Assessing laser ablation multi‑collector inductively coupled plasma mass spectrometry as a tool to study archaeological and modern human mobility through strontium isotope analyses of tooth enamel

To evaluate the possibility of obtaining detailed individual mobility data from archaeological teeth, the strontium isotope ratios on 28 human teeth from three separate Early-Mid Holocene, Swedish, foraging contexts (Norje Sunnansund, Skateholm and Västerbjers) were analysed through laser ablation. The teeth/individuals have previously been analysed using traditional bulk sampled thermal ionisation mass spectrometry. To validate the conclusions regarding the archaeological teeth, a tooth from a modern man with a known background was also analysed. The result shows that all of the teeth display less than 0.4% discrepancy between the mean values of the laser ablation profiles and the previously published bulk data and 25 (89%) of the teeth display less than a 0.2% discrepancy. By calculating linear and polynomial trendlines for each ablated tooth, it was possible to illustrate a strong correlation for the transition pattern between the measurements when following a chronological sequence from the tip to the cervix. Such correlations were not reproduced when the data sequence was randomized. The analyses show that the chronologically sequenced ablation data fit with a transition between local bioavailable strontium regions, that the measurements do not fluctuate between extremes and that their values are not caused by end-member mixing. This indicates an increasing data resolution when reducing strontium isotope ratio averaging time by minimizing the sampling area. The results suggest strontium incorporation in human teeth can be measured on an ordinal scale, with a traceable chronological order to enamel mineralization when sampled from tip to cervix at an equal distance from the surface. Micro-sampling enamel is considered a valid method to assess prehistoric, but not modern, human mobility; laser ablation technology increases the amount of information obtained from a single tooth while rendering minimal damage to the studied specimen.


Mammal tooth formation and its application in archaeology
Understanding how elements, chemical components and isotopes are incorporated in a living body is a key to interpreting the data. As a consequence of living tissue remodelling, mineral content and isotopic signals in soft tissue, hair and bone are continuously replaced throughout life. Teeth do not remodel and remain unaltered once they have formed, thus obtaining their chemical and isotopic composition from a relatively narrow period (Kierdorf et al. 2013;Papakyrikos et al. 2020).
Tooth enamel is a frequently used data source in archaeological research due to its hard and dense tissue, which is resistant to contamination and diagenesis (Hoppe et al. 2003;Kohn and Cerling 2002). There are two main stages in mammal enamel formation: secretion and maturation (Smith 1998). During the maturation phase, the enamel mineralizes and most of the minerals are deposited (Robinson et al. 1997). The mineral and isotopic record from the secretion phase is considered to become largely overwritten during maturation, as enamel mineralizes and obtains its main chemical and isotopic signatures (Balasse 2002;Kohn 2004;Montgomery 2010;Montgomery et al. 2010; 1 3 2019). The time for mineralization, thereby, constitutes the temporal boundary of main interest for archaeological studies.
Mammal teeth develop similarly, starting at the cusp and forming down towards the root (Hillson 2005). Where mammal tooth development is rapid, easily studied and possible to age determination (Brown et al. 1960;Goodman et al. 1980;Magnell and Carter 2007;Reid and Dean 2006), the enamel mineralization is more difficult to investigate. Different models have been created to understand its complexity (Hoppe et al. 2004;Passey and Cerling 2002;Suga 1989;Trayler and Kohn 2017), but uncertainties related to acquiring a well-defined spatio-temporal resolution during an extended enamel maturation phase have made it difficult to make full use of mineral and isotopic data in tooth enamel (Balasse 2002(Balasse , 2003Humphrey 2014;Kohn 2004;Montgomery and Evans 2006). Since most of the minerals and isotopes locked in tooth enamel derive from the mineralization phase, it has resulted in questions of whether it is possible to obtain a temporally limited and chronologically defined record (Montgomery and Evans 2006;Montgomery et al. 2010).
In recent years, technological advances have made it possible to distinguish several more stages in enamel mineralization. These include the creation of an enamel layer that is most highly mineralized at its surface, with the degree of mineralization decreasing towards the dentine-enamel junction (DEJ) until the innermost layer is reached, where mineralization is increased (Nanci 2017). This suggests that while mineralization is not as easily studied and it is difficult to determine the exact age of spot-specific mineralization, there might be a pattern to mineralization that can be used.
This was investigated in late 2017 through synchrotron imaging of teeth from 45 sheep (Ovis aries) who died between 1 and 540 days of age (Green et al. 2017). In their study, Green et al. (2017) clearly show how the enamel mineralization in sheep progresses from the cusp towards the cervix. Cuspal enamel mineralizes earlier than cervical enamel and matures over a shorter time (Fig. 1A, B). The enamel near the enamel-dentine junction (EDJ) matures more slowly, while surface enamel proceeds from secretion to maturation more quickly and, in general, takes less time Fig. 1 A Schematic of enamel mineralization in growing sheep viewed in longitudinal section. Mineralization initiates at the dentine horns (left) and proceeds towards the cervix (right) until the crown formation is completed. Lines within enamel show incremental addition over time, and colours indicate maturation extent from low (green) to high (red). Solid lines represent formed enamel and den-tine, while dotted lines depict future crown outlines. The schematic is based on the first molar (M1) enamel of a 14-week-old animal. B The mineralization per cent over time (circles) was determined from quantitative X-ray imaging. Figure compiled of Figs. 1A and 6 in Green et al. (2017) and are available and reproduced through a CC by 4.0 licence to mineralize (Fig. 1B). At the surface, mineralization appears rapid, and 20-90% of the spot-specific mineralization happens over a limited number of days/weeks, with some slight variation depending on specific location on the tooth (Fig. 1B).
With 70% of the surface enamel mineralizing within a few weeks, combined with the suggestions of mineralization overwriting the mineral signals from the secretion phase, it is possible to sample a sheep tooth and, with high accuracy, relate the sample to a specific age of the animal. The mineralization pattern suggests increasing ages from the tip of the tooth to the cervix if comparable depths from the enamel surface are examined (Fig. 1A), but similar studies of high-resolution enamel mineralization are not available across different species and exact chronologies cannot be broadly established. The ability to connect spot-specific areas of a tooth to a limited temporal frame suggests that ordinal sequenced measurements may be obtainable. High-resolution studies on enamel have facilitated research on e.g. seasonality , ancient climate , stress (Austin et al. 2016;Joannes-Boyau et al. 2019), nursing and weaning (Beaumont et al. 2015;Smith et al. 2021) and diet (Sponheimer et al. 2006). However, the temporal and chronological resolution related to provenience and mobility within a tooth has not been comprehensively investigated.

