Oxygen Isotopes in Carbonate and Phosphate of Modern Mammal Bioapatite: New Data and Critical Revision after about 25 Years from the First Recognitions

: Oxygen and carbon isotopes of well-preserved skeletal remains give relevant support to archaeological and environmental reconstructions. However, the preservation of the skeletal remains must be preliminarily checked. About twenty-ﬁve years ago, a diagnostic method based on the oxygen isotope ratio in the phosphate, δ ( 18 O/ 16 O ) Ph , and carbonate, δ ( 18 O/ 16 O ) Carb , of bioapatite of modern mammals was proposed: for well-preserved samples, the δ ( 18 O/ 16 O ) Ph and δ ( 18 O/ 16 O ) Carb should plot near the regression line δ ( 18 O/ 16 O ) Ph on δ ( 18 O/ 16 O ) Carb obtained for modern mammals. In the last twenty years, techniques of analysis have changed. In the past, BiPO 4 or Ag 3 PO 4 were precipitated from dissolved bioapatite and analysed with the ﬂuorination technique, whereas at present, temperature reduction (HTR) in a glassy carbon reactor with CO release is commonly used. Taking into account the HTR technique, for some modern mammals, we report a new δ ( 18 O/ 16 O ) Ph + 1 on δ ( 18 O/ 16 O ) Carb + 1 regression line, and related dispersion of the data that, in addition to mineralogical and structural methods, may be used to select samples reliable for archaeological use. In the past, other similar regression lines on modern mammals were deﬁned by several authors. However, statistical results indicate that data used for these regression lines cannot be pooled because the hypothesis of a similar elevation is rejected.


Introduction
In this paper, the parameter delta (δ) is defined according to IUPAC (International Union of Pure and Applied Chemistry):

Significance of the Measured δ 18 O/ 16 O
The δ 18 O/ 16 O for carbonate of minerals (in our case bioapatite and low-Mg calcite) is not directly determined but obtained by measuring the isotope ratios of gaseous carbon dioxide, CO 2gas , produced, at the defined temperature T, by the dissolution of the mineral in orthophosphoric acid with the defined concentration of the H 3 PO 4 component. The definition of "oxygen isotope phosphoric acid fractionation factor", α T ACID(Ap) , between CO 2 gas , produced by dissolution of bioapatite, and the carbonate of bioapatite at temperature T allows us to understand the significance of the measured δ( 18  The oxygen isotopic composition of CO 2 gas produced depends on several important factors (e.g., [28][29][30][31][32][33][34][35][36][37][38][39][40]). Among these factors, we emphasize the following: (1) pre-treatment of the sample; (2) temperature of reaction of the sample with H 3 PO 4 ; (3) concentration of the H 3 PO 4 chemical component in the acid; (4) composition of bioapatite; (5) interaction of the new-formed CO 2 with endogenic water that is generated by the reaction producing CO 2 ; (6) solution species that formed with phosphorous-bearing anions and cations liberated by the mineral dissolution.

Materials
The δ( 18 O/ 16 O) values for carbonate and phosphate have been determined on tooth (enamel) and bone bioapatite from several modern mammals (Canis aureus, Vulpes vulpes, Vulpes zerda, Vulpes lagopus, Alces alces) that lived in different localities under variable climatic conditions. Only one portion of bone or tooth for each individual was analysed. The data reported are the average of two experimental values obtained during the same analytical run.

Calibration for Sample Analysis
Calibration is generally done using several international or in-house standards. In the case that the linearity of the final instrumental response is verified, matrix effect, errors on the isotopic measurements and errors on the isotopic values of the standards used for the regression are absent, the standards will be perfectly aligned along the regression line of the form δ( 18  , present in generic substance i, and c is a constant. In terms of δ + 1 values referred to the laboratory working standard w, relation (2) is written as: which represents a straight line passing through the origin.
Systematic errors and random errors in the measurements of the standards occur; matrix effect for standards of different material may be present; in general, the instrument response is not perfectly linear. Thus, the scattering of data around the calibration line and the intercept significantly different from zero are frequent. Note that, in this case, intercept is significantly different from zero, only new values of the analysed samples that fall in the range of the delta values of standards may be accepted; practically, only very small extrapolation is allowed.

