with an average value converging on around –434 per meg (Passey and Levin, 2021) for all studies.

The ¹⁷O anomaly in O₂ is driven by the stratospheric reaction cycle, primarily the photodissociation of O₃ into an excited state of atomic oxygen, O(¹D), and subsequent isotopic exchange of O(¹D) with stratospheric CO₂ (Young et al., 2014). Higher atmospheric CO₂ concentrations (or lower O₂:CO₂ ratios) allow for increased exchange with O(¹D), thereby increasing the ¹⁷O anomaly — leading to lower Δ'¹⁷O (O₂) values. The negative anomaly in Δ'¹⁷O (O₂) is then passed down to the troposphere. Because tropospheric O₂ and CO₂ are key components of the global carbon cycle, the ¹⁷O anomaly is partially removed by global processes such as photosynthesis and respiration (Bender et al., 1994). Tropospheric O₂ thus carries a unique isotopic signature, reflecting a balance between isotope anomalies produced in the stratosphere and their subsequent modification through biospheric processes at the surface. In this context, the Δ'¹⁷O value of atmospheric O₂ is sensitive to the relative contributions of gross primary productivity (GPP) and CO₂ ratios (see schematic in Fig. 1). Higher GPP levels reduce the ¹⁷O anomaly in atmospheric O₂ by facilitating greater exchange with ocean and terrestrial waters (mostly leaf water-associated oxygen). The result is higher Δ'¹⁷O (O₂) values. On the other hand, increasing atmospheric CO₂ levels drive Δ'¹⁷O (O₂) values lower, (partially) counterbalancing the increases in Δ'¹⁷O (O₂) due to GPP.

The relationship between Δ'¹⁷O and GPP:CO₂ has been used to evaluate changes in planetary primary productivity over Quaternary glacial-interglacial cycles, using ice core records of atmospheric O₂ (Bender et al., 1994; Blunier et al., 2002, 2012). During glacial periods, Δ'¹⁷O (O₂) is up to 40 per meg higher than in interglacials, with a tight anticorrelation between Δ'¹⁷O and atmospheric CO₂ concentrations. Within glacials, the two variables are only decoupled at mid-glacial stages, indicating modest changes in GPP (range between –10 and +15% of full glacial values, Yang et al. (2022): Fig. 4). The decoupling between CO₂ and Δ'¹⁷O is more pronounced when comparing mid-glacial stages to the present day, with productivity during the last mid-glacial period estimated to be 55%–87% of modern (Pre-Industrial) levels.

<figure><img src="image_5.png" /><figcaption>Fig. 1. Schematic showing the sources of variability in the triple oxygen isotope composition of animal body water, Δ'¹⁷O<sub>bw</sub> (center of figure). Animal body water oxygen reflects the balance of both inhaled tropospheric O₂ (left box), and ingested plant and meteoric water O₂ (right box). Direction of Δ'¹⁷O (O₂) change shown for relative increases in GPP and CO₂. The parameters influencing body water composition include: body mass (m), the fraction of H₂O in food (f<sub>H₂O-in-food</sub>), and the Water Economy Index (WEI). These factors are considered by different animal body water models (Hu et al., 2023; Feng et al., 2024), and are discussed in Section 1.3. The direction of each arrow, for the central box, indicates the direction of Δ'¹⁷O (O₂) change for a relative increase in each parameter.</figcaption></figure>

### 1.1. Triple oxygen isotopes in biominerals as a proxy of CO₂/GPP

Ice core studies provide a detailed view of biospheric productivity changes, and their relationship to past CO₂ levels. However, there at present are few proxies to assess changes in planetary productivity for timescales beyond the current limit of ice core records (i.e. ~800 ka). The lack of information becomes especially important when considering that climate states of the late Cenozoic, such as the warmer climates of the Miocene Epoch (Steinthorsdottir et al., 2021), are considered analogues for near-future anthropogenic warming, under a higher CO₂ atmosphere. Beyond Quaternary ice core records, the potential of Δ'¹⁷O values of terrestrial biomineral apatite as a CO₂/GPP proxy was first suggested by Pack et al. (2013), and subsequently applied to mammalian teeth from the Palaeocene-Eocene Thermal Maximum, ca. 55.8 Ma (Gehler et al., 2016). The logic behind this proxy is that animals inherit a substantial proportion of the tropospheric anomaly ¹⁷O through metabolic respiration (CH₂O + O₂ → CO₂ + H₂O), thus transferring the anomaly to the body water pool and from there to bioapatite, which forms under equilibrium conditions and within the relatively narrow range of animal body temperature. However, unlike ice core records, the isotopic composition of body water (hence, bioapatite) is modulated by animal-specific factors such as physiology, mass, and dietary behavior (Pack et al., 2013; Feng et al., 2022; Hu et al., 2023; Feng et al., 2024). Globally, meteoric waters range between approximately +60 to –60 per meg on the VSMOW-SLAP scale (Aron et al., 2021). Leaf water Δ'¹⁷O values are similarly high, ranging between +21 and –150 per meg according to a survey of European locations (Landais et al., 2006). Consequently, biomineral Δ'¹⁷O values lie somewhere between those of very negative inhaled atmospheric Δ'¹⁷O (O₂), and higher, ingested meteoric and leaf water Δ'¹⁷O values (Fig. 1).

The first measurements of the triple oxygen isotope composition of biomineral carbonate were made by Passey et al. (2014), focusing on bird and dinosaur eggshells, as well as mammalian tooth enamel (also see the studies of Lehmann et al. (2022) and Feng et al. (2022)). These studies reveal that a significant ¹⁷O depletion exists in biominerals relative to meteoric waters, indicating that biomineral carbonate also carries the imprint of inhaled atmospheric O₂, modulated by
2023, Table 5), achieved by brute force Monte Carlo sampling, shows that the 5 parameters with the most significant influence on emu body water $\delta^{18}$O$_{bw}$ values in the Hu2023 model are (in order of most to least significant):

1. RH, relative humidity,

2. $\delta^{18}$O$_{mw}$, of meteoric water,

3. $f_{H_2O-in-food}$, the fraction of food-associated free H$_2$O,

4. $r_{l/s}$, the proportion of leaves consumed in relation to both leaves and stems, and

5. WEI, the Water Economy Index, a measure of the water use per unit of metabolized energy (Nagy and Peterson, 1988).

The first two of these parameters depend on environment, the second two relate to diet and ecology, and the third to animal physiology. The parameters with the most influence on body water $\Delta^{17}$O$_{bw}$ are identical to the ones listed above, but in a different order, and include $\Delta^{17}$O (O$_2$) in place of $\delta^{18}$O$_{mw}$ (Hu et al., 2023). Collectively, these parameters are the most important inputs to Hu2023. Note that almost all of these parameters, with the addition of body mass, may be unknown in paleo contexts.

The Hu2023 model was previously applied to eggshell data from emus (Hu et al., 2023) and therefore poses several advantages as a useful starting point for our study. First, the parameter set focused on by these authors is specific to ratites (the model itself is a generalized model for terrestrial vertebrates, with parameters set to make it specific for different taxa). Second, it can be trained on $\Delta^{17}$O$_{bw}$ and $\delta^{18}$O$_{mw}$ measurements from modern eggshells, for which the above parameters are independently constrained. Third, it provides a convenient basis for inversion to solve for some (or all) of the above parameters in a Bayesian framework, given $\Delta^{17}$O$_{bw}$ and $\delta^{18}$O$_{mw}$ measurements. The ultimate aim here is to infer the $\Delta^{17}$O value of atmospheric O$_2$ from fossil eggshell, whilst at the same time obtaining the parameters which relate to animal physiology and dietary behavior (as a check on the inversion strategy, and the reasonableness of the model itself). Whilst the Hu2023 model is not new, it has never been used to obtain the $\Delta^{17}$O value of atmospheric O$_2$ in this way.

The specific predictions of our study are as follows:

1. ratites, as nonobligate drinkers, should reflect a greater proportion of atmosphere-derived $^{17}$O,

2. the triple oxygen isotope composition of ratite body water can be used to reconstruct the triple oxygen isotope composition of atmospheric O$_2$, if physiological and dietary factors are accounted for,

3. periods of highest CO$_2$ will result in lowest body water $\Delta^{17}$O values, and vice versa (assuming no change in GPP),

4. conversely, periods of lowest GPP will result in lowest body water $\Delta^{17}$O values, and vice-versa (assuming no change in CO$_2$), and

5. within a given time period, body water from the same region (i.e. reflecting similar parent water) should plot on an unique curve in $\Delta^{17}$O – $\delta^{18}$O space.

## 2. Materials & methods

### 2.1. Selection and preparation of ratite eggshell

In this study, we present triple oxygen isotope data from two different analytical methods, as described below. Both methods standardized sample isotope measurements onto the VSMOW-SLAP abundance scale, using carbonate reference materials NBS18 and IAEA603. All samples analyzed in this work are ratite eggshell collected from southern Africa, with ages spanning the middle Miocene to modern.

Most of the samples presented in this work (sample IDs UPMC, Table 1) were originally collected from the central and southern Namib

<figure><img src="image_6.png" /><figcaption>Fig. 3. (a) Site map of ratite eggshell samples reported in this work overlain with modern mean annual precipitation (mm/yr). White squares indicate Central Namib sites, light blue triangles indicate Southern Namib sites, dark blue triangle indicates West Coast, South Africa site. (b) $\delta^{18}$O of Namib eggshell samples as originally reported by Ségalen et al. (2006), converted to the VSMOW-SLAP scale. (c) Reconstructed atmospheric pCO$_2$ (ppmv) from the Miocene to present, according to the (CenCO2PIP et al., 2023) multi-proxy integration project (purple line represents ice core data, blue line shows median and 95% credible intervals).</figcaption></figure>

Desert (Ségalen et al., 2002, 2006). Previous study on the fossil ratite eggshells from Namibia showed good preservation of microstructures and mineralogical features of the inorganic matrix (Dauphin et al., 1998). In modern ostrich eggshells, the percentage of organics is between 1.5% and 3.5% of the matrix, and these organics degrade rapidly over a few thousand years (Von Schirnding et al., 1982). For the Namibian specimens, the organic matrix was highly altered, and trace element analysis pointed to possible contamination by sediments on the shell surfaces and in the pore structures (Dauphin et al., 1998). On the other hand, the inorganic matrix of these eggshells is well-preserved, and was also extensively reported by Pickford and Dauphin (1993) and Dauphin et al. (1996). Therefore, to summarize the sample preparation performed by the previous authors (Ségalen et al., 2002, 2006); both internal and external shell surfaces were cleaned via abrasion and ultrasound, samples were pre-screened via X-ray diffraction and cathodoluminescence to verify good preservation of the low-magnesium primary calcite and generally low Mn$^{2+}$ (the main activator for luminescence in calcite) concentrations, and sample drilling was performed on the thickest parts of the shell and far from pore structures containing secondary calcite with notably high Mn$^{2+}$ (Ségalen et al., 2006). In addition, atomic absorption spectroscopy was performed on these samples at UPMC, using a Hitachi Z9100 Zeeman spectrometer. Samples had low Mg/Ca ratios (<0.004) and low Sr/Ca ratios (<0.0012), and Sr, Mn, and Mg abundances were much lower in primary eggshell calcite than in the surrounding sediments, in support of the findings of Dauphin et al. (1998).

A subset of these original studies' samples were selected for this work, with the intention of spanning the widest $\delta^{18}$O range possible for each age-region coupling (Table 1). This empirical pre-screening allowed for coverage of a wide range of potential environments (e.g. RH), and global climatic conditions, e.g. pCO$_2$ and GPP, through time (Fig. 3), as well as having the added benefit of comparing TILDAS measured $\delta^{18}$O values with those originally reported. For Miocene samples, those aged 16–12 Ma are considered Middle Miocene (Langhian, Serravalian ages), and those aged 12–5 Ma considered Late Miocene (Tortonian, Messinian ages). These samples span a number of extinct ratite species: *Namornis oshanai*, *Diamantornis corbetti*, and *Diamantornis spaggiari* from the Middle Miocene, and *Diamantornis laini* and *Diamantornis wardi* from the Late Miocene. The absolute Neogene chronostratigraphy of the Namib desert is uncertain; however, the age of these species has been determined from intracontinental correlations with other fossil
<caption>**Table 1**</caption>

Sample information. δ¹⁸O values of CO₂ evolved by acid digestion of eggshell carbonate at 70 °C by Ségalen et al. (2006) are shown in per mil (‰), and converted from the VPDB scale (that paper) to the VSMOW scale using the IUPAC recommended correction of Brand et al. (2014).