Prerequisites for strontium isotope analyses
Strontium isotope ratios in soils and bedrock have been substantially analysed and researched to determine their age and origin (Faure and Powell 1972). 87 Sr forms through the emission of negative β particles from rubidium 87 ( 87 Rb) (Faure and Mensing 2005) whereas 86 Sr is non-radiogenic and remains constant. The 87 Sr/ 86 Sr ratio in the bedrock is dependent on both the original content of rubidium and the age since rock formation. The half time of 87 Rb is around 49 billion years, whereby no additional Rb decay needs to be accounted for in archaeological studies. No fractionation of 87 Sr/ 86 Sr ratios occurs as it is transferred from the bedrock to the top soil and further into water and plants in a particular area (Graustein 1989).
Strontium isotope ratios in biological remains derive from the bedrock of a particular region, and the variations in 87 Sr/ 86 Sr ratios depend on the type of substratum and its age since formation (Malainey 2011). Apart from the bedrock itself, many other factors influence the strontium ratios in biological specimens, such as the composition of the loose soil cover, precipitation levels, evapotranspiration patterns, aeolian dust, sea spray and, for modern specimens, the use of fertilizers. For these reasons, the strontium isotope "background" data, used for relating the strontium ratios of the analysed specimen to specific regions or areas, are most often based on data from biological samples with limited mobility and known geographic origin (Holt et al. 2021).
The principle behind the use of bioavailable strontium isotope ratios is based on plants absorbing strontium from their local environment. When animals eat and drink, they incorporate and store the available 87 Sr/ 86 Sr values, as obtained from a specific location. When strontium is incorporated in mammalian bodies, it substitutes for calcium in hydroxyapatite (Bentley 2006;Johnson et al. 1966). Plants have significantly higher concentrations of strontium than animal flesh or freshwater. Consequently, omnivores primarily receive their 87 Sr/ 86 Sr ratios from plants and meat must account for more than 50% of the diet before noticeably affecting the strontium isotope ratios (Bentley 2006).
It has been suggested that the best way to establish reliable regional bioavailable strontium ranges is to use plant strontium ratios (Holt et al. 2021;Snoeck et al. 2020) or strontium data from archaeologically retrieved rodent teeth, e.g. from mice (Muridae) and voles (Cricetidae) (Kootker et al. 2016). Strontium ratios from various water bodies have also provided 87 Sr/ 86 Sr ratios similar to strontium data from plants (Blank et al. 2018;Maurer et al. 2012). Consequently, strontium analyses on water may, depending on circumstances, also serve as a viable option to determine bioavailable baseline ratios.

Methods of strontium analysis
Strontium isotope analyses have, for several decades, facilitated studies of provenance of both prehistoric and historic human and animal natives as well as immigrants (Bentley et al. 2003;Ericson 1985;Ezzo et al. 1997;Price et al. 1994;van der Merwe et al. 1990). 87 Sr/ 86 Sr isotope analyses on tooth enamel have traditionally been conducted by thermal ionisation mass spectrometry (TIMS). TIMS analyses are most commonly done on bulk sampled teeth, which gives highprecision values of the average strontium ratios for the enamel mineralization period. By comparing the averaged strontium values from teeth with different mineralization periods, it has been possible to identify the movement between different locations (Blank et al. 2021;Haverkort et al. 2008).
It is possible to use micro-drilling analysis to extract small amounts of enamel for TIMS analyses, but the process is timeconsuming (and costly) and, when it has been done on multiple samples from a single tooth, it has most often been done for method-evaluating purposes (see e.g. Copeland et al. 2008;Willmes et al. 2016). During the last decades, spot-specific strontium analyses have mostly been done using laser ablation multi-collector inductively coupled plasma mass spectrometry (LA-MC-ICP-MS) (Benson et al. 2013;Boethius et al. 2021;Glykou et al. 2018;Müller and Anczkiewicz 2016;Reitmaier et al. 2018). Bulk sampling is more destructive than using spot-specific laser ablation or micro-drilling analyses.