Analytical Methods
Since the results obtained in this paper may be compared with data obtained from archaeological and palaeontological samples, in agreement with the Criterion of Identity Treatment, the modern samples of this study were chemically treated as ancient samples.

Oxygen of the Carbonate
Initial considerations. Different procedures of sample preparation frequently give different isotopic results not only on ancient, but also on modern samples. This argument has been widely discussed in the literature (e.g.,: [35,36,39,[41][42][43][44][45]). In particular, Crowley and Wheatley [43] suggest that pre-treatment with NaClO or H 2 O 2 and Ca-buffered acetic acid solution produces similar results for enamel carbonate, whereas NaClO is not recommended for tissues with higher organic content, such as bone and dentine. Our experience, however, suggests that it is difficult to obtain complete elimination of high content of organic components using H 2 O 2 and that, on bones, a very low concentration of NaClO (2% solution) allows results that, in the limit of the analytical uncertainty of our analyses, are comparable with those obtained using H 2 O 2 . Thus, also for a better comparison with data produced in our laboratory in the past, we preferred to follow our routine procedure with the use of NaClO.
Halas et al. [48] prepared three new samples of Ag 3 PO 4 (UMCS-1, UMCS-2, and AGPO-SCRI) for inter-laboratory comparison. These samples were analysed in two different laboratories together with the standards NIST SRM 120c and the samples TU-1 and TU-2 mentioned above. The data were normalised to IAEA-601 (benzoic acid), IAEA-602 (benzoic acid), IAEA-CH6 (sucrose), and IAEA-C3 (cellulose) or to IAEA-601 and IAEA-602. In spite of the use of these standards does not match the Principle of the Identical Treatment [46]; for the standards TU-1 and TU-2, the agreement between data reported by Vennemann et al. [27] and by Halas et al. [48] (Dundee Laboratory data) was very good (p (same average) ≈ 1) whereas the agreement for the standard NIST SRM 120c, was not so good (p (same average) ≈ 0.10), but still acceptable.
Based on the results reported above, we emphasize the following points: (1) The matrix effect apparently is not largely relevant for calibration; this makes the use of silver phosphate standards not strictly necessary. (2) Practically, the new phosphate BOKU cannot substitute the use of the standards listed above because calibration with only one standard is risky. Sample BOKU could be used only for "quality control".
Analysis of our samples. The chemical treatment of the samples to obtain silver phosphate followed the protocol by Stephan [50]. About 50 mg of powdered sample was placed in 2.5%wt. NaClO solution for 24 h to eliminate organic material. After that, the supernatant was removed and the pellet was washed several times to neutralise it. Then, a 0.125 M NaOH solution was added (this is frequently used to dissolve humic substances possibly present in archaeological samples) and samples were left for 48 h for reacting. After the dissolution of the sample in 2M HF at 25 • C for 24 h, the precipitated CaF 2 was separated from the phosphate solution by centrifugation and the solution was neutralized with 3 mL of 2M KOH solution in a 250 cm 3 beaker. Doubly distilled water was added to make up the apatite solution to a total volume of 200 cm 3 . Later, 30 cm 3 of buffered silver nitrate solution (AgNO 3 0.2 M, NH 4 NO 3 0.3 M, NH 3 0.7 M) was added and the solution was gradually warmed to 70 • C for 3 h. The crystals of silver phosphate were collected on a millipore filter, and then washed and air-dried overnight at 50 • C. A total of 0.3 mg of sample was weighed in silver capsules together with 0.3 mg of glassy carbon and 0.5 mg of AgCl (the latter two act as catalysts for the combustion reaction). The oxygen isotope composition was analysed using a thermal conversion-elemental analyser unit (1420 • C) online with a mass spectrometer (Finnigan TC/EA-Delta Plus XP, Thermo Fisher Scientific, Bremen, Germany). The yield for oxygen was checked for all samples.
As discussed above, apparently the matrix effect is not relevant for calibration. Thus, standards IAEA-601 (benzoic acid, δ( 18 O/ 16 O) = 23.14‰ ± 0.10‰ VSMOW, approximate standard error of the mean better than 0.1‰, [51]), IAEA-CH-6 (sucrose, δ( 18 O/ 16 O) = 36.4‰ ± 0.15‰ VSMOW, [52]) and IAEA-600 (caffeine, δ( 18 O/ 16 were used for calibration in this paper. Sulphate standards were disregarded because the yield of these substances was generally lower than 100% (down to 80%). As far as the Ag 3 PO 4 from the samples is concerned, we disregarded two samples that gave a yield for oxygen of less than 100%. Unfortunately, the calibration with these three standards did not exactly match the Equation (1). A regression line in the form: with A = 0 was established. Thus, the calibration line is: Equation (3) may be due to the absence of linearity of the spectrometric response (actual absence of linearity is not rare, [15,53]). If linearity is not perfect, the calibration line obtained with more than one standard is not a straight line but a curve. It is noteworthy, however, that the standards used in this paper cover a narrow range of values and, thus, in this range, the calibration curve approaches a straight line. Moreover, the samples of this paper fall in the delta interval of standards, and thus, no extrapolation was done.