<table><thead><tr><th>Sample ID</th><th>Species</th><th>Latitude</th><th>Longitude</th><th>δ¹⁸O</th><th>Region</th><th>Epoch</th><th>Age/Stage</th></tr></thead><tbody><tr><td colspan="8"><strong>Middle Miocene (16–12 Ma), CO₂ = 441–472 ppm<sup>c</sup></strong></td></tr><tr><td>UPMC-Ro-1-NO</td><td><em>Namornis oshanai</em></td><td>-28.24</td><td>16.62</td><td>40.70</td><td>Southern Namib</td><td>Miocene</td><td>Langhian</td></tr><tr><td>UPMC-K-4-DC</td><td><em>Diamantornis corbetti</em></td><td>-28.07</td><td>16.25</td><td>46.49</td><td>Southern Namib</td><td>Miocene</td><td>Langhian</td></tr><tr><td>UPMC-AW-7-NO</td><td><em>Namornis oshanai</em></td><td>-25.38</td><td>15.65</td><td>51.35</td><td>Central Namib</td><td>Miocene</td><td>Langhian</td></tr><tr><td>UPMC-AW-4-NO</td><td><em>Namornis oshanai</em></td><td>-25.38</td><td>15.65</td><td>41.96</td><td>Central Namib</td><td>Miocene</td><td>Langhian</td></tr><tr><td>UPMC-AW-3-DC</td><td><em>Diamantornis corbetti</em></td><td>-25.38</td><td>15.65</td><td>41.85</td><td>Central Namib</td><td>Miocene</td><td>Langhian</td></tr><tr><td>UPMC-K-3-DC</td><td><em>Diamantornis corbetti</em></td><td>-28.07</td><td>16.25</td><td>34.73</td><td>Central Namib</td><td>Miocene</td><td>Langhian</td></tr><tr><td>UPMC-K-3-DS</td><td><em>Diamantornis spaggiarii</em></td><td>-28.07</td><td>16.25</td><td>32.63</td><td>Central Namib</td><td>Miocene</td><td>Serravallian</td></tr><tr><td colspan="8"><strong>Late Miocene (12–8 Ma), CO₂ = 241–392 ppm<sup>c</sup></strong></td></tr><tr><td>UPMC-RO-1-DL</td><td><em>Diamantornis laini</em></td><td>-28.24</td><td>16.62</td><td>35.40</td><td>Southern Namib</td><td>Miocene</td><td>Tortonian</td></tr><tr><td>UPMC-RO-4-DL</td><td><em>Diamantornis laini</em></td><td>-28.24</td><td>16.62</td><td>41.56</td><td>Southern Namib</td><td>Miocene</td><td>Tortonian</td></tr><tr><td>UPMC-RO-9-DW</td><td><em>Diamantornis wardi</em></td><td>-28.24</td><td>16.62</td><td>38.20</td><td>Southern Namib</td><td>Miocene</td><td>Tortonian</td></tr><tr><td>UPMC-K-11-DW</td><td><em>Diamantornis wardi</em></td><td>-28.07</td><td>16.25</td><td>35.74</td><td>Central Namib</td><td>Miocene</td><td>Tortonian</td></tr><tr><td>UPMC-AW-8-DL</td><td><em>Diamantornis laini</em></td><td>-25.38</td><td>15.65</td><td>50.04</td><td>Central Namib</td><td>Miocene</td><td>Tortonian</td></tr><tr><td>UPMC-Ts-2-DL</td><td><em>Diamantornis laini</em></td><td>-24.54</td><td>15.84</td><td>33.54</td><td>Central Namib</td><td>Miocene</td><td>Tortonian</td></tr><tr><td>UPMC-AW-27-DL</td><td><em>Diamantornis laini</em></td><td>-25.38</td><td>15.65</td><td>42.48</td><td>Central Namib</td><td>Miocene</td><td>Tortonian</td></tr><tr><td colspan="8"><strong>Last Glacial Maximum<sup>a</sup>, CO₂ = 190 ppm</strong></td></tr><tr><td>BAS-98–395</td><td><em>Struthio camelus</em></td><td>-32.99</td><td>17.98</td><td>–</td><td>West Coast, South Africa</td><td>Quaternary</td><td>MIS2</td></tr><tr><td>BAS-98–326</td><td><em>Struthio camelus</em></td><td>-32.99</td><td>17.98</td><td>–</td><td>West Coast, South Africa</td><td>Quaternary</td><td>MIS2</td></tr><tr><td>BAS-98–380</td><td><em>Struthio camelus</em></td><td>-32.99</td><td>17.98</td><td>–</td><td>West Coast, South Africa</td><td>Quaternary</td><td>MIS2</td></tr><tr><td>BAS-98–419</td><td><em>Struthio camelus</em></td><td>-32.99</td><td>17.98</td><td>–</td><td>West Coast, South Africa</td><td>Quaternary</td><td>MIS2</td></tr><tr><td>BAS-98–591</td><td><em>Struthio camelus</em></td><td>-32.99</td><td>17.98</td><td>–</td><td>West Coast, South Africa</td><td>Quaternary</td><td>MIS2</td></tr><tr><td colspan="8"><strong>Modern (Pre-Industrial)<sup>b</sup>, CO₂ = 280 ppm</strong></td></tr><tr><td>UPMC-Ka-1-SC</td><td><em>Struthio camelus</em></td><td>-28.07</td><td>16.25</td><td>47.45</td><td>Central Namib</td><td>Quaternary</td><td>Unknown</td></tr><tr><td>UPMC-Ka-2-SC</td><td><em>Struthio camelus</em></td><td>-28.07</td><td>16.25</td><td>41.39</td><td>Central Namib</td><td>Quaternary</td><td>Unknown</td></tr><tr><td>UPMC-AW-6-SC</td><td><em>Struthio camelus</em></td><td>-25.38</td><td>15.65</td><td>45.11</td><td>Central Namib</td><td>Quaternary</td><td>Unknown</td></tr><tr><td>UPMC-K-2-SC</td><td><em>Struthio camelus</em></td><td>-28.07</td><td>16.25</td><td>42.53</td><td>Central Namib</td><td>Quaternary</td><td>Unknown</td></tr><tr><td>UPMC-Ro-1-SC</td><td><em>Struthio camelus</em></td><td>-28.24</td><td>16.62</td><td>41.38</td><td>Southern Namib</td><td>Quaternary</td><td>Unknown</td></tr><tr><td>UPMC-GPP-2-SC</td><td><em>Struthio camelus</em></td><td>-28.42</td><td>16.48</td><td>39.21</td><td>Southern Namib</td><td>Quaternary</td><td>Unknown</td></tr><tr><td>UCT-6882</td><td><em>Struthio camelus</em></td><td>–</td><td>–</td><td>–</td><td>Southern Namib</td><td>Quaternary</td><td>Holocene</td></tr></tbody></table>

faunal assemblages (Pickford and Senut, 2000; Pickford et al., 1995), as well as, in the case of the Late Neogene, by U-Pb silcrete and terrestrial cosmogenic nuclide exposure dating (Ritter et al., 2023). Our age assignments of these materials follow those of previous studies (Pickford et al., 1995; Ségalen et al., 2002; Ségalen and Lee-Thorp, 2009), but are grouped into larger bins than these previous studies, and are thus more conservative estimates.

In addition, eggshells of modern ostrich (Struthio camelus) from the LGM (MIS2) and modern (Pre-Industrial) were similarly prepared. LGM samples were collected from a fossil hyaena den at Besaansklop, West Coast, South Africa, and modern samples from the central and southern Namib. These samples were abraded on the internal and external surfaces and sonicated for 10 min in deionized water. OES was drilled under 10x magnification to avoid pores. Splits of the Besaansklop ostrich eggshells analyzed here (identified by the label 'BAS' in Table 1) were dated by AMS radiocarbon at the University of Georgia's Center for Applied Isotope Studies. They range in age from 12,950 ± 35 to 13,740 ± 40 ¹⁴C years BP (~15.3 to 16.8 cal ka BP) (Sokolowski et al. Under Revision).

## 2.2. Analytical methods

We produced CO₂ from eggshell carbonate by phosphoric acid digestion. We used two different methods to determine the triple oxygen isotope composition of CO₂: (1) Tunable Infrared Laser Direct Absorption Spectroscopy (TILDAS, described in Hare et al. (2022), Perdue et al. (2022), Bajnai et al. (2023), and (2) sequential conversion of CO₂ to O₂ by reduction/fluorination, followed by extended-collection-time dual-inlet IRMS, described in Passey et al. (2014). Below, we outline the two different methods.

### 2.2.1. Isotopic analysis of eggshell by tunable infrared laser direct absorption spectroscopy

Eggshell samples (n = 22, Table 1) were analyzed using a dual-laser tunable infrared laser direct absorption spectrometer (TILDAS, Aerodyne Research Inc.), operating in “dual-inlet” mode, and interfaced with a custom-built automated preparation system built at the Stable Light Isotope Laboratory, University of Cape Town (for a detailed description of the system, see Hare et al. (2022)). Approximately 1 mg of carbonate was reacted with 100% H₃PO₄ at a temperature of 70 °C, overnight, using a Thermo GasBench II. After passing through the two GasBench nafion traps, the dried CO₂ is then directed to the automated preparation system, and trapped using liquid N₂. For each sample, the system measured the CO₂ yield, afterward diluting the thawed CO₂ to a nominal 420 µmol mol⁻¹ in 99.999% N₂, in a 500 mL spherical glass flask, specially designed to ensure adequate mixing. The total pressure, after the dilution step, was around 550 Torr at 21 °C. As a final step, a leak-tight diaphragm pump (P/N 009-0294-900, Parker Hannifin Corp, USA) circulated the sample mixture through the flask at a rate of 750 mL min⁻¹ for 2.5 min before measurements began.

In analogy to dual-inlet IRMS, sample aliquots were interleaved with a working reference gas (WR gas). Each sample aliquot or WR aliquot was measured in the TILDAS optical cell for 60 s. Changeover was rapid; the complete WR-sample-WR measurement cycle took 3 min. For each sample, between 9 and 15 measurement cycles were performed for the CO₂/N₂ mixture. The WR gas was a 50 L high-pressure cylinder of CO₂ diluted with 99.999% N₂ to a concentration of 421 µmol mol⁻¹, Air Liquide South Africa (Pty) Ltd, and regulated at around 450 Torr. When dosed into the TILDAS cell of optical absorption path length 36 m, via a critical orifice, sample and WR gases had a pressure during measurement of ~28.5 Torr, which generally varied by <50 mTorr within a single WR-sample-WR measurement cycle,

<footnote>a ¹⁴C-dated to 15.5–16.5 cal ka BP. Samples reflect an atmosphere closer to 18–20 ka BP, given a residence time of atmospheric O₂ of ~10³ years (Bender et al., 1994).</footnote>

<footnote>b Likewise, samples reflect a Pre-Industrial atmosphere, given atmospheric O₂ residence time of ~10³ years.</footnote>

<footnote>c CenCO2PIP et al. (2023) (Cenozoic CO₂ Proxy Integration Project (CenCO2PIP) Consortium), 97.5% C.I.</footnote>

<footnote>d Schmitt et al. (2012) value for 1850 CE.</footnote>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Concentration dependence of raw (uncorrected) $\Delta^{17}O_{L2}$ values measured by TILDAS, for CO$_2$ analyte evolved by phosphoric acid digestion of two carbonates at 70 °C: IAEA603 (blue circles), and NBS18 (red circles), over 6 analytical sessions, from February 2023 until June 2024. CO$_2$ analyte gas is mixed in N$_2$ to within 0.9 µmol mol$^{-1}$ of the reported value. The plot includes the standards reported in Table 2, from multiple analytical runs. The average slope, $f_{421}$, across all standards and all analytical runs is -7.7 ± 7 per meg mol µmol$^{-1}$. For the color version of this figure, the reader is directed to the online paper.</figcaption></figure>

and <100 mTorr across an entire analytical session. Cell temperatures were stable to < 5 mK within a single WR-sample-WR measurement cycle, and room temperature variability was controlled to < 0.1 K min$^{-1}$ during all measurements. All samples were run in duplicate or triplicate, as is convention in triple oxygen isotope studies (e.g. Pack et al. (2013), Passey et al. (2014)). For each sample, the first three measurement cycles were discarded, and outliers more than three scaled median absolute deviations (MAD) from the median, were removed. Approximately every 6–10 samples, duplicates of two international carbonate standards, NBS18 and IAEA603 were placed in the analytical session, and run in the same manner as the other carbonate samples, and used to normalize TILDAS data to the VSMOW-SLAP abundance scale. Raw values of all standards for all TILDAS analytical sessions, can be found in Table 2, and more information about the normalization procedure is presented below, in Section 2.2.3. For a more detailed description of the measurement procedure, see Hare et al. (2022).