Suggested problems with micro-sampled strontium analyses
Although a temporal data resolution cannot be obtained by averaged data from bulk enamel analyses, this method is used based on previous suggestions that there are difficulties in obtaining temporally separated strontium isotope ratios related to the timing of enamel mineralization (Bentley 2006) and on suggestion that strontium is randomly incorporated into enamel (Montgomery and Evans 2006;Montgomery et al. 2010). The process of strontium incorporation into the body is affected by the turnover rate and the added residence time in the body (Bowen 1979;Dahl et al. 2001). Strontium stored in the body enters bone tissue during its continuous ongoing remodelling phases, averaging the 87 Sr/ 86 Sr ratios in bone tissues over time. Although it is not clear exactly how these "internally" averaging effects affect the incorporation of strontium in enamel, it has contributed to the suggestion that bulk sampling is the best approach when studying 87 Sr/ 86 Sr ratios in enamel (Montgomery and Evans 2006;Montgomery et al. 2010).
The delays in strontium incorporations in the body have added further arguments to avoid micro-sampling enamel. For example, based on the analysis of bovine enamel from a British Iron Age cow (Bos taurus), a long-time averaging effect from strontium stored in the body and a complex, and random, system of enamel mineralization have been suggested to result in minimal temporal resolution within different areas in a tooth . In their study, Montgomery et al. (2010) suggest that the interim values between the end-members (the first measurement closest to the tip and the last measurement closest to the cervix) are nothing more than a mix of the end-values, which prevents chronological differentiation and results in a linear relationship between the individual ablations.

Research potential if micro-sampled strontium isotope ratios provide temporally limited data
The ability to obtain strontium isotope ratios from a more limited temporal window of spot-specific enamel mineralization could, if correlated with high-resolution bioavailable baseline data, indicate visited areas more precisely than averaged bulk sampled data. For both animals and humans, this could offer insights into the extent and appearance of possible territories and home ranges. In regions where there is variation in bioavailable baseline data, this could increase the precision of locating where wild animals were hunted, how domesticated animals were herded and where they were kept, which would provide information on how and where humans moved to hunt, herd or manage the animals.
If temporally limited spot-specific enamel data can be obtained and if it is measurable in an ordinal sequence, the intra-tooth strontium measurements could be arranged in chronological order. A chronological data resolution would increase the potential of micro-sampling enamel even further. Under the right conditions, it could enable studies of how an animal or a human moved through the landscape, i.e. if they moved between different isotope regions of variable bioavailable baseline during the time of enamel mineralization. It could also be possible to study seasonal or yearly foraging patterns if the diet were hunted, gathered or fished from different strontium regions at different times and brought back to the main settlement to be consumed.
There are some caveats concerning the measured strontium signals and thus the interpretations. For example, while the exact timing of spot-specific mineralization (i.e. strontium incorporation in enamel) is available for Dorset sheep (Green et al. 2017), similar data is not available across species. Uncertainties in the timing and sequence of enamel mineralization will affect the ability to connect strontium incorporation to an actual age. In addition, even if future studies would map the mineralization pattern across other species, strontium residence time and turnover rate would still add an averaging effect to the data. Diagenesis and alterations of enamel strontium ratios, due to various contaminations, may also affect the strontium signals, whereby possible diagenetic effects must be taken into consideration. Because of the vast potential in studying temporally limited strontium data by minimizing the sampling area and due to the added available information, if a chronological resolution could be obtained, further investigations are both needed and warranted.