Analytical Uncertainty
Usually, papers only report repeatability and reproducibility, and very rarely the prediction uncertainty related to the calibration line [54]. This is surprising because prediction uncertainty is the only value which is relevant for the comparison of data obtained in the same laboratory or in different laboratories.
Repeatability and reproducibility. During our routine analysis of carbonate, repeatability for δ( 18 where Y st and X st are average values for the standard; X st refers to each standard; t (α(2),ν) is the Student's t-value (two-tailed test); α is the significance level; g, for each individual i, it is the number of experimental values with average value Y i (in our case, two experimental values); n is the number of experimental values for the standards; s(yx) is the standard error of regression; υ the degree of freedom (υ = n − 2). However, in our case, X st is affected by some uncertainty, s(X st ). In this case, Taylor  Accuracy. The accuracy of the data was checked using the standard BOKU for which we obtained 13.90‰ ± 0.35‰ (average of two experimental values, ± prediction uncertainty, [54]) against the declared value of 13.71‰ ± 0.34‰. Table 1 and Figure 1 report the obtained results. The range of delta values is a little bit narrower than the ranges obtained by Bryant et al. [20] and Iacumin et al. [21] (Table 2).   [20] used laboratory standards; Iacumin et al. [21] used a laboratory standard for the analysis of CO 2gas and quartz NBS28 for the oxygen of phosphate analysis; Zazzo et al. [56] used international standards NBS18 and NBS19 for the oxygen analysis of CO 2gas . Iacumin et al. [21] analysed the oxygen isotope of phosphate by fluorination of BiPO 4 precipitated from dissolved bioapatite and Bryant et al. [20] by fluorination of Ag 3 PO 4 . Zazzo et al. [56] analysed Ag 3 PO 4 by graphite method (since with this method the oxygen yield in only 25%, they corrected the data using a constant offset of +0.5‰). Miller et al. [57] analysed Ag 3 PO 4 by HTR.

Data Obtained at Different Temperatures
The temperature of the acid dissolution is a critical parameter for the δ( 18 O/ 16 O) CO 2 (Ap) value of the CO 2 gas produced by the dissolution of apatite. For instance, using Gas-Bench (Thermo-Finnigan, Bremen, Germany) as a preliminary test, we determined the Unfortunately, however, the standards commonly used (this is also our case) are low-Mg calcites, not phosphates. Thus, data obtained at different temperatures must be corrected, as indicated in the Appendix A. The oxygen isotope analyses on the carbonate reported by Iacumin et al. [21] and by Zazzo et al. [56] refer to CO 2 produced at 50 • C, whereas the data reported by Bryant et al. [20] and Miller et al. [57] was of CO 2 produced at 90 • C. Thus, the δ( 18 O/ 16