### 2.2.2. Correction of TILDAS measurements for concentration dependence

All spectroscopic $\delta$-values measured by TILDAS depend on the measured concentration of the most abundant isotopologue of CO$_2$, $^{12}C^{16}O^{16}O$, denoted in this paper by [CO$_2$]. The effect arises theoretically, because there are offsets in isotopic composition between a working reference (WR) gas and an isotope abundance scale (e.g. VSMOW-SLAP), and also due to instrument-specific responses (Griffith et al., 2012; Hare et al., 2022). For triple oxygen isotopes, the concentration dependence of TILDAS $\delta$-values has been noted by previous authors (Steur et al., 2021; Bajnai et al., 2023). The concentration dependence can be eliminated if analyte gas concentrations are precisely matched to the WR gas to within 1 µmol mol$^{-1}$ or so (e.g. Bajnai et al. (2023)). However, in our study we did not match the WR concentration to the sample concentration exactly, and therefore an empirical correction was necessary.

Fig. 4 shows the concentration effect on $\Delta^{17}O$ across all analytical runs, for IAEA603 and NBS18 from February 2023 to June 2024 (data are also presented in Table 2). $\Delta^{17}O_{L2}$ is the measured value from the TILDAS laser 2 (L2). Across all runs, raw $\Delta^{17}O_{L2}$ values were negatively correlated with [CO$_2$]$_{L2}$ ($R^2$ = 0.94 for NBS18 and $R^2$ = 0.86 for IAEA603). There is a constant offset of ~ 130 per meg between

IAEA603 and NBS18. The average slope, $f_{421}$, across all standards and all runs was -7.7 ± 7 per meg mol µmol$^{-1}$, which is close to the slope recently reported by Bajnai et al. (2023) of -6 per meg mol µmol$^{-1}$, for a similar TILDAS instrument.

For this study, all $\Delta^{17}O_{L2}$ values were corrected to match the nominal concentration of the WR gas (421 µmol mol$^{-1}$), using the following equation:

$$ \Delta^{17}O_{421} = \Delta^{17}O_{L2} + f_{421}(421 - [CO_2]), \quad (3) $$

where $f_{421}$ was taken as -7.7 ± 7 per meg mol µmol$^{-1}$, and [CO$_2$] was the concentration of the most abundant isotopologue, $^{12}C^{16}O^{16}O$, measured by TILDAS. This relatively simple correction improves analytical precision. Table 2 shows the triple oxygen isotope measurements for the carbonate standards IAEA603 and NBS18, over all sessions from February 2023 until June 2024. On average, the 1$\sigma$ precision for $\Delta^{17}O_{421}$ improved by a factor of 2.8 for IAEA603, and by a factor of 1.4 for NBS18 (average improvements over all sessions).

### 2.2.3. Correction of all TILDAS measurements to VSMOW-SLAP abundance scale

After correction for scale-offs due to concentration dependence (Section 2.2.2), $\Delta^{17}O_{421}$ measurements by TILDAS were corrected to the VSMOW-SLAP abundance scale using values determined for international carbonate standards by Wostbrock et al. (2020), i.e. -0.048 $\%_0$ for NBS18 and -0.100 $\%_0$ for IAEA603. We applied a similar two point-correction to anchor our $\delta^{18}O_{L2}$ measurements to VSMOW-SLAP, using the IAEA recommended values (i.e. 28.47 $\%_0$ for IAEA603, and 7.2 $\%_0$ for NBS18). Note that both $\Delta^{17}O_{421}$ and $\delta^{18}O_{L2}$ values for CO$_2$ evolved by phosphoric acid at 70 °C are thus corrected directly to the calcite values ($\Delta^{17}O_{corr}$, Table 2) without the need to use an explicit $\theta_{acid}$ value. This approach is only possible because NBS18 and IAEA603 samples were placed regularly in the analytical runs, and digested in a similar manner to other carbonates, across all of our analytical sessions.

### 2.2.4. Isotopic analysis of eggshell by sequential acid digestion/reduction/fluorination approach (O$_2$/CO$_2$ conversion method)

For this study, an additional 5 eggshells were analyzed at Johns Hopkins University (JHU) for triple oxygen isotopes using the methods of Passey et al. (2014), with slight modifications. Briefly, eggshell calcite (~7–9 mg) was placed into silver capsules and reacted in a common bath of 100% phosphoric acid at 90 °C under vacuum to release CO$_2$. The CO$_2$ was purified and reduced to H$_2$O using an iron catalyst at 560 °C for 20 min (CO$_2$ + 4H$_2$ → CH$_4$ + 2H$_2$O). The resulting water was then fluorinated by passing through cobalt trifluoride at 360–370 °C (H$_2$O + 2CoF$_3$ → 2CoF$_2$ + 2HF + 1/2 O$_2$), as described in Passey et al. (2014) and other authors (Lehmann et al., 2022; Hu et al., 2023). The final O$_2$ product was analyzed using dual-inlet isotope ratio mass spectrometry on a Thermo Scientific MAT 253, with extended collection times to enhance precision.

Samples were run in duplicate or triplicate, and the stability of isotope measurements was checked using external standards, including international carbonates NBS18 and NBS19, an in-house carbonate (102-GC-AZ01), and a CO$_2$ gas standard (Tank#2 CO2). Water standards, SLAP2 and VSMOW2, were injected directly into the fluorination reactor to produce O$_2$ for calibration. VSMOW2 and SLAP2 analyses were interspersed throughout each analytical session for accuracy. Normalization of $\delta^{17}O$ and $\delta^{18}O$ data followed the procedure outlined by Schoenemann et al. (2013), using VSMOW2 ($\delta^{18}O$ = 0 $\%_0$, $\delta^{17}O$ = 0 $\%_0$) as the primary reference and scaling to SLAP2 ($\delta^{18}O$ = -55.5 $\%_0$, $\delta^{17}O$ = -29.7 $\%_0$) with a reference slope of $\theta$ = 0.528. In order for consistency, normalized $\delta^{17}O$ and $\delta^{18}O$ values from the oxygen analyte were all converted to carbonate equivalent values (e.g. Table 4), using fractionation factors from Huth et al. (2022), i.e. $^{18}A_{c-O_2}$ = 0.9918723, and $^{17}A_{c-O_2}$ = 0.9957458. To finalize, a correction was made for each analytical session to align our carbonate $\Delta^{17}O_c$ values for NBS19 with those reported by Wostbrock et al. (2020). Consistency across analytical sessions and with other materials, such as NBS18 and Tank#2
<caption>**Table 2**</caption>

Isotopic reproducibility of TILDAS measurements based on repeated analyses of CO₂ from reference materials IAEA603 and NBS18, after reaction with phosphoric acid at 70 °C. All values are in units of per mil (‰), unless otherwise stated, and relative to the VSMOW-SLAP scale determined by analysis of VSMOW2 and SLAP2 by Wostbrock et al. (2020), with λ = 0.528. L1 and L2 subscripts indicate simultaneous isotope measurements made on laser one and laser two, respectively. Δ¹⁷O₄₂₁ is the raw laser 2 measurement corrected for linear concentration dependence due to scale-offset errors according (see Methods Section for further details).