Study premises and research questions
To evaluate the potential in micro-sampling human teeth when studying strontium isotope ratios, the results from LA-MC-ICP-MS analyses conducted on teeth from three separate Swedish archaeological hunter-fisher-gatherer contexts (Boethius et al., Submitted) will be examined and compared to data from previously published bulk strontium TIMS analyses (Ahlström and Price 2021;Kjällquist and Price 2019;Price et al. 2021). The different datasets will be compared, and the spatio-temporal resolution will be examined in connection with the chronological sampling sequence of the laser ablation data.
The results from the archaeological samples will also be compared to the LA-MC-ICP-MS data obtained from a modern man with a known background. Contrasting the strontium data from a diet derived from a modern store, with potentially globally derived strontium sources, against the strontium signals derived from a hunted, gathered and fished diet from the surrounding landscape will facilitate our understanding of strontium incorporation into the enamel. The pattern generated by the ablations on the modern human tooth will be used to frame the conclusions regarding the archaeological teeth.
To test LA-MC-ICP-MS analyses as a tool for studying mobility and provenance through strontium isotope ratios, a set of criteria must be met and must respond to the following postulated suggestions.
Provenance If LA-MC-ICP-MS analyses are to be used instead of TIMS analyses, both accuracy and precision are required. While accuracy is difficult to test without knowing the exact composition of the diet, it can be compared to measurements obtained by TIMS and studied in relation to this data. However, TIMS and LA-MC-ICP-MS analyses require different sampling sizes for successful analysis. Larger samples mean larger periods involved in the mineralization of the analysed part of a tooth and data averaged over longer time slices. Furthermore, as evidenced by detailed studies of sheep enamel mineralization (Green et al. 2017), if the two methods of analysis aim to target the same time slice, the enamel needs to be sampled both at the exactly same depth from the surface and at the same distance from the cusp. While sampling at comparable depths may be easily done using laser ablation technology, where the pre-ablation allows you to remove the surface enamel with a precision of a few microns, it may be more difficult to facilitate by microdrilling prior to a TIMS analysis. Thereby, even if the two different analyses were made with the intention of obtaining perfectly comparable data, it would still be difficult to target the exactly same time of mineralization and a perfect match between the two datasets may not be expected. We suggest that if LA-MC-ICP-MS measurements are to be considered valid, they must not differ greatly from the TIMS data; the different datasets must show a strong correlation; and they must not display systematic deviating measurements, i.e. constantly higher or lower values, when the same area of a tooth is analysed with the two methods.
Spatio-temporal resolution Optimal use of micro-sampling methods requires that tooth enamel contains spatio-temporal information obtainable through LA-MC-ICP-MS analyses. This means that the data from each ablation must contain nonrandom information of strontium incorporated during a limited period. If no spatio-temporal resolution is present when microsampling a tooth from the tip (first measurement) to the cervix (last measurement), the interim measurements between these end-members should be aligned along a linear end-member gradient, i.e. as suggested by Montgomery et al. (2010).
However, if there is a temporal resolution in enamel and if this is obtainable through laser ablation, the data from different teeth should display different types of patterns. Consequently, we suggest that if a spatio-temporal resolution can be obtained through laser ablations, the interim measurements would not fall on the end-member gradient except in a few unique situations. Such situations would include teeth where the input of strontium did not change during mineralization (i.e. a constant diet and no mobility) or when the input of strontium changed linearly over time, e.g. if the subject was on the move and thus changed diet from a low strontium ratio baseline range to a gradually increasing range, or vice versa. This means that if a spatio-temporal resolution is obtainable in human enamel, individual interim measurements will be located both inside and outside of the end-member gradient.
Chronological enamel mineralization The ability to obtain spatio-temporally limited measurements is a prerequisite for the possibility to study the timing of strontium incorporation in human enamel. If the interim laser ablation measurements do not all linearly align along the end-member gradient, sampling minor sections of a tooth can reduce the time slice of averaged strontium in the enamel and enable more precise (temporally limited) data to be obtained.
High-resolution strontium analyses on the enamel from sheep and goats from the Altai Mountains, Mongolia, suggest that mobility is traceable by LA-MC-ICP-MS analyses. When the innermost enamel, closest to the dentine, was sequentially measured at the same depth but with increasing distance from the cusp, it showed a traceable mobility pattern. This pattern agreed with the actual, GPS-tracked mobility of the herd, with a median displacement lag of 41 days, and corresponded with the regional isoscapes, which were established by the analyses of plants from 156 different sites within the study area (Lazzerini et al. 2021).
Based on strontium concentration peaks and its subsequent return to normal levels in wild orangutan (Pongo pygmaeus) canine tooth enamel, estimations suggest it takes between 10 and 24 days (mean 16.3) for strontium concentrations to return to the "pre-concentration-peak" baseline (Dean et al. 2020). This is similar to the 10 days (blood plasma) to 4 weeks (bone) it took for strontium plateaus to be reached in rats (Rattus) after being administered high strontium concentrations orally (Dahl et al. 2001). In orangutan teeth, these estimations are based on enamel mineralization data close to the EDJ. More rapid mineralization along the enamel surface could shorten the time for overprinting and the return to normal strontium concentrations further (Dean et al. 2020), as is also suggested by the more rapid enamel mineralization speed in sheep enamel surface compared to the enamel closer to the EDJ (Green et al. 2017).
While strontium concentration data from orangutan enamel is not directly transferable to human strontium residence time in the body, and the orangutan sample sizes were small and the reasons behind the observed strontium concentration peaks may only be speculated (Dean et al. 2020: 12), it gives some hint of the overprinting time in primate enamel. The presence of concentration spikes suggests that the strontium incorporated in enamel comes from a combination of the most abundant strontium levels at a particular time, i.e. from the recent diet, and the residence strontium stored in the body. Thereby, temporally limited "strontium-events" will affect strontium incorporation in enamel with a measurable spatio-temporal resolution. In orangutan canines, this temporal resolution spans over a couple of weeks and covers an average of 100 μm of tooth enamel (Dean et al. 2020).
If the same applies to humans, the strontium ratios from any given ablation should contain averaged strontium data from a limited period corresponding to the days, weeks or month of spot-specific mineralization. The resident strontium in the body would slowly be replaced as new strontium enters the body (Dahl et al. 2001), and a new plateau is reached. If this process is measurable using LA-MC-ICP-MS, it may provide spatially limited data related to the specific time of enamel mineralization. If the mineralization is chronologically arranged, the pattern generated by the ablations should follow a distinct order, presenting a gradual change in 87 Sr/ 86 Sr ratios when measured at equal depths in a consecutive sequence from the tip to the cervix. We suggest that the strontium ratios from this gradual change derive from a combination of the averaging effect of resident strontium and the diet, presumed to mainly consist of animals and plants from a specific region of the local environment. If, on the other hand, a spatio-temporal resolution of enamel formation is available, but it follows a random mineralization pattern unrelated to initial enamel deposition/ tooth development, we suggest that the measurements should oscillate between extremes without any discernible pattern.
Lastly, we suggest that if chronological strontium data is obtainable through laser ablation, there will be differences between the patterns generated by analyses of the modern tooth and the pattern from the archaeological teeth and that this may be attributed to how the strontium incorporation in enamel reflects the diet. Since a modern diet lacks correlation with the local landscape, daily acquiring strontium ratios from many different areas (i.e. from a store), the strontium ratios would, despite being averaged by the strontium residence time in the body, behave more randomly. Thus, even if the spatio-temporal resolution connected to specific time slices of enamel formation is measurable and follows a chronological pattern from the tip to the cervix, a random pattern would still be expected in a modern tooth (Table 1).
By comparing TIMS data to LA-MC-ICP-MS measurements, obtained in a sequence from the tip to the cervix, and by relating this to the LA-MC-ICP-MS measurements from a modern tooth with known background, the study is constructed to address five main questions: 1) Do spot-specific measurements of strontium ratios in human enamel increase the spatio-temporal resolution providing more precise data? 2) If true, is this information accessible through LA-MC-ICP-MS analyses? 3) Does strontium incorporation in human enamel follow a chronological pattern from the tip of the tooth to the cervix? 4) If true, is the data relatable to an exact age of the studied individual? 5) Is it possible to relate the enamel data from both archaeological and modern teeth to bioavailable strontium ratios in the landscape?