The Regression Lines
For the oxygen isotopes present in phosphate and carbonate of bioapatite, the apparent equilibrium isotope fractionation factor between phosphate and carbonate at a defined temperature is expressed as: from which we obtain: Consider the linear equation: The regression line obtained using the experimental data allows us to verify immediately the agreement of our data with Equation (5) Table 2. The regression lines are the following (Equations (7)-(10) [20,21,56,57], respectively, and Equation (11) The null hypothesis for the intercept, H o : A = 0, cannot be rejected at α = 0.1 for all the data groups considered. However, for the data from Bryant et al. [20], we obtained a low value for p(homoscedasticity) (0.03); moreover, both for the data from Bryant et al. [20] and Miller et al. [57], for residuals the value p(normal) is low to very low (0.03 and <0.001, respectively). Thus, the hypotheses reported below (such as differences between slopes and elevation of straight lines) are only tentative. Finally, always in the limit of the analytical uncertainty, we obtained p A=0 ≥ 0.2 (except for [20]). The high probability for A = 0 is not in contrast with the hypothesis of equilibrium of oxygen isotope in carbonate and phosphate of bioapatite, this, of course, is within the limit of the analytical errors.
Comparison of slopes and elevations for regression Equations (7)- (11) were done according to Zar [58] the different lines exhibit high probability for the same slope (p same slope ∼ = 0.9), whereas the null hypothesis for the same elevation is rejected (p same elevation << 0.001). Therefore, theoretically, the data would not be pooled altogether for obtaining a common regression line.

The Role of Different Species and of Tooth (Enamel)/Bone Bioapatite on the Regressions
In the regressions reported in Section 4.2.3, we pooled the data for different genus/species and for bones and teeth. Now the question is: in the limit of our approach, was it correct? The following points must be taken into account in the discussion: (a) The body temperature of the investigated modern mammals is very similar (approximately in the range 35-39 • C, [59]). (b) Bioapatite is a mineral, its crystallization is a slow process; thus, as commonly occurs for minerals, intra-lattice equilibrium is very probably reached. (c) Material commonly used for isotope determination of modern, recent (Holocene) and fossil mammals is enamel and bone bioapatite. Enamel bioapatite and bone bioapatite have similar crystal lattice and chemical composition; only crystal size and content of organic matter are significantly different. Thus, for a given temperature, teeth and bones are expected to behave similarly as far as the oxygen isotope fractionation between carbonate and phosphate is concerned.
Before comparing genus/species and bones and teeth, we note, that the standard error of the regression, s(yx), for the regression lines (7)-(11) is up to more than twice the prediction uncertainty for δ 18 O/ 16 O Ph (0.00031-0.00085 against 0.00035). This indicates that the scattering of the data around the regression lines is not only due to analytical uncertainty, but also to other reasons, not excluding a priori genus/species and teeth/bones effect. In this work, however, we are not interested in comparing regressions on teeth and bones and on different genus/species, but only to verify if data from teeth and bones and for different genus/species may be pooled to obtain single regression lines. This was tested using data from Iacumin et al. [21]. The distribution of data for the different genus are so chaotic that we cannot recognize systematic differences between the different genus. As far as the role of bones and teeth are concerned, the two independent regression lines δ 18 O/ 16 O Ph + 1 on δ 18 O/ 16 O # Carb + 1, calculated separately for teeth enamel (t) and bones (b), estimate the same statistical population (p (same regression) = 0.84). Therefore, there is a very high probability that regression lines obtained on teeth and bones do not differ significantly and, thus, the data may be pooled.

Final Considerations
The differences among the regression lines obtained using samples dissolved at the same temperature could be prevalently due to the following reasons: (a) Different standard materials used for calibration. (b) Difference in technical procedures. (c) Although the role of standard materials and procedures would need a separate approach, the effect of materials and procedures on the slope and elevation cannot be identified separately. As far as phosphate is concerned, there is no unequivocal answer because different authors frequently used different techniques and did not use international standards, or they did not always indicate the international standards to which the in-house standards used were referred. For instance, Iacumin et al. [21] determined oxygen of carbonate using in-house standards and Bryant et al. [20] used in-house standards for both carbonate and phosphate. Miller et al. [57] used in-house standards for determining the oxygen isotope ratio in precipitated Ag 3 PO 4 .
(b) For phosphate, this point has been approached and discussed by several authors (e.g.,: [27,60] and references therein) to which we address the attention of the reader. For carbonate, point (b) has been briefly discussed above (Sections 2 and 3.3.1).