<table><thead><tr><th>Analytical ID</th><th>δ¹⁷O<sub>L2</sub></th><th>δ¹⁸O<sub>L2</sub></th><th>δ¹⁸O<sub>L1</sub></th><th>Δ¹⁷O<sub>L2</sub><br>(per meg)</th><th>Δ¹⁷O<sub>421</sub><br>(per meg)</th><th>[CO₂]<sub>L1</sub><br>(µmol mol<sup>-1</sup>)</th><th>Δ¹⁷O<sub>corr</sub><br>(per meg)</th><th>δ¹⁸O<sub>corr</sub></th></tr></thead><tbody><tr><td colspan="9"><strong>2023 - Session 1 - IAEA-603</strong></td></tr><tr><td>IAEA603-15</td><td>14.195</td><td>26.857</td><td>27.676</td><td>15</td><td>-189</td><td>394.6</td><td>-94</td><td>28.276</td></tr><tr><td>IAEA603-16</td><td>14.424</td><td>27.491</td><td>28.106</td><td>-91</td><td>-212</td><td>405.4</td><td>-103</td><td>28.717</td></tr><tr><td>IAEA603-17</td><td>14.248<br>avg.(±1σ)</td><td>26.995</td><td>27.814<br>27.87 (0.22)</td><td>-6<br>-27 (56)</td><td>-210<br>-204 (13)</td><td>394.5</td><td>-102<br>-100 (5)</td><td>28.418<br>28.47 (0.23)</td></tr><tr><td colspan="9"><strong>2023 - Session 2 - IAEA-603</strong></td></tr><tr><td>IAEA603-18</td><td>14.403</td><td>27.335</td><td>27.945</td><td>-30</td><td>-128</td><td>408.3</td><td>-106</td><td>28.482</td></tr><tr><td>IAEA603-19</td><td>14.468</td><td>27.486</td><td>27.970</td><td>-45</td><td>-98</td><td>414.1</td><td>-85</td><td>28.508</td></tr><tr><td>IAEA603-20</td><td>14.274</td><td>27.050</td><td>27.736</td><td>-8</td><td>-142</td><td>403.6</td><td>-117</td><td>28.265</td></tr><tr><td>IAEA603-21</td><td>14.412<br>avg.(±1σ)</td><td>27.070</td><td>28.082<br>27.93 (0.14)</td><td>119<br>10 (75)</td><td>-108<br>-119 (20)</td><td>391.6</td><td>-92<br>-100 (14)</td><td>28.623<br>28.47 (0.15)</td></tr><tr><td colspan="9"><strong>2023 - Session 3 - IAEA-603</strong></td></tr><tr><td>IAEA603-22</td><td>14.437</td><td>27.350</td><td>28.125</td><td>-4</td><td>-181</td><td>398.1</td><td>-105</td><td>28.478</td></tr><tr><td>IAEA603-23</td><td>14.455</td><td>27.519</td><td>28.059</td><td>-75</td><td>-162</td><td>409.7</td><td>-97</td><td>28.412</td></tr><tr><td>IAEA603-24</td><td>14.571</td><td>27.729</td><td>28.334</td><td>-70</td><td>-170</td><td>408.0</td><td>-100</td><td>28.690</td></tr><tr><td>IAEA603-29</td><td>14.410<br>avg.(±1σ)</td><td>27.525</td><td>27.948<br>28.12 (0.16)</td><td>-123<br>-70 (50)</td><td>-166<br>-170 (8)</td><td>415.5</td><td>-98<br>-100 (3)</td><td>28.299<br>28.47 (0.16)</td></tr><tr><td colspan="9"><strong>2023 - Session 4 - IAEA-603</strong></td></tr><tr><td>IAEA603-31</td><td>14.599</td><td>28.046</td><td>28.216</td><td>-221</td><td>-232</td><td>419.6</td><td>-87</td><td>28.266</td></tr><tr><td>IAEA603-33</td><td>14.744<br>avg.(±1σ)</td><td>28.169</td><td>28.625<br>28.42 (0.29)</td><td>-248<br>-235 (19)</td><td>-355<br>-294 (87)</td><td>407.1</td><td>-113<br>-100 (18)</td><td>28.674<br>28.47 (29)</td></tr><tr><td colspan="9"><strong>2023 - Session 5 - IAEA-603</strong></td></tr><tr><td>IAEA603-37</td><td>14.321</td><td>26.885</td><td>28.038</td><td>125</td><td>-206</td><td>378.1</td><td>-105</td><td>28.445</td></tr><tr><td>IAEA603-38</td><td>14.397</td><td>27.509</td><td>28.008</td><td>-128</td><td>-196</td><td>412.2</td><td>-101</td><td>28.414</td></tr><tr><td>IAEA603-39</td><td>14.444<br>avg.(±1σ)</td><td>27.411</td><td>28.143<br>28.063 (0.71)</td><td>-29<br>-10 (13)</td><td>-181<br>-194 (12)</td><td>401.2</td><td>-94<br>-100 (6)</td><td>28.552<br>28.47 (7)</td></tr><tr><td colspan="9"><strong>2024 - Session 1 - IAEA-603</strong></td></tr><tr><td>IAEA603-43</td><td>13.813</td><td>26.477</td><td>26.857</td><td>-167</td><td>-202</td><td>416.5</td><td>-100</td><td>30.233</td></tr><tr><td colspan="9"><strong>2024 - Session 2 - IAEA-603</strong></td></tr><tr><td>IAEA603-45</td><td>14.061</td><td>26.693</td><td>27.288</td><td>-33</td><td>-156</td><td>405.1</td><td>-109</td><td>28.271</td></tr><tr><td>IAEA603-46</td><td>14.123</td><td>26.785</td><td>27.462</td><td>-20</td><td>-158</td><td>403.1</td><td>-111</td><td>28.453</td></tr><tr><td>IAEA603-48</td><td>14.369</td><td>27.443</td><td>27.739</td><td>-121</td><td>-111</td><td>422.3</td><td>-77</td><td>28.742</td></tr><tr><td>IAEA603-50</td><td>14.061</td><td>26.610</td><td>27.324</td><td>11</td><td>-135</td><td>402.0</td><td>-95</td><td>28.309</td></tr><tr><td>IAEA603-51</td><td>14.099</td><td>26.413</td><td>27.487</td><td>152</td><td>-134</td><td>383.8</td><td>-94</td><td>28.479</td></tr><tr><td>IAEA603-53</td><td>14.201</td><td>27.043</td><td>27.583</td><td>-78</td><td>-169</td><td>409.2</td><td>-118</td><td>28.579</td></tr><tr><td>IAEA603-54</td><td>14.168<br>avg.(±1σ)</td><td>26.973</td><td>27.458<br>27.5 (0.2)</td><td>-74<br>-23 (89)</td><td>-138<br>-143 (19)</td><td>412.8</td><td>-96<br>-100 (14)</td><td>28.449<br>28.47 (0.16)</td></tr><tr><td colspan="9"><strong>2023 - Session 1 - NBS-18</strong></td></tr><tr><td>NBS18-16</td><td>3.666</td><td>6.776</td><td>7.140</td><td>88</td><td>-61</td><td>401.7</td><td>-47</td><td>7.200</td></tr><tr><td colspan="9"><strong>2023 - Session 2 - NBS-18</strong></td></tr><tr><td>NBS18-17</td><td>3.604</td><td>6.749</td><td>7.194</td><td>40</td><td>-71</td><td>406.6</td><td>-65</td><td>6.996</td></tr><tr><td>NBS18-18</td><td>3.667</td><td>6.721</td><td>7.222</td><td>119</td><td>-20</td><td>403.1</td><td>-27</td><td>7.026</td></tr><tr><td>NBS18-19</td><td>3.953</td><td>7.353</td><td>7.730</td><td>70</td><td>-56</td><td>404.6</td><td>-54</td><td>7.551</td></tr><tr><td>NBS18-20</td><td>3.848<br>avg.(±1σ)</td><td>7.239</td><td>7.416<br>7.4 (0.3)</td><td>25<br>70 (90)</td><td>-38<br>-46 (22)</td><td>412.9</td><td>-41<br>-48 (16)</td><td>7.227<br>7.20 (0.26)</td></tr><tr><td colspan="9"><strong>2023 - Session 3 - NBS-18</strong></td></tr><tr><td>NBS18-21</td><td>3.661</td><td>6.759</td><td>7.241</td><td>92</td><td>-67</td><td>400.4</td><td>-56</td><td>7.299</td></tr><tr><td>NBS18-22</td><td>3.618</td><td>6.569</td><td>7.197</td><td>150</td><td>-66</td><td>392.9</td><td>-56</td><td>7.255</td></tr><tr><td>NBS18-23</td><td>3.732</td><td>6.729</td><td>7.279</td><td>179</td><td>-41</td><td>392.5</td><td>-45</td><td>7.339</td></tr><tr><td>NBS18-24</td><td>3.588</td><td>6.459</td><td>6.975</td><td>177</td><td>-34</td><td>393.6</td><td>-42</td><td>7.030</td></tr><tr><td>NBS18-26</td><td>3.868</td><td>7.118</td><td>7.405</td><td>110</td><td>-17</td><td>404.5</td><td>-35</td><td>7.466</td></tr><tr><td>NBS18-27</td><td>3.570</td><td>6.538</td><td>6.959</td><td>118</td><td>-63</td><td>397.5</td><td>-54</td><td>7.013</td></tr><tr><td>NBS18-31</td><td>3.652</td><td>6.715</td><td>7.053</td><td>107</td><td>-46</td><td>401.3</td><td>-47</td><td>7.109</td></tr><tr><td>NBS18-32</td><td>3.631<br>avg.(±1σ)</td><td>6.834</td><td>7.033<br>7.14 (0.16)</td><td>23<br>12 (5)</td><td>-48<br>-48 (17)</td><td>411.8</td><td>-48</td><td>7.088<br>7.20 (0.16)</td></tr><tr><td colspan="9"><strong>2023 - Session 4 - NBS-18</strong></td></tr><tr><td>NBS18-33</td><td>3.722</td><td>7.044</td><td>7.268</td><td>3</td><td>-79</td><td>410.4</td><td>-55</td><td>7.390</td></tr><tr><td>NBS18-34</td><td>3.576<br>avg.(±1σ)</td><td>6.541</td><td>6.887<br>7.08 (0.27)</td><td>122<br>60 (80)</td><td>-14<br>-50 (50)</td><td>403.4</td><td>-41<br>-48 (10)</td><td>7.01<br>7.20 (0.27)</td></tr><tr><td colspan="9"><strong>2023 - Session 5 - NBS-18</strong></td></tr><tr><td>NBS18-38</td><td>3.570</td><td>6.120</td><td>7.351</td><td>339</td><td>-100</td><td>364.0</td><td>-53</td><td>7.278</td></tr><tr><td>NBS18-40</td><td>3.672<br>avg.(±1σ)</td><td>6.803</td><td>7.199<br>7.28 (0.11)</td><td>81<br>210 (18)</td><td>-73<br>-87 (19)</td><td>401.0</td><td>-39<br>-48 (9)</td><td>7.122<br>7.20 (0.11)</td></tr></tbody></table>

(continued on next page)
<table><caption>**Table 2 (continued).**</caption><thead><tr><th>Analytical ID</th><th>δ<sup>17</sup>O<sub>L2</sub></th><th>δ<sup>18</sup>O<sub>L2</sub></th><th>δ<sup>18</sup>O<sub>L1</sub></th><th>Δ<sup>'17</sup>O<sub>L2</sub><br>(per meg)</th><th>Δ<sup>'17</sup>O<sub>L2</sub><br>(per meg)</th><th>[CO<sub>2</sub>]<sub>L1</sub><br>(μmol mol<sup>-1</sup>)</th><th>Δ<sup>'17</sup>O<sub>corr</sub><br>(per meg)</th><th>δ<sup>18</sup>O<sub>corr</sub></th></tr></thead><tbody><tr><td colspan="9"><strong>2024 - Session 1 - NBS-18</strong></td></tr><tr><td>NBS18-41</td><td>3.586</td><td>7.108</td><td>6.887</td><td>-167</td><td>-85</td><td>431.7</td><td>-57</td><td>6.910</td></tr><tr><td>NBS18-43</td><td>3.848<br>avg.(±1σ)</td><td>7.213</td><td>7.383<br>7.14 (0.35)</td><td>40<br>-60 (15)</td><td>-34<br>-60 (36)</td><td>411.5</td><td>-39<br>-48 (13)</td><td>7.489<br>7.20 (0.41)</td></tr><tr><td colspan="9"><strong>2024 - Session 2 - NBS-18</strong></td></tr><tr><td>NBS18-46</td><td>3.402</td><td>6.263</td><td>6.745</td><td>95</td><td>-78</td><td>398.7</td><td>-53</td><td>6.855</td></tr><tr><td>NBS18-47</td><td>3.662</td><td>6.972</td><td>7.140</td><td>-19</td><td>-89</td><td>412.0</td><td>-61</td><td>7.267</td></tr><tr><td>NBS18-48</td><td>3.555</td><td>6.550</td><td>6.870</td><td>97</td><td>-70</td><td>399.4</td><td>-47</td><td>6.986</td></tr><tr><td>NBS18-49</td><td>3.619</td><td>6.127</td><td>7.090</td><td>384</td><td>-36</td><td>366.5</td><td>-22</td><td>7.215</td></tr><tr><td>NBS18-50</td><td>3.854</td><td>7.412</td><td>7.413</td><td>-59</td><td>-81</td><td>418.2</td><td>-55</td><td>7.552</td></tr><tr><td>NBS18-51</td><td>3.735<br>avg.(±1σ)</td><td>6.998</td><td>7.194<br>7.08 (0.24)</td><td>40<br>89 (16)</td><td>-63<br>-70 (19)</td><td>407.7</td><td>-42<br>-48 (13)</td><td>7.323<br>7.20 (0.25)</td></tr></tbody></table>

CO₂, confirmed the reliability of this correction. Further details on normalization procedures are available in Passey et al. (2014).

### 2.2.5. Overall reproducibility of isotope measurements in this study

There is presently no established community standard protocol for reporting and normalizing high-precision triple oxygen isotope data from carbonates. However, our strategy is to align both TILDAS and IRMS Δ¹⁷⁰O results with values for VSMOW2 and SLAP2 reported by Wostbrock et al. (2020), facilitating consistency across different laboratories and techniques, as recommended by Sharp and Wostbrock (2021).

For TILDAS measurements (Table 2), the average 1σ reproducibility of Δ¹⁷⁰O<sub>corr</sub> values was 11 per meg, for both NBS18 and IAEA603 (pooled standard error = 7 per meg, across 7 sessions). The average 1σ reproducibility of δ¹⁸O<sub>corr</sub> was 0.17 ‰ for IAEA603 and 0.24 ‰ for NBS18. For the samples measured by IRMS, pooled standard deviation (1σ) for the reference materials was 0.9 ‰ for δ¹⁸O and 10 per meg for Δ¹⁷⁰O (i.e. comparable with TILDAS measurements).

Additionally, it is possible to compare both TILDAS and IRMS measurements (“conversion method”) with previously-published measurements of δ¹⁸O<sub>corr</sub> for the same carbonate samples. Fig. 5 shows that there is a 1:1 relationship between the original values of Ségalen et al. (2006). With the exception of just one sample (UPMC-AW-4-NO), the general relationship is evidence for acceptable agreement between both TILDAS and IRMS techniques used in this study.

For TILDAS, we have observed that the average values of uncorrected standards can shift slightly between analytical sessions. The average spacing between Δ¹⁷⁰O<sub>L2</sub> values of NBS18 and IAEA603 ranges between -73 per meg and -250 per meg (average spacing = -130 per meg). We have observed that this spacing changes with abrupt shifts in instrumental parameters (e.g. laser tuning rate, defined by the user), or optical purge flow rate (N₂, which is used through the beam path outside of the optical cell). These effects are still not fully understood, and underscore the importance of regularly interleaving several international standards within a session.

### 2.3. Conversion of eggshell isotope data to body water equivalent values

To enable direct comparison of our triple oxygen isotope data with the body water model of Hu et al. (2023), we chose to convert carbonate isotopic data to the body water reference frame. We used the following relationship: δ¹⁸O<sub>bw</sub> = (1/¹⁸α<sub>c-bw</sub>)(1000+δ¹⁸O<sub>c</sub>) - 1000, where ¹⁸α<sub>c-bw</sub> is the CaCO₃·H₂O fractionation factor. For all samples this was 1.0258 ± 0.0008 (95% C.I.), which is the value determined by Passey et al. (2014). To calculate Δ¹⁷⁰O<sub>bw</sub> we used a fractionation exponent of λCaCO₃·H₂O = 0.5246 ± 0.0003, which is the eggshell mean and 95% C.I. for all samples from Passey et al. (2014). Note that in that paper, ¹⁸α<sub>c-bw</sub> was originally multiplied by 1.0081, which is the fractionation factor for acid digestion at 90 °C (Kim and O'Neil, 1997), to yield a CO₂·H₂O fractionation factor of 1.0379.