Archaeological human remains
Teeth from 28 Stone Age hunter-gatherer-fishers were analysed using LA-MC-ICP-MS with between 5 and 27 individual measurements on each tooth with a total of 434 individual measurements. Specific LA-MC-ICP-MS data for each ablation, including photographic information of the exact location of each ablation, is available in Boethius et al. (submitted). The teeth/individuals have all been previously analysed with TIMS, and the original data is available (Ahlström and Price 2021; Kjällquist and Price 2019; Larsson and Price 2022; Price et al. 2021). No information on the exact area for TIMS analysis or on the depth from the enamel surface was presented in these studies, but the teeth were, as evidenced by the section of removed enamel, TIMS-sampled from the tip to the cervix. The teeth were selected based on availability (Table 2). They include five teeth from Norje Sunnansund, an Early Mesolithic, Maglemose culture site from Blekinge in south-eastern Sweden dated to 9600-8600 calibrated (cal) before present (BP) (for detailed information about various aspects of the site, see e.g. Boethius 2016Boethius , 2017Boethius , 2018Boethius et al. 2021;Kjällquist  All measurements located within endmember gradient, no distinguishable data pattern All measurements not located within end-member gradient, no distinguishable data pattern All measurements not located within endmember gradient, no distinguishable data pattern Prehistoric teeth All measurements located within endmember gradient, no distinguishable data pattern All measurements not located within end-member gradient, no distinguishable data pattern All measurements not located within end-member gradient, chronologically traceable data pattern 2020; Kjällquist et al. 2016). Eight teeth from Skateholm I and II, a Late Mesolithic, Ertebølle culture site from southern Scania in southernmost Sweden dated to 7200-6800 cal BP (see e.g. Larsson 1985;Larsson 1988Larsson , 1993Larsson , 2016) for more information) and 15 teeth from Västerbjers, a middle Neolithic, Pitted Ware Culture site from the Swedish island of Gotland dated to 5000-4600 cal BP (Ahlström and Price 2021).

Modern man comparison
To evaluate and contextualize strontium incorporation and spatio-temporal resolution in archaeological data, a tooth from a modern man from Sölvesborg, south-eastern Sweden, with known childhood background, was analysed using LA-MC-ICP-MS (Table 3).

Archaeological tooth LA-MC-ICP-MS data
The LA-MC-ICP-MS analyses were done at the Vegacenter, at the Museum of Natural History, Stockholm, Sweden, and followed the methodology as described in Boethius et al. (Submitted). Detailed information of the instrument settings, the operating conditions, data on each measurement and the interpretation of the mobility pattern and societal consequences thereof can be found there.

Modern man tooth LA-MC-ICP-MS data
To enable comparison, to provide a frame for understanding the pattern generated by the ablations and to assess the value of applying LA-MC-ICP-MS analyses to archaeological teeth, a tooth from a modern human with known age and geographical background during enamel mineralization was analysed. The preparation and analysis procedure was the same as for the archaeological teeth. The tooth was soaked and washed in distilled water and cleaned with a soft toothbrush. Following cleaning, the tooth was air-dried at room temperature and transported to the Vegacenter to be mounted and fixed in a sample cell on a movable mounting table.
All ablations were sequentially made, from the tip to the cervix, at equal depths from the outer surface of the tooth enamel. The tracks to be analysed on the enamel were pre-ablated using a laser spot size of 150 μm, and the outer few (~ 10) μm of the enamel was removed to expose a fresh surface. Twenty-one parallel tracks of ca. 400 μm lengths with a spot size of 130 μm were then ablated on the pre-ablated enamel surface.
Ratios for 87 Sr/ 86 Sr were obtained measuring the enamel surface in an NWR193 excimer laser ablation system (Elemental Scientific Lasers, Portland, OR, USA) connected to a Nu Plasma II multi-collector ICP mass spectrometer (Nu Instruments, Ltd., Wrexham, UK). The tooth was measured in February 2020, and the instrument operating conditions along with the details and isotope data for the ablations are listed in Supplementary Tables S1 and S2. Possible isobaric interferences were corrected by subtracting a gas blank ( 84 Kr) and by peak stripping (e.g. doubly charged REE, Ca-dimers/argides, 87 Rb). All corrections were applied online, which resulted in interference-free 87 Sr/ 86 Sr ratios for each data point.
A polyatomic interference ((Ca/Ar) 31 P 16 O + ) on m/z 87 has been reported (Horstwood et al. 2008) to introduce a significant offset in 87 Sr/ 86 Sr in samples with low strontium concentrations, resulting in inaccurate LA-MC-ICP-MS results . This interference was reduced by low oxide tuning of the gases (Willmes et al. 2016) and accurate 87 Sr/ 86 Sr ratios have been demonstrated at low concentrations, down to C Sr ~ 7 ppm (Boethius et al. 2021).