Identification of Potential Diagenetic Processes
If diagenetic processes affect bioapatite, two different types of deviations from the δ ( (11) allows us to recognise samples that possibly underwent diagenesis. This may give support to other mineralogical, spectroscopic, and geochemical methods used to identify diagenetic transformation. The new value, of course, must be obtained using the same standard and the same procedure as this paper.
In addition to the mineralogical and structural investigation, we propose a very simple way for the selection of samples with potential diagenetic transformation affecting bone or tooth remains of animals which lived in the past. Assume that for a new sample i we obtained the experimental value X i = δ( 18 O/ 16 O) #,T Carb + 1 and Y i = δ( 18 O/ 16 O) Ph + 1 and that, for simplicity, these are not affected by uncertainty. Moreover,Ŷ i is the value estimated from the experimental X i using the regression line (11) and s(yx) = 0.00064 is the standard error of the regression (11) ( Table 2). Consider the value t (α(2),ν=n−2) s(yx), where t (α(2),ν=n−2) = 2.145 is the Student's t value (two-tailed) for significance level α(2) = 0.05, n = 16 = numbers of couples of data used for regression (11), and ν = n − 2 = 14. Moreover, according to Taylor  Thus:Ŷ whereŶ i is the estimated value. The suspicion of diagenetic transformations could not be rejected for values outside the array defined by ±1.5‰. Figure 2 reports an example referred to Holocene mammal bone remains from Sudan. Based on the selection criteria discussed above, some of the samples could be considered as not reliable for archaeological considerations because they fall outside the array ± 1.5‰ on the y axis around the regression line (11). Obviously, the significance level α(2) = 0.05 may be changed according to particular needs.  (11); discontinuous lines define the array ± 1.5‰.

472
It is noteworthy that if oxygen data are not reliable because they are potentially af-473 fected by diagenesis, the values δ( C/ C 12 13 ) obtained for the carbonate of bioapatite must 474 also be regarded with suspicion and not immediately used to do inference on the diet of 475 the individuals. To summarise, regression line (11) has relevance not only for oxygen, but 476 also for carbon isotopes.  It is noteworthy that if oxygen data are not reliable because they are potentially affected by diagenesis, the values δ 13 C/ 12 C obtained for the carbonate of bioapatite must also be regarded with suspicion and not immediately used to do inference on the diet of the individuals. To summarise, regression line (11) has relevance not only for oxygen, but also for carbon isotopes.  [20,21,56,57] on bioapatite of teeth (enamel) and bones of modern mammals (Ph = PO 3− 4 , HPO 3− 4 and Carb = CO 2− 3 of bioapatite). The hypothesis that the slopes of the different regression lines are the same cannot be rejected (p same slope ∼ = 0.9); on the contrary, the elevation varies significantly (p same elevation << 0.001). Thus, the data of the different authors considered do not belong to the same statistical population and they cannot be pooled to obtain a total or a common regression line. The new regression line we obtained using the procedure at Section 4. (2) Probably, the systematic difference in the elevation is prevalently due to different methods and standards used in the different laboratories. (3) The temperature of H 3 PO 4 acid dissolution used for CO 2 gas production for spectrometric analyses has some influence on the final isotopic results. Thus, it is better to perform analyses at the same temperature in all laboratories. For a given temperature T, the "oxygen isotope phosphoric acid fractionation factor" for low-Mg calcite and bioapatite, is defined as are values for the CO 2 gas produced by dissolution with H 3 PO 4 at a given temperature T. Unfortunately, for most substances the "oxygen isotope phosphoric acid fractionation factor" is not known (this is the case, for instance, for bioapatite). Thus, usually, Equation (A1) is extended to substances different from low-Mg calcite, i.e., in the case of bioapatite: Carb value at temperature T 2 only knowing the ratio α T 1 ACID(Cal) /α T 2 ACID(Cal) between the values of "oxygen isotope phosphoric acid fractionation factor" for calcite at temperature T 1 and T 2 ; we also need the value of the ratio α Carb . It is noteworthy that comparison between Equations (A6) and (A7) indicates that the two regressions have different slope (p B A6 =B A7 = 0.005). This demonstrates that, at different temperature, bioapatite and low-Mg calcite exhibit different behaviour in acid dissolution.