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Oxygen isotope composition of carbonate CO₂ sampled in this study (y-axis) versus those obtained in the previous study of Ségalen et al. (2006) for the same samples (x-axis, values also in Table 1), showing good general agreement between the different methods. Open circles are measurements made by TILDAS, after acid digestion at 70 °C. Filled triangles show JHU samples, for which CO₂ was evolved after acid digestion at 90 °C, and converted to O₂ analyte and analyzed on a Thermo MAT 253 mass spectrometer. Hence, JHU samples are converted to the 70 °C reference frame assuming CO₂·CaCO₃ fractionation factors from Kim and O'Neil (1997).</figcaption></figure>

### 2.4. Bayesian implementation of body water model for triple oxygen isotopes of eggshell

We applied a Bayesian parameter estimation method using Markov Chain Monte Carlo (MCMC) to interpret our triple oxygen isotope data. A MCMC Bayesian framework generates parameter distributions that iteratively converge towards an optimal solution. This approach was applied to the Hu et al. (2023) animal body-water isotope model, allowing for robust estimation of physiological and environmental parameters such as δ¹⁸O<sub>mw</sub> (meteoric water oxygen isotope values), WEI (Water Economy Index), and r<sub>1/s</sub> (the ratio of leaves to stems consumed) from our measured δ¹⁸O<sub>bw</sub> and Δ¹⁷⁰O<sub>bw</sub> values from eggshell carbonate. Given the complexity of the model and the lack of direct analytical solutions for inverse problems with multiple poorly-constrained parameters, the MCMC framework was chosen for its ability to account for uncertainties and propagate errors efficiently.

The MCMC procedure was implemented in MATLAB using the DRAM (Delayed Rejection Adaptive Metropolis) algorithm (Haario et al., 2006), which is well-suited for parameter estimation problems in isotope geochemistry (Hare and Lavergne, 2021). The MATLAB MCMC toolbox (mjlaine.github.io/mcmcstat) was utilized to maximize the likelihood of observed Δ¹⁷⁰O values from biominerals, given the parameters of interest. Briefly, in a Bayesian framework, our MCMC
<caption>**Table 3**</caption>

Choice of parameter priors used in this study for the Bayesian inversion of the Hu2023 model for body water triple oxygen isotope composition. The priors denoted by $N'(\mu, \sigma^2)$ are those estimated within our MCMC Bayesian framework.

<table><thead><tr><th>Parameter</th><th>Prior (or constant)</th><th>[min, max]</th></tr></thead><tbody><tr><td><strong>Animal specific parameters</strong></td><td></td><td></td></tr><tr><td>Mass (kg)</td><td>84<sup>a</sup></td><td>–</td></tr><tr><td>Metabolic pre-exponent (Met_pre_exp)</td><td>2.955</td><td>–</td></tr><tr><td>Metabolic exponent (Met_exp)</td><td>0.727</td><td>–</td></tr><tr><td>Water economy index (WEI, ml/kJ)</td><td>N'(0.17, ∞)<sup>b</sup></td><td>[0.05,0.6]</td></tr><tr><td>Body Temperature (K)</td><td>312.15<sup>a</sup></td><td>–</td></tr><tr><td><strong>Environmental parameters</strong></td><td></td><td></td></tr><tr><td>Relative humidity (RH)</td><td>N'(0.5, ∞)</td><td>[0.1,0.9]</td></tr><tr><td>Meteoric water δ<sup>18</sup>O (δ<sup>18</sup>O<sub>mw</sub>, ‰)</td><td>N'(-4.0, 3.0<sup>2</sup>)<sup>c</sup></td><td>[-30,15]</td></tr><tr><td>Meteoric water Δ<sup>17</sup>O (Δ<sup>17</sup>O<sub>mw</sub>, ‰)</td><td>0.020<sup>c</sup></td><td>–</td></tr><tr><td><strong>Climatic parameters</strong></td><td></td><td></td></tr><tr><td>Atmospheric δ<sup>18</sup>O (O<sub>2</sub>, ‰)</td><td>N'(24.046, 0.107<sup>2</sup>)<sup>d</sup></td><td>[20,27]</td></tr><tr><td>Atmospheric δ<sup>17</sup>O (O<sub>2</sub>, per meg)</td><td>N'(-434, 22)<sup>d</sup></td><td>[-1500,-100]</td></tr><tr><td><strong>Food parameters (fractional)</strong></td><td></td><td></td></tr><tr><td>Food associated free H<sub>2</sub>O content (f<sub>H<sub>20</sub>-food</sub>)</td><td>0.55<sup>b</sup></td><td>–</td></tr><tr><td>Plant/(Plant+Meat) ratio</td><td>1.0</td><td>–</td></tr><tr><td>Ingested leaf/(stem+leaf) ratio (r<sub>l/s</sub>)</td><td>N'(0.75, ∞)</td><td>[0,0.1,0]</td></tr></tbody></table>

procedure maximized the log-likelihood of Δ¹⁷O, given (1) the parameters (collectively, Θ), (2) the model (i.e. function, denoted f, from Hu2023), (3) measured δ¹⁸O values in the body water reference frame, and (4) analytical errors σ:

$$ \ln \mathcal{L}(\Delta^{17}\text{O} | \Theta, \sigma, \delta^{18}\text{O}, f) = -\frac{1}{2} \sum_{n} \frac{(\Delta^{17}\text{O}_n - f(\theta, \delta^{18}\text{O}_n))^2}{\sigma_n^2} $$

Gaussian priors were set for key inputs: δ¹⁸O_mw (mean = -4 ‰, σ = 3 ‰), r₁/s (mean = 0.6), and WEI (mean = 0.17 mL kJ⁻¹). Following Hu et al. (2023), the choice of the latter two priors were based on previous values for ostriches (e.g. Williams et al. (1993)). RH is given a weakly-informative prior, with a range between 0.1 and 0.9. In other words, any RH between 10% and 90% is considered equally likely (also see Table 3). Our choice is motivated by the consideration that terrestrial photosynthesis (which drives leaf water Δ¹⁷O values lower, at lower RH) does not generally occur at 100% RH, or 0% RH. 10% to 90% is also a somewhat conservative range, because it is greater than that inferred by Hu et al. (2023) for emus of between 37% and 68%. Additionally, for our procedure, δ¹⁸O_mw was assumed to lie somewhere between -30 and +15‰, which is a larger range of possible values for both modern and paleo contexts, considering contemporary measurements of southern African δ¹⁸O_mw values of between -15 to 5‰ (Geppert et al., 2022). Additionally, we assumed a Gaussian prior for δ¹⁸O_mw, with a nominal mean of -4‰ and a 1σ of about 3 ‰, which is based on the spread of δ¹⁸O_mw value for the southern African region including the West Coast of South Africa, and the Namib (Geppert et al., 2022). In practice, changing the nominal value of the prior mean for δ¹⁸O_mw did not affect the algorithm convergence. r₁/s is given a “weakly-informative” prior (infinite variance), and constrained to lie between 0 and 1 (corresponding to ratites consuming entirely stems, and entirely leaves, respectively). WEI also has a weakly-informative prior, adopted from the range for WEI suggested by the MC simulations of Hu et al. (2023). Further details of all priors, can be found in Table 3.

The model was iterated until convergence was achieved, typically within 25–30 steps, and posterior distributions for each parameter were derived from 50,000 steps. This approach allowed for simultaneous estimation of δ¹⁸O_mw, r₁/s, and WEI. Post-MCMC optimization used the MATLAB function *fminsearch*, which was applied to the joint posterior distributions of all parameters, to estimate Δ¹⁷O (O₂) more accurately.

# 3. Results

## 3.1. Temporal trends in ratite triple oxygen isotopes

Triple oxygen isotope compositions of ratite eggshells, and their body water equivalent values, can be found in Table 4. The results are plotted in Fig. 6. For each period, and for each region, Δ¹⁷O<sub>bw</sub> values vary inversely with δ¹⁸O<sub>bw</sub> values. Additionally, Fig. 6 shows that body water equivalent isotopes are strongly partitioned with climate. The highest Δ¹⁷O<sub>bw</sub> value was for the LGM (11 ± 8 per meg), whereas the lowest value was for the Middle Miocene (-217 ± 15 per meg). LGM samples share little overlap in Δ¹⁷O-δ¹⁸O space with all other samples. Data for the Late Miocene and Modern (PI) periods fall between that of the Middle Miocene and the LGM. In addition, the Middle Miocene showed the greatest range of Δ¹⁷O<sub>bw</sub> values: -101 to -173 per meg for the southern Namib, and -58 to -217 per meg for the central Namib. Data for the central and southern Namib fall on the same array during the Middle Miocene. However, for both the Late Miocene and Modern (PI), the arrays of Δ¹⁷O values from the southern Namib are lower than that of the central Namib.

Our results validate the predictions that body water equivalent data of ratites from the same region plot on unique arrays in Δ¹⁷O-δ¹⁸O space, and that the ¹⁷O anomaly is strongly reflected in ratite body water. JHU data, after standardization to the Wostbrock et al. (2020) values for IAEA603 and NBS18, show acceptable agreement with UCT data, i.e. data obtained from both methods result in arrays of similar slope on the Δ¹⁷O-δ¹⁸O biplot (Fig. 6).

## 3.2. Body water model parameters from Bayesian analysis

Best-fit parameters for the isotope-enabled body water model of Hu et al. (2023) are shown in Table 5, and corresponding Bayesian model plots are shown in Fig. 7. Models are plotted together with measured data, and the MCMC procedure was applied separately for each period and region (subfigures A-H). In addition, subfigure G shows the model fitting for previously published emu data from Queensland, Australia (Hu et al., 2023). The MCMC procedure produces reasonable fits to each dataset. Most measured data fall within the bounds of the modeled relationships for each period/region (Fig. 7, light blue curves). The two exceptions are for the central Namib, during the Late Miocene and the Middle Miocene, where two δ¹⁸O<sub>bw</sub> values fall outside of the modeled region.

<footnote>a Average ostrich mass and body temperature from Schmidt-Nielsen et al. (1969).</footnote>

<footnote>b Estimated from field studies by Williams et al. (1993).</footnote>

<footnote>c Typical environmental conditions during ratite breeding season, used by Hu et al. (2023).</footnote>

<footnote>d Atmospheric O₂ isotope data from Wostbrock et al. (2020).</footnote>
<caption>**Table 4**</caption>

Measured isotopic composition of eggshell carbonate, and equivalent body water compositions. δ¹⁸O values are in per mil (‰), and Δ¹⁷O values are in per meg units. All values are on the VSMOW-SLAP scale of Wostbrock et al. (2020), with θ = 0.528. N denotes number of sample replicates, where each sample involved acid digestion of carbonate to produce analyte gas.