Modern man background documentation
To obtain sufficient background information about the diet and travelling habits of the modern man whose tooth was used in the study, a preliminary interview was done in early 2020, prior to us obtaining the tooth. A year later, this was followed up by a questionnaire, where the modern man was asked to elaborate on his diet, drinking and travelling habits during childhood. After he had conferred his memories with his mother and asked if she had further input, he submitted his answer on the 21 st of April, 2021. On the 28 th of August, 2021, he was asked one final time to read the part of the manuscript connected to his background. After his final read through, some minor adjustments and a few additional details were added according to his suggestions.

Comparing TIMS and LA-MC-ICP-MS data
In the present study, the premises for dataset comparisons are not optimal. The TIMS analyses were not always done on the same tooth, they were done several years before the LA-MC-ICP-MS and the entire enamel length, from the tip to the cervix, was sampled, with no available information on what parts were used in the subsequent analyses. Consequently, each TIMS measurement potentially includes averaged strontium information from the entire enamel mineralization period (several years), whereas the individual LA-MC-ICP-MS measurements represent strontium averaged over significantly smaller periods (days or weeks). To facilitate comparison, each tooth was analysed with multiple laser ablations, covering the entire length of available enamel, and the combined LA-MC-ICP-MS measurements were contrasted to the TIMS data. The 87 Sr/ 86 Sr values obtained from   Buikstra and Ubelaker (1994), Goodman et al. (1980) and Reid and Dean (2006).
Sr is incorporated in enamel during mineralization (after deposition) but the timing is unknown. No data for location of TIMS is available, but all teeth have been TIMS-sampled from the tip to the cervix ***Valid ablations exclude ablations that struck dentine ****Average weighted by Sr intensity, to account for possible areas of elevated Sr concentration, which, if present, can dominate the bulk/averaged values. Small variation in Sr concentrations may also serve as an indicator that similar enamel depths were targeted along the side of each tooth, as the distance from the EDJ correlates with gradually decreasing Sr concentrations towards the enamel surface (Dean et al. 2020). Bulk Sr TIMS data for Norje Sunnansund (NS) from Kjällquist and Price (2019)

Spatio-temporal resolution evaluation
To investigate if diminishing the sampling area in tooth enamel increases temporal resolution, the data from the interim ablations, between the end-members in the measurement series of a tooth, were investigated. Linear regression was established between the two end-members of each tooth, and a "maximum end-member mixing range", as derived from the area covered by the measurement ranges between the 2 SD external errors of each LA-MC-ICP-MS measurement, was established. The LA-MC-ICP-MS measurements from each tooth were studied in connection to the end-member linear gradient and its mixing range limit. This was deemed the best approach as the strontium concentration levels varied very little across the enamel surface of each tooth (cf. average and weighted average 87 Sr/ 86 Sr ratios in Table 2 and the data from each ablation line in Boethius et al. (Submitted).

Chronological data assessment
To assess if there is a chronological sequence connected to strontium incorporation, the pattern generated by the individual LA-MC-ICP-MS measurements on each tooth was investigated. The data patterns were studied both when the measurements were put in a chronological sequence from tip to cervix (i.e. following the enamel matrix deposition order) and in random order. The studies were made by describing the pattern generated by both the chronological and the random measurement sequence data for linear and 2 nd to 5 th orders of polynomial trendlines and by calculating the R-squared value for each tooth and trendline. The data sequence was analysed at the Vegacenter from the tooth tip to the cervix. The randomized data sequences were obtained by using the RAND function in Excel, which allows the creation of a fifteen-decimal random number between 0 and 1. The generated numbers can thereafter be related to the individual ablation and sorted from low to high. Since the generated random numbers are connected to the different measurements from each tooth, the originally chronologically sampled measurement sequence is randomized. Lastly, a two-sided Welch's t test was used to assess whether strontium measurements from n lines measured on a tooth have equal means (Welch 1947). As the variances among lines on a single tooth vary, this test is more appropriate than the standard t test. The significance level (0.05) was adjusted according to the Bonferroni correction, as testing n lines along a tooth involves multiple comparisons (i.e. p = 0.05/n). The results from the different teeth in the study are given as a matrix, with t values in the lower diagonal and the associated degrees of freedom in the upper diagonal, where the non-significant t values are printed in red (Tables S3-S30, Table S32).