<table><thead><tr><th rowspan="2">Sample ID</th><th rowspan="2">Lab.<sup>a</sup></th><th rowspan="2">N</th><th colspan="4">Measured values</th><th colspan="4">Calculated values (T = 39°C)<sup>c</sup></th></tr><tr><th>δ¹⁸O<sub>c</sub><sup>b</sup></th><th>1σ</th><th>Δ¹⁷O<sub>c</sub><sup>b</sup></th><th>1σ</th><th>δ¹⁸O<sub>bw</sub><sup>d</sup></th><th>±<sup>e</sup></th><th>Δ¹⁷O<sub>bw</sub><sup>f</sup></th><th>±<sup>e</sup></th></tr></thead><tbody><tr><td colspan="11"><strong>Central Namib - Modern (Pre-Industrial)</strong></td></tr><tr><td>UPMC-Ka-2-SC</td><td>UCT</td><td>2</td><td>41.453</td><td>0.69</td><td>-153</td><td>1</td><td>15.27</td><td>1.22</td><td>-66</td><td>8</td></tr><tr><td>UPMC-K-2-SC</td><td>JHU</td><td>2</td><td>43.555</td><td>2.22</td><td>-150</td><td>9</td><td>17.32</td><td>3.11</td><td>-64</td><td>14</td></tr><tr><td>UPMC-AW-6-SC</td><td>UCT</td><td>2</td><td>46.040</td><td>0.42</td><td>-151</td><td>3</td><td>19.74</td><td>0.98</td><td>-64</td><td>9</td></tr><tr><td>UPMC-Ka-1-SC</td><td>UCT</td><td>2</td><td>47.790</td><td>0.63</td><td>-186</td><td>4</td><td>21.45</td><td>1.17</td><td>-100</td><td>10</td></tr><tr><td colspan="11"><strong>Central Namib - Late Miocene</strong></td></tr><tr><td>UPMC-Ts-2-DL</td><td>UCT</td><td>2</td><td>33.485</td><td>0.02</td><td>-144.0</td><td>0.1</td><td>7.50</td><td>0.79</td><td>-57</td><td>8</td></tr><tr><td>UPMC-K-11-DW</td><td>JHU</td><td>2</td><td>36.735</td><td>1.98</td><td>-164</td><td>5</td><td>10.67</td><td>2.79</td><td>-77</td><td>11</td></tr><tr><td>UPMC-AW-27-DL</td><td>UCT</td><td>2</td><td>43.517</td><td>0.38</td><td>-147</td><td>11</td><td>17.28</td><td>0.95</td><td>-61</td><td>17</td></tr><tr><td>UPMC-AW-8-DL</td><td>UCT</td><td>2</td><td>49.975</td><td>0.05</td><td>-216</td><td>4</td><td>23.58</td><td>0.80</td><td>-130</td><td>9</td></tr><tr><td colspan="11"><strong>Central Namib - Middle Miocene</strong></td></tr><tr><td>UPMC-K-3-DS</td><td>JHU</td><td>2</td><td>30.804</td><td>3.46</td><td>-159</td><td>6</td><td>4.89</td><td>4.75</td><td>-72</td><td>11</td></tr><tr><td>UPMC-K-3-DC</td><td>JHU</td><td>2</td><td>33.058</td><td>2.01</td><td>-145</td><td>11</td><td>7.08</td><td>2.83</td><td>-58</td><td>17</td></tr><tr><td>UPMC-AW-3-DC</td><td>UCT</td><td>2</td><td>41.673</td><td>0.85</td><td>-246</td><td>56</td><td>15.48</td><td>1.39</td><td>-160</td><td>78</td></tr><tr><td>UPMC-AW-4-NO</td><td>UCT</td><td>4</td><td>45.267</td><td>0.91</td><td>-250</td><td>16</td><td>18.99</td><td>1.18</td><td>-164</td><td>18</td></tr><tr><td>UPMC-AW-7-NO</td><td>UCT</td><td>2</td><td>50.773</td><td>0.03</td><td>-303</td><td>9</td><td>24.35</td><td>0.80</td><td>-217</td><td>15</td></tr><tr><td colspan="11"><strong>Southern Namib - Modern (Pre-Industrial)</strong></td></tr><tr><td>UPMC-GPP-2-SC</td><td>UCT</td><td>3</td><td>39.574</td><td>0.20</td><td>-200</td><td>5</td><td>13.44</td><td>0.82</td><td>-114</td><td>10</td></tr><tr><td>UPMC-Ro-1-SC</td><td>UCT</td><td>3</td><td>41.551</td><td>0.86</td><td>-254</td><td>16</td><td>15.36</td><td>1.24</td><td>-167</td><td>19</td></tr><tr><td>UCT-6882</td><td>UCT</td><td>2</td><td>42.991</td><td>0.08</td><td>-213</td><td>40</td><td>16.77</td><td>0.80</td><td>-126</td><td>55</td></tr><tr><td colspan="11"><strong>Southern Namib - Late Miocene</strong></td></tr><tr><td>UPMC-RO-1-DL</td><td>UCT</td><td>2</td><td>35.203</td><td>0.01</td><td>-130</td><td>1</td><td>9.18</td><td>0.79</td><td>-44</td><td>8</td></tr><tr><td>UPMC-RO-9-DW</td><td>JHU</td><td>2</td><td>39.358</td><td>0.44</td><td>-207</td><td>6</td><td>13.23</td><td>0.99</td><td>-121</td><td>11</td></tr><tr><td>UPMC-RO-4-DL</td><td>UCT</td><td>2</td><td>41.446</td><td>0.33</td><td>-161</td><td>10</td><td>15.26</td><td>0.91</td><td>-75</td><td>17</td></tr><tr><td colspan="11"><strong>Southern Namib - Middle Miocene</strong></td></tr><tr><td>UPMC-K-1-NO</td><td>UCT</td><td>2</td><td>35.020</td><td>0.23</td><td>-188</td><td>20</td><td>9.00</td><td>0.85</td><td>-101</td><td>29</td></tr><tr><td>UPMC-Ro-1-NO</td><td>UCT</td><td>2</td><td>40.946</td><td>0.11</td><td>-259</td><td>25</td><td>14.77</td><td>0.81</td><td>-173</td><td>36</td></tr><tr><td>UPMC-K-4-DC</td><td>UCT</td><td>2</td><td>45.624</td><td>0.09</td><td>-235</td><td>33</td><td>19.33</td><td>0.80</td><td>-148</td><td>46</td></tr><tr><td colspan="11"><strong>West Coast (South Africa) - LGM</strong></td></tr><tr><td>BAS-98-419</td><td>UCT</td><td>2</td><td>30.219</td><td>0.31</td><td>-100</td><td>15</td><td>4.32</td><td>0.89</td><td>-14</td><td>23</td></tr><tr><td>BAS-98-380</td><td>UCT</td><td>2</td><td>32.655</td><td>2.34</td><td>-82</td><td>1</td><td>6.69</td><td>3.26</td><td>5</td><td>8</td></tr><tr><td>BAS-98-326</td><td>UCT</td><td>2</td><td>32.757</td><td>0.05</td><td>-75</td><td>2</td><td>6.79</td><td>0.79</td><td>11</td><td>8</td></tr><tr><td>BAS-98-395</td><td>UCT</td><td>2</td><td>36.245</td><td>0.07</td><td>-102</td><td>1</td><td>10.19</td><td>0.79</td><td>-16</td><td>8</td></tr><tr><td>BAS-98-591</td><td>UCT</td><td>2</td><td>37.449</td><td>1.91</td><td>-124</td><td>27</td><td>11.36</td><td>2.70</td><td>-37</td><td>38</td></tr></tbody></table>

<sup>a</sup> Laboratories were either: UCT, University of Cape Town; or JHU, Johns Hopkins University. At the UCT Lab, sample CO₂ was analyzed directly by TILDAS. JHU sample CO₂ was converted to O₂ analyte by reduction of CO₂ by H₂ to produce H₂O, followed by fluorination of H₂O to produce O₂, and analyzed on a Thermo MAT 253 mass spectrometer, as described in Methods.

<sup>b</sup> UCT samples were generated from reaction with 100% phosphoric acid at 70 °C, whereas JHU samples were generated at 90 °C.

<sup>c</sup> Body temperatures are generic estimates, and the same as used in Passey et al. (2014).

<sup>d</sup> Calculated using δ¹⁸O<sub>bw</sub> = (1/¹⁸α<sub>c-bw</sub>)(1000 + δ¹⁸O<sub>c</sub>) - 1000, where ¹⁸α<sub>c-bw</sub> is the CaCO₃-H₂O fractionation factor of 1.0258 ± 0.0008 (Passey et al., 2014). Further details in the Methods Section.

<sup>e</sup> Values are propagated errors using 95% confidence intervals reported in Passey et al. (2014). Sample errors used in the calculation are 1.96×S.E.M (standard error of measurement). S.E.M.= σ/√N. Also see Hu et al. (2023).

<sup>f</sup> Calculated using Δ¹⁷O<sub>bw</sub> = Δ¹⁷O<sub>c</sub> + 1000ln(¹⁸α<sub>c-bw</sub>)(0.528 - λ<sub>c-bw</sub>), where λ<sub>c-bw</sub> = 0.5246 ± 0.0003 (eggshell mean and 95% C.I. for all samples from Passey et al. (2014)).

Our modeled estimates of WEI, and r₁/s are presented in Table 5. WEI values fall between 0.18 (Modern/PI) and 0.27 mL kJ⁻¹ (central Namib, Middle Miocene), and all our ratites had a range of r₁/s values between 0.71 and 0.84, consistent with the field study values for modern ostriches by Williams et al. (1993). The high degree of consistency in these two parameters between ratites from different periods, and regions, gives us confidence in our modeling approach. We observe variability in the modeled δ¹⁸O<sub>mw</sub> values, which are lowest for the central Namib Middle Miocene ratites (−1.8‰) and highest for modern ostriches from the central Namib (2.3‰). For the Late Miocene, and the Modern samples, modeled δ¹⁸O<sub>mw</sub> values are ~2‰ higher in southern Namib than in the central Namib. However, this difference is not significantly different for the Middle Miocene, where southern Namib and central Namib had similar δ¹⁸O<sub>mw</sub> values (−1.4‰ and −1.8‰, respectively).

### 3.3. Δ¹⁷O (O₂) variability through time

The strongest trend in the modeled parameters (see Table 5) is for atmospheric Δ¹⁷O (O₂). Our modeled Δ¹⁷O (O₂) values show a substantial range of around ~435 per meg over different climate states of the late Cenozoic. Δ¹⁷O (O₂) values are lowest during the Middle

Miocene (−678 ± 54 per meg, pooled estimate), and highest during the LGM (−243 ± 3 per meg, single estimate). Δ¹⁷O (O₂) values for the Late Miocene and Modern (Pre-Industrial) and are within range of one another (pooled estimates of −461 ± 98 per meg and −416 ± 50 per meg, respectively), and thus lie between values for the LGM and Middle Miocene. Notably, Table 5 shows that our modeled values vary inversely with CO₂ estimates obtained from multi-proxy studies (e.g. CenCO2PIP et al. (2023)).

Because we present data from multiple regions for each timeframe, it is possible to evaluate the degree of concordance in our modeled Δ¹⁷O (O₂) values. We observe that multiple regions give concordant estimates of Δ¹⁷O (O₂) for the same period (i.e. for each “temporal ensemble”). For example, the spread in modeled Δ¹⁷O (O₂) between the central and southern Namib for the Middle Miocene is 50 per meg (1σ, n = 2), and for the Late Miocene it is 100 per meg (1σ, n = 2). The difference between the pooled estimate for the Middle Miocene and the Modern Period is greater than the spread within a particular timeframe, indicating that the “signal” of Δ¹⁷O (O₂) is still resolvable. However, it must be noted that our study is confined to only two regions for each timeframe, and more regions might be needed for a more definitive evaluation of the spread in modeled Δ¹⁷O (O₂) values. Note that this concordance approach, across different temporal ensembles is more or
<caption>**Table 5**</caption>

Fitted parameters of the isotope-enabled animal body water model of Hu et al. (2023), obtained by Bayesian inverse methods applied to the datasets in the present study. $\Delta'^{17}\text{O}$ (O₂) values are in per meg, and $\delta'^{18}\text{O}_{\text{mw}}$ is in per mil.

<table><thead><tr><th>Region</th><th>δ<sup>18</sup>O<sub>mw</sub></th><th>WEI (mL kJ<sup>-1</sup>)</th><th>r<sub>1/s</sub></th><th>Calculated Δ<sup>17</sup>O (O<sub>2</sub>)</th></tr></thead><tbody><tr><td><strong>Middle Miocene (16–12 Ma)</strong>, CO<sub>2</sub> = 441–472 ppm<sup>a</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>Cent. Namib</td><td>-1.8 ± 2.9</td><td>0.27 ± 0.16</td><td>0.67 ± 0.26</td><td>-720 ± 10</td></tr><tr><td>South. Namib</td><td>-1.4 ± 3.1</td><td>0.24 ± 0.16</td><td>0.71 ± 0.25</td><td>-640 ± 30</td></tr><tr><td></td><td></td><td></td><td><strong>avg.(±1σ)</strong></td><td><strong>-680 ± 50</strong></td></tr><tr><td><strong>Late Miocene (12–5 Ma)</strong>, CO<sub>2</sub> = 241–392 ppm<sup>a</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>Cent. Namib</td><td>-1.68 ± 3.0</td><td>0.26 ± 0.15</td><td>0.67 ± 0.27</td><td>-530 ± 10</td></tr><tr><td>South. Namib</td><td>-0.16 ± 2.9</td><td>0.20 ± 0.13</td><td>0.78 ± 0.21</td><td>-390 ± 4</td></tr><tr><td></td><td></td><td></td><td><strong>avg.(±1σ)</strong></td><td><strong>-460 ± 100</strong></td></tr><tr><td><strong>Modern (Pre-Industrial)<sup>b</sup></strong>, CO<sub>2</sub> = 280 ppm<sup>d</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>Cent. Namib</td><td>-0.2 ± 2.5</td><td>0.19 ± 0.13</td><td>0.81 ± 0.17</td><td>-332 ± 3</td></tr><tr><td>South. Namib</td><td>2.3 ± 3.6</td><td>0.18 ± 0.13</td><td>0.84 ± 0.19</td><td>-500 ± 1</td></tr><tr><td></td><td></td><td></td><td><strong>avg.(±1σ)</strong></td><td><strong>-420 ± 120</strong></td></tr><tr><td><strong>Last Glacial Maximum</strong>, CO<sub>2</sub> = 190 ppm<sup>c</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>W. Coast, S. A.</td><td>-0.7 ± 2.5</td><td>0.21 ± 0.14</td><td>0.78 ± 0.17</td><td>-243 ± 3</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Triple oxygen isotope compositions of ratite body water calculated from measurements of eggshell carbonate, reported in this study (Table 3), as well as calculated from previous ostrich eggshell measurements (Passey et al., 2014, black crosses), showing partitioning according to climate. All values are on the VSMOW-SLAP scale of Wostbrock et al. (2020), with $\lambda = 0.528$. Blue squares are West Coast (LGM). Circles are central Namib, and triangles are southern Namib. Orange is Middle Miocene, yellow is Late Miocene, and open symbols are Modern/Pre-Industrial samples. Error bars represent propagated errors using 95% confidence intervals. Further information about the error propagation can be found in Methods. For interpretation of the references to color in the legend, the reader is referred to the online version of this article.</figcaption></figure>

less an equivalent implementation of the concordance approach first proposed by Passey and Levin (2021).

# 4. Discussion

## 4.1. Trends in $\Delta'^{17}\text{O}$, and implications for late Cenozoic CO₂/GPP

Our $\Delta'^{17}\text{O}$ values for atmospheric O₂, inferred from ratite eggshell ensembles, can be compared to estimates of $\Delta'^{17}\text{O}$ (O₂) previously modeled by Young et al. (2014). The predictions of this box model, at 60%, 100%, and 140% of modern GPP levels, are shown in Fig. 8, alongside our inferred values of $\Delta'^{17}\text{O}$ (O₂) from ratite eggshell ensembles, for comparison. Fig. 8 shows that the $\Delta'^{17}\text{O}$ (O₂) value from modern (PI) ratite eggshell ensembles, -420 per meg, is in agreement

with the average value of atmospheric O₂ of -434 per meg obtained from multiple studies (Passey and Levin, 2021), and is also consistent with modern GPP levels, according to Young et al. (2014) (heavy solid line, Fig. 8).

The clearest trend in our dataset is the low atmospheric $\Delta'^{17}\text{O}$ (O₂) value inferred from the Middle Miocene ratite eggshell ensembles, relative to both the Late Miocene and Modern (Pre-Industrial) eggshells. According to CenCO2PIP et al. (2023) authors, CO₂ concentrations during the Middle Miocene ranged between 441 and 472 ppm at 95% confidence. Using this range of CO₂ concentrations, our low atmospheric $\Delta'^{17}\text{O}$ (O₂) values would imply that Middle Miocene GPP fell to below 60% of modern values, according to the Young et al. (2014) model (compare orange circle in Fig. 8 with dashed line for 60% GPP). A significant decline in primary productivity during the Middle Miocene would be consistent with observations of a decline in browsing ungulate species, relative to the Early Miocene (Janis et al., 2000). It would also be consistent with marine proxy records, which show decreased (oceanic) paleoproduction during the Middle Miocene, relative to widespread increases in paleoproduction during the Late Miocene (approximately 9 to 3.5 Ma, e.g. Farrell et al. (1995), Diester-Haass et al. (2002), Karatsolis et al. (2022)) - an observation that has been linked to the reorganization of oceanic circulation patterns, expansion of Antarctic Sea Ice, and establishment of regional upwelling systems (Diester-Haass et al., 2002) at this time. Our $\Delta'^{17}\text{O}$ (O₂) values for the Late Miocene (yellow circle, Fig. 8) also support higher GPP during this time (near modern levels).

Our estimate of $\Delta'^{17}\text{O}$ (O₂) for the LGM, obtained from a single ratite eggshell ensemble, is -243 per meg (not plotted), i.e. higher than the modern value for atmospheric O₂. This result is expected due to the relationship between (high) $\Delta'^{17}\text{O}$ and (low) CO₂ levels (see Fig. 1) at the LGM. The same trend towards higher $\Delta'^{17}\text{O}$ values is recorded in O₂ from ice cores (Blunier et al., 2002, 2012; Yang et al., 2022), but the elevation recorded in ice cores is more modest than in the LGM eggshells (i.e. +40 per meg, and +200 per meg, respectively). It is difficult to evaluate the reasons for the disagreement, considering that our estimate is only based on one site (i.e. Besaansklip, West Coast, South Africa), and that errors associated with eggshell-derived values are typically quite large, even in the case where multiple ensembles are available for the same period (e.g. the ensembles from the central and southern Namib differ in $\Delta'^{17}\text{O}$ (O₂) by 100 per meg for the Late Miocene, and 50 per meg for the Middle Miocene).

We emphasize that although the trends in GPP that we identify are promising, they need to be treated with caution, because there are multiple factors that could bias our estimate of $\Delta'^{17}\text{O}$ (O₂) from ratite eggshell. First, atmospheric CO₂ concentrations during the Middle

<footnote>a CenCO2PIP et al. (2023) (Cenozoic CO2 Proxy Integration Project (CenCO2PIP) Consortium), 95% C.I.</footnote>

<footnote>b Schmitt et al. (2012) value for 1850 CE.</footnote>

<footnote>c Hare et al. (2018), Schmitt et al. (2012), Antarctic Ice Core Compilation.</footnote>

<footnote>d See note b in Table 1.</footnote>
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Modeled output (dark blue curves) compared with the data in this paper (open circles). Each subplot shows a different time period, and location of ratite eggshell. Subfigures A, B, and C are for the central Namib. Subfigures D, E, and F are for the southern Namib. G is Queensland, Australia (emu dataset from Hu et al. (2023)), and H is from the West Coast (LGM, Last Glacial Maximum). Models: the isotope-enabled animal body water model of Hu et al. (2023) was modified for parameter estimation, using Bayesian inverse methods (see text for details). The light blue curves show the range of Markov Chain Monte Carlo (MCMC)-based estimates drawn from the joint posterior distribution of the model, for each dataset. The model parameters estimated by MCMC for each subplot include: $\delta^{18}\text{O}_{\text{bw}}$, WEI, $r_{1/s}$, and $\Delta^{17}\text{O}(\text{O}_2)$; and are presented in Table 5.</figcaption></figure>

Miocene are still uncertain, due to disagreement between different proxy records. Most proxies now converge on a range of CO₂ concentrations between 400 and 600 ppm for the Middle Miocene (Steinthorsdottir et al., 2021), although some proxies indicate levels as high as 800 ppm during the Middle Miocene Climatic Optimum (e.g. Stoll et al. (2019)). CO₂ levels higher than ~ 700 ppm would imply that our Middle Miocene GPP estimate is consistent with modern-day GPP, according to the Young et al. (2014) model (Fig. 8). However, considering both the multi-proxy estimate of 441–472 ppm (CenCO2PIP et al., 2023), and the wider, consensus range of proxy estimates (400–600 ppm), it is more likely that GPP was lower than modern-day levels.

Second, our estimate of $\Delta^{17}\text{O}(\text{O}_2)$ is inferred from Bayesian inversion of the Hu et al. (2023) body water model for modern-day ratites. At present, this model assumes that ratites are (or were) nonobligate drinkers that get their dietary oxygen from two main sources — leaves and the atmosphere. However, the model does not currently account for scenarios in which ratites consume waters or plants that are pre-evaporated (Hu et al., 2023). Reassuringly, field studies of modern ostriches show little consumption of water (Williams et al., 1993), and our Bayesian inversion provides values of WEI and $r_{1/s}$ that are consistent with the field observations. But, it is entirely possible that ratites may have consumed significant quantities of pre-evaporated waters during past, non-analogue environments.

Third, all of our triple oxygen isotope measurements have been anchored to the VSMOW-SLAP scale using $\Delta^{17}\text{O}$ values of reference materials recommended by Wostbrock et al. (2020). It is possible that

the ~ 50 per meg spacing between NBS18 and IAEA603 implied by this study is inaccurate, in which case the scaling of our $\Delta^{17}\text{O}$ values from our eggshell is also inaccurate, along with our interpretation of changes in past GPP levels. In other words, using the values for NBS18 and IAEA603 recommended by Wostbrock et al. (2020), our eggshell carbonate $\Delta^{17}\text{O}$ values range by over 200 per meg. If we were to use the smaller NBS18-IAEA603 spacing recently published by Chaillot et al. (2025), then there would be scale contraction of our eggshell carbonate $\Delta^{17}\text{O}$ values, and hence, the inferred changes in GPP would be smaller. These uncertainties are yet to be resolved, and more community efforts are needed to better standardize $\Delta^{17}\text{O}$ measurements to the VSMOW-SLAP scale (Passey and Levin, 2021).

## 4.2. Comparison with previous datasets, and overall model performance

In general, our Bayesian inversion of the Hu2023 body water model produces acceptable fits to our ratite datasets (Fig. 7), and to previously-published data for emus (Hu et al., 2023). Our reconstructed WEI and $r_{1/s}$ parameters (Table 5) are comfortably within the range expected for ratite physiology and dietary behavior (Nagy and Peterson, 1988; Williams et al., 1993). In addition to obtaining estimates of WEI, and $r_{1/s}$, our inversion provides us with a range of meteoric water $\delta^{18}\text{O}_{\text{mw}}$ values, for each period, and region. The ranges of our $\delta^{18}\text{O}_{\text{mw}}$ values, for all periods, are broadly consistent with a range of -15 ‰ to +5 ‰ for rainfall in modern southern Africa, previously published by Geppert et al. (2022), and for the Namib in particular by Kaseke et al. (2016, 2018).
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** $\Delta^{17}\text{O}$ values for atmospheric $\text{O}_2$, inferred from ratite eggshell ensembles (orange, yellow, and white circles) compared to Late Cenozoic atmospheric $\text{CO}_2$ levels. Solid heavy line is the modeled relationship between $\Delta^{17}\text{O}$ ($\text{O}_2$) and $\text{CO}_2$ for 100% of modern (PI) GPP levels, according to Young et al. (2014). Dashed blue line is the relationship for 140%, and dot-dashed red line is 60% of modern (PI) GPP levels, respectively. Solid error bars show 95% Confidence Intervals for $\Delta^{17}\text{O}$ values (i.e., $\pm 1.96 \times \sigma/\sqrt{n}$ where $1\sigma$ is from Table 5). The horizontal dashed error bar is the range of most proxy $\text{CO}_2$ values for the Middle Miocene, considered in the review of Steinhorsdottir et al. (2021). Note: the raw $\Delta^{17}\text{O}$ value in Blunier et al. (2002) was originally reported relative to a VSMOW of $\Delta^{17}\text{O} = +173$ per meg, with (modern) atmospheric $\Delta^{17}\text{O}$ defined as 0, without uncertainty (and a different $\lambda_{\text{ref}}$ of 0.516). In this figure, we have re-scaled their value (grey square) to a modern (PI) $\Delta^{17}\text{O}$ ($\text{O}_2$) value of $-434$ per meg, and $\Delta^{17}\text{O}$ (VSMOW) of 0 per meg. For interpretation of the references to color in the legend, the reader is referred to the online version of this article.</figcaption></figure>

Modern-day rainfall in the eastern Summer Rainfall Zone (eSRZ) of southern Africa, which extends to the central Namib (Fig. 3), is consistently more depleted in $^{18}\text{O}$, relative to other rainfall zones. In this region, re-circulated continental air masses are prominent moisture sources. Geppert et al. (2022) identified that prolonged travel and rain-out times, associated with re-circulation, lead to isotopic depletion in eSRZ rainfall. For the Middle Miocene, we note that our $\delta^{18}\text{O}_{\text{mw}}$ values for the central Namib are similar to the southern Namib (both around -1.6 ‰). Yet, for both the modern (PI) and Late Miocene, our results show that median $\delta^{18}\text{O}_{\text{mw}}$ for the central Namib was consistently 1.5 to 2.0 ‰ more depleted in $^{18}\text{O}$, relative to the southern Namib, as expected. It is tempting to interpret this as evidence for the establishment of general circulation patterns from the Late Miocene onwards (Ségalen et al., 2006), but caution is advised. First, the uncertainties associated with our estimates are too large (2.5 to 3.6 ‰, $1\sigma$) for these trends to be considered significant.