Results
The results show a general high correspondence between the TIMS bulk measurements and the average, weighted average and median laser ablation data from each tooth ( Table 4).
The largest and smallest (max, min) difference between TIMS and LA-MC-ICP-MS data for the investigated teeth with average, weighted average and median difference for all teeth combined is shown. Individual ablation data in Boethius et al. (Submitted) Data from three teeth display comparably large discrepancies between bulk and laser ablation measurements (> 0.2% difference). Two of these are from Norje Sunnansund (NS:99 and NS:101), and one is from Västerbjers (VB:34). Data from three additional teeth show an elevated discrepancy between bulk and laser ablation analyses (0.1-0.2% difference) (NS:100, VB:36 and VB:51). The remaining 22 individuals show data with less than 0.1% difference (Fig. 2). The teeth with the largest measurement discrepancies show the highest regional 87 Sr/ 86 Sr ratios among the teeth in the study, and they are among the teeth with the highest intra-tooth variation in the strontium ratios obtained by the laser ablation ( Fig. 2 and Boethius et al. Submitted). Despite these six teeth with elevated TIMS and LA-MC-ICP-MS value discrepancies, the general correlation between the datasets is high and shows a strong linear relationship (Fig. 2B).

Obtaining a spatio-temporal resolution of strontium incorporation in tooth enamel
The TIMS dataset and the median/average data obtained from LA-MC-ICP-MS show a strong correlation with minor discrepancies and only differed more than 0.2% for 3 of the 28 individuals analysed with both methods, which suggests that the datasets are comparable. However, validating the averaged measurements from the teeth gives no information on what timeframe the individual ablation tracks represent, if strontium is randomly incorporated in enamel or if it follows a distinguishable pattern. As seen in Figs. S1-S29, the individual LA-MC-ICP-MS measurements are, in general, not linearly aligned (see also  Table 5 for data on the linear correlation of all measurements from each tooth) and the interim measurements do not fall on the linear gradient connecting the two end-members. If expanding the linear gradient to encompass the maximum end-member mixing range limit, 24 of the 28 archaeological teeth have measurements falling outside the range and, in total, 174 of the 378 interim measurements (46%) fall outside of these maximum measurement ranges, showing that the measured values cannot be the results of end-member mixing.
Lastly, Welch's t tests were constructed for each tooth, to statistically evaluate each ablation point and measure if they have equal means (Tables S3-S30, Table S32). The results from the t test are comparable to those observed in the chronologically ordered sampling sequence of each tooth and, in most cases, show significant differentiation from the other measurements. In the cases where non-significant t values are demonstrated, the indicated measurements align on the y-axle of the respective plot (cf . Tables S3-S30, Table S32 and Figs. S1-S29). The t tests validate the measurement sequence and offer no other explanations for the observable data pattern.

Assessing the prospect of obtaining chronological data related to the life history of the investigated subject
Showing that end-member mixing is not the cause of the interim strontium values does not mean that the LA-MC-ICP-MS method applied here provides chronological information. A random enamel mineralization pattern, even if from a temporally limited time of strontium incorporation in the enamel, might still render data unrelated to a chronological pattern (see Table 1). To investigate if there is a chronological order in enamel mineralization or if strontium is randomly incorporated in the enamel, the sequence of the individual measurement from each tooth was randomized and contrasted against the chronological sampling sequence.
To understand what types of patterns can be expected if a chronological and temporally limited strontium uptake in the enamel is the case, some considerations must be made. The strontium values in enamel reflect the diet as obtained from the bioavailable baseline in a specific area. Even if strontium incorporation in enamel is temporally limited and there is a reflection of the averaged baseline ratios of the diet consumed during a limited enamel mineralization period, the generated pattern, following the individual ablations in subsequent order from the tooth tip to the cervix, would not, with three exceptions, display a linear pattern.
The exceptions where a linear pattern would appear are as follows: (1) if the subject stayed in one area and consumed a uniform diet throughout the entire tooth mineralization process (generating horizontal linearity), (2) if the subject was on the move (or changed its diet) from a low 87 Sr/ 86 Sr baseline area to a high area (generating positive linearity) and (3) if the subject was on the move (or changed its diet) from a high 87 Sr/ 86 Sr baseline area to a low area (generating negative linearity). If the mobility was done in any other way (any combination of backand-forth mobility between different strontium isotope regions) or if the diet varied or was seasonally derived from different areas within the period of enamel mineralization, the chronologically sequenced ablations would display a non-linear pattern.
To describe the pattern in the potentially non-linear data and determine the ability to create a transitional model connecting the different measurements, the R-squared values for both linear and polynomial trendlines, between the 2 nd and 5 th orders, were calculated for both the chronological and randomized sampling sequences (  5). The decision to limit the models to between the 2 nd and 5 th polynomial orders is related to increasing equation complexity with higher polynomial orders. This is evidenced by Runge's phenomenon, which shows that a higher polynomial degree does not always improve accuracy (Runge 1901) due to increasing oscillation at the edges of an interval. A 5 th -order polynomial encompasses up to four constraints (allowing a trendline to curve up to four times) and is thus able to illustrate transhumance, should such be evident in the data; higher orders were considered redundant. datasets are compared in a scatter plot, where the weighted average of the LA-MC-ICP-MS measurements is set at the x-axis with 2 SD, added to account for the internal data ranges (the spot-specific 2 SD external precision range is not included, see Supplementary Information), and TIMS data is set at the y-axis. A trendline is added to show the correlation between the two datasets To assess if the Sr incorporation in the enamel surface is temporally limited, non-random and related to a chronological mineralization pattern, or if it is completely random, the R-squared values for linear and 2 nd -5 th polynomial order trendlines were calculated. The values are illustrated according to their ability to represent the sequence of the individual ablations for both the chronological and the randomized sampling sequences. The divisions were done following general considerations regarding coefficients of determination where r 2 ≤ 30 (red) indicates no correlation with the data sequence, 30 < r 2 ≤ 50 (yellow) indicates a low correlation, 50 < r 2 ≤ 70 (blue) indicates a moderate correlation and r 2 > 70 (green) indicates a strong correlation.
As seen in Table 5 and illustrated in Figs. 3, 4 and 5, there are large discrepancies between the chronologically sequenced data Data is colour coded according to the trendline correlation with the chronological and the randomized sampling sequence. Red = no correlation: r 2 ≤ 30; yellow = low correlation: 30 < r 2 ≤ 50; blue = moderate correlation: 50 < r 2 ≤ 70; green = strong correlation: r 2 > 70 Fig. 3 The measured 87 Sr/ 86 Sr ratio data, as obtained by LA-MC-ICP-MS, from Norje Sunnansund put in a chronological sequence, following the initial sweep of the enamel formation from the tip to the cervix, and b randomized order. Linear and polynomial trendlines of the 2 nd to 5 th orders added to each tooth to illustrate the R-squared data presented in Table 5; red = no correlation: r 2 ≤ 30; yellow = low correlation: 30 < r 2 ≤ 50; blue = moderate correlation: 50 < r 2 ≤ 70; green = strong correlation: r 2 > 70 97 Page 14 of 28 Archaeological and Anthropological Sciences (2022) 14: 97 Fig. 4 The measured 87 Sr/ 86 Sr ratio data, as obtained by LA-MC-ICP-MS, from Skateholm put in a chronological sequence, following the initial sweep of the enamel formation from the tip to the cervix, and b randomized order. Linear and polynomial trendlines of the 2 nd to 5 th orders added to each tooth to illustrate the R-squared data presented in Table 5; red = no correlation: r 2 ≤ 30; yellow = low correlation: 30 < r 2 ≤ 50; blue = moderate correlation: 50 < r 2 ≤ 70; green = strong correlation: r 2 > 70