Second, in two instances, for the central Namib Late Miocene and the Middle Miocene datasets, the Hu2023 body water model is inconsistent with three of the highest $\delta^{18}\text{O}_{\text{bw}}$ values obtained from our ratite eggshells. The misfit could be explained by a number of factors. First, in all of our modeling, we have assumed that the H₂O content of food, $f_{\text{H}_2\text{O-food}}$ was 0.55 (Table 3), following the mean of modern field observations of Williams et al. (1993), which ranged from 0.37 to 0.70. If $f_{\text{H}_2\text{O-food}}$ is increased to the upper end of this range, 0.7, then our model fits for the Miocene improve substantially, with highest $\delta^{18}\text{O}_{\text{bw}}$ values for the Middle Miocene lying well within model bounds. In this scenario, modeled $\delta^{18}\text{O}_{\text{mw}}$ for the central Namib was $-2.3 \pm 2.8$ ‰, slightly lower than the original scenario of $-1.8 \pm 2.9$ (Table 5), but uncertainty associated with this result is too large for any firm conclusion to be drawn with respect to changes in source water and atmospheric circulation. Most importantly, a higher $f_{\text{H}_2\text{O-food}}$ value

would not significantly affect our finding of low GPP during the Middle Miocene, because the inferred value of $\Delta^{17}\text{O}$ ($\text{O}_2$) with $f_{\text{H}_2\text{O-food}} = 0.7$ becomes $-650 \pm 30$ per meg, i.e. within error of our original estimate. This result underscores our finding that the clearest trend in the data is the relationship between $\Delta^{17}\text{O}$ ($\text{O}_2$) values and $\text{CO}_2$ concentrations.

On the other hand, the misfit could also be explained if the Miocene central Namib ratites consumed waters and/or plants that were pre-evaporated, driving $\delta^{18}\text{O}_{\text{mw}}$ higher than expected. However, the Hu2023 model currently cannot account for such an effect, and our estimates of $\delta^{18}\text{O}_{\text{mw}}$ (and WEI, $r_{1/\text{s}}$, and atmospheric $\Delta^{17}\text{O}$) could be biased. We briefly note that other sources of model uncertainty could also plausibly contribute to a misfit. One source of model uncertainty is the fractionation exponent for exchange between exhaled $\text{CO}_2$ and body water, $\theta_{\text{CO}_2-\text{bw}}$. Hu et al. (2023) use a value of $\theta_{\text{CO}_2-\text{bw}} = 0.5248$, based on theoretical calculations by Cao and Liu (2011), which seems to yield acceptable fits to our modern datasets, but this value is at present not properly constrained by measurements.

### 4.3. Limitations, and potential of triple oxygen isotopes in ratite eggshell

To our knowledge, this is the first time that a Bayesian inversion of an isotope-enabled body water model has been successfully used to obtain multiple parameters of interest, which is a promising development for future paleoclimate and paleoecology studies. A particular advantage of our approach is that ratite eggshell is commonly-associated with Neogene and Quaternary paleontological/archeological sites from across Africa and Eurasia. Our study shows that the predominant signal in the triple oxygen isotope composition of ratite eggshell is global carbon cycling (i.e. $\text{CO}_2$/GPP via the link with atmospheric $\Delta^{17}\text{O}$), meaning that with further refinement, a relatively common material can be used to reconstruct changes in planetary primary productivity, and its relationship to $\text{CO}_2$, for periods beyond the ice core record. However, one limitation as a GPP proxy is that the technique might be less useful for older periods, during which $\text{CO}_2$ is less certain. This is because the $\Delta^{17}\text{O}$ value of atmospheric $\text{O}_2$ reflects the ratio between GPP and $\text{CO}_2$ - two global variables which are intrinsically linked via the carbon cycle.

Another limitation of our study is that our values for $\Delta^{17}\text{O}$ ($\text{O}_2$) for the Miocene are derived from only two ratite eggshell ensembles (southern Namib and central Namib). The uncertainty associated with the concordant $\Delta^{17}\text{O}$ ($\text{O}_2$) values (~50–100 per meg) is acceptable to identify significant changes in GPP. However, ensembles from more regions, and potentially, species, would be needed to fully evaluate the uncertainty in GPP change.

Another significant limitation that we have identified is that the environmental imprint (of $\delta^{18}\text{O}_{\text{mw}}$, in particular) on eggshell $\Delta^{17}\text{O}$ is not as strong as the climatic imprint of $\text{CO}_2$/GPP. The large uncertainties in $\delta^{18}\text{O}_{\text{mw}}$, discussed above, limit the applicability of triple oxygen isotopes to reconstructing changes in local environments (unless the magnitude of changes in $\delta^{18}\text{O}_{\text{mw}}$ significantly exceed the typical uncertainty associated with the Bayesian inversion, ~ 3 ‰). Future versions of this analysis would be improved by: (1) incorporating direct measurements of the $\theta_{\text{CO}_2-\text{bw}}$ value into the body water model, (2) better constraining $f_{\text{H}_2\text{O-food}}$ values in the parameter estimation, (3) incorporating consumption of pre-evaporated waters into the model, and (4) increasing sample size within each ensemble.

Another important factor to consider, for future studies, is diagenesis. Our Namib eggshells were screened for preservation of primary calcite via XRD and cathodoluminescence. These samples, together with our LGM and modern materials are from contexts in which there is a low likelihood of diagenetic change. If present, open system diagenesis causes elevation in carbonate $\Delta^{17}\text{O}_C$ values, towards the $\Delta^{17}\text{O}$ of meteoric water (Gehler et al., 2011). Therefore, for eggshell samples where alterations, which influence their oxygen isotope ratios, cannot be ruled out, $\Delta^{17}\text{O}_{\text{bw}}$ values should be regarded as upper estimates (and GPP changes could be larger than implied by these measurements).
It is worth emphasizing the importance of accurate measurements of (paleo-)GPP for questions of global climate change. Plants and soils on land are currently mitigating climate change by removing ~30% of the carbon dioxide emitted by human activities (Friedlingstein et al., 2022). As CO₂ increases, GPP is stimulated (the “CO₂ fertilization effect”) – particularly in temperate and boreal regions where warming also plays a role – though both effects eventually must saturate (Heimann and Reichstein, 2008). In contrast, respiration increases exponentially with temperature and is unaffected by CO₂. As warming continues, the net carbon uptake by terrestrial ecosystems may decline, reducing the rate at which plants and soils buffer anthropogenic emissions. Critically, the timing and likelihood of biosphere tipping points hinge on accurately understanding GPP responses, which has been a long-standing goal in ecological research (Carlstad and Boering, 2023). A robust paleo proxy for GPP would be one important tool to constrain long-term feedbacks between the biosphere and climate.

## 5. Conclusion

We have presented a large dataset of the triple oxygen isotope composition of ratite eggshell from the Middle Miocene until the present. Our dataset significantly expands on previous measurements of $\Delta^{17}\text{O}$ of biominerals (Passey et al., 2014; Feng et al., 2022; Lehmann et al., 2022; Hu et al., 2023), and offers a more extensive test of the potential of these materials to record variations in the $\Delta^{17}\text{O}$ values of atmospheric O₂ (Gehler et al., 2016), by measuring ratite eggshell ensembles across different climate states of the late Cenozoic. Our results confirm that ratite eggshell carbonate carries the imprint of atmosphere-derived $^{17}\text{O}$. Middle Miocene and LGM eggshells reflect especially low and high $\Delta^{17}\text{O}$ values, respectively — in broad agreement with expected relationship between atmospheric $\Delta^{17}\text{O}$ and GPP:CO₂ ratios (Bender et al., 1994; Pack et al., 2013; Young et al., 2014).

Our Bayesian inversion of the Hu et al. (2023) body water model allows us to obtain reasonable estimates for the $\Delta^{17}\text{O}$ value of atmospheric O₂ using a concordance approach that relies on sampling eggshells from different regions and periods. This modeling approach enables us to successfully account for the effects of ratite physiology on the triple oxygen isotope composition of biomineral carbonate, and can, in principle, be applied to other species, and materials. However, the model relies on the assumption that ratites obtain the bulk of their dietary oxygen from leaves and the atmosphere - a condition which might be reasonable in the present day, but might not have been met in the past.

Historically, changes in planetary productivity have proved difficult to reconstruct for timescales older than those covered by ice cores (~800 ka). Here, we have presented evidence from ratite eggshells that GPP levels dropped to below 60% of modern values, during the Middle Miocene, before returning to near-modern levels during the Late Miocene. A decline in GPP during the Middle Miocene is potentially of great significance, because this period has been suggested as an analogue for future climate change scenarios (Steinthorsdottir et al., 2021). The present day global average CO₂ level (420 ppm), is very close to that of the Middle Miocene according to CenCO2PIP et al. (2023) (441 – 472 ppm, 95% confidence). Considering most future emissions scenarios suggested by the IPCC 6th assessment report (Lee et al., 2023), it is likely that the Earth will either meet, or exceed Middle Miocene CO₂ levels in the coming century. A concomitant drop in global primary productivity would substantially impact the ability of the biosphere to buffer future emissions. Further studies, and development of the triple oxygen isotope proxy for GPP, are essential to confirm such trends, and to investigate the implications for the carbon cycle.

## CRediT authorship contribution statement

**Vincent J. Hare:** Writing – original draft, Visualization, Supervision, Software, Methodology, Investigation, Funding acquisition, Conceptualization. **Drake A. Yarian:** Writing – original draft, Visualization, Software, Investigation. **J. Tyler Faith:** Writing – review & editing, Resources. **Chris Harris:** Writing – review & editing, Supervision. **Julia A. Lee-Thorp:** Writing – review & editing, Resources. **Benjamin H. Passey:** Writing – review & editing, Investigation. **Kathryn G. Sokolowski:** Writing – review & editing, Investigation. **Loïc Ségalen:** Writing – review & editing, Resources, Investigation.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The co-author is an Associate Editor for this journal and was not involved in the editorial review or the decision to publish this article.

## Acknowledgments

This work was supported by the South African Biogeochemistry Research Infrastructure Platform (BIOGRIP), through MSc scholarship funding to DY, and by acquisition of the TILDAS instrument. The financial assistance of the Department of Science and Innovation (Republic of South Africa), through a grant from the Palaeoscience Centre of Excellence (COEOP2020-12), is gratefully acknowledged. Prof. Naomi Levin's correspondence on recalibration of previously published data to the VSMOW-SLAP scale (using Wostbrock values) is acknowledged. BAS eggshell was sampled under HWC permit 22030306AM1118 issued to JTF, with the financial assistance of the U.S. National Science Foundation (Grant 1826666). The authors thank the two anonymous reviewers for their thoughtful suggestions.

## Appendix. Supplementary material

The GitHub repository (see Data Availability Section) contains MATLAB code that implements a Bayesian Markov Chain Monte Carlo (MCMC) approach for estimating parameters related to the triple oxygen isotope composition of biominerals, specifically ratite eggshells. For this code to work properly, the MCMC toolbox by Marko Laine (https://mjlaine.github.io/mcmcstat/) needs to be installed in the working directory. We ran this code in MATLAB R2017b, and to the best of our knowledge it should work in other versions. The GitHub repository contains the following four MATLAB files: (1) "TripleOxygenBayes.m", which is a wrapper script which executes the entire MCMC fitting procedure, where the prior parameter matrix $\theta$ is defined, and the dataset is called, (2) "BWM_Emu_st.m", which is the body water model itself, (3) "TripleOxygenss.m", the sum-of-squares function (described in Section 2.4), and (4) "SS_over_rh.m", a separate sum-of-squares function called during the post-MCMC numerical optimization of $\Delta^{17}\text{O}$ (O₂). Additionally, this repository contains MATLAB .mat files, for data ensembles, e.g. "TripleO_Central_Modern.mat" in the case of the modern ratite eggshell from the Central Namib.

## Data availability

All model code, and sample datasets, can be accessed via GitHub repository (https://github.com/vinhare/MCMC-17O). You are free to modify the code and distribute either the original or your modified version. However, when using this code, please cite this publication, along with Hu et al. (2023).
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