Fig. 5
The measured 87 Sr/ 86 Sr ratio data, as obtained by LA-MC-ICP-MS, from Västerbjers put in a chronological sequence, following the initial sweep of the enamel formation from the tip to the cervix, and b randomized order. Linear and polynomial trendlines of the 2 nd to 5 th orders added to each tooth to illustrate the R-squared data presented in Table 5; red = no correlation: r 2 ≤ 30; yellow = low correlation: 30 < r 2 ≤ 50; blue = moderate correlation: 50 < r 2 ≤ 70; green = strong correlation: r 2 > 70 and the data put in randomized order. The chronologically sequenced data show a more distinguished data pattern, and the R-squared values for the chronologically sequenced trendlines show a higher correlation with the data compared to the randomized data sequence. This means that it is, in general, possible to find a pattern in the chronological data sequence while the random data sequence shows no such general tendencies. For the chronological data sequence, data from three teeth show a strong linear correlation, one from each of the three sites. If allowing one curve on the trendline (i.e. a 2 nd -order polynomial trendline), eight teeth show a strong correlation. This increases to 13 teeth when allowing two curves on the trendline (3 rd -order polynomial trendline). Data from 16 teeth show a strong correlation when allowing three curves (4 th -order polynomial trendline) while 19 teeth generate a strong trendline correlation when 4 curves are allowed (5 th -order polynomial trendline). If also including moderately strong trendline representation, data from only two teeth fail to present a moderate to strong trendline correlation (i.e. 93% of the teeth shows a distinct chronological pattern in the data). The same number regarding the randomized data sequence shows that only three teeth produce a moderate to strong correlation for the trendline when the data is put in random order (i.e. 11% of the teeth shows a strong to moderate correlation pattern with the data when the order is randomized). If also considering that the two teeth that did show a strong data correlation only had five respectively six valid ablations (i.e. if a trendline is allowed to curve 4 times, it will automatically connect all the values), it further shows that the random pattern is not similar to the chronologically sequenced one.

Modern man tooth data
The second premolar from the right maxilla of a modern man was analysed with 21 individual ablations to be used as a contrast to the archaeological data. The tooth had been surgically removed when the investigated person was in his early teens, and kept in a box during the last 30 years. Similar to the archaeological data, the sequence of the individual measurement from each tooth was put in both chronological (tip to cervix) and randomized orders. R-squared calculations for linear and 2 nd to 5 th orders of polynomial trendlines were used to identify the correlation with the data sequence ( Table 6). The generated trendline patterns are also illustrated (Fig. 6).

Modern man diet and travelling background
As for most modern individuals born in Sweden in the early 1970s, the food eaten growing up was not farmed where one lived but bought at a local grocery store. While it is not possible to consult the records of the store primarily used for purchasing food by the investigated man's parents, it is a fairly safe statement that the food available in the store was not primarily local. In the 1970s, globalization had not gone as far as it has today, with groceries being bought and traded from all over the world. The food available at stores was produced by national farms and food producers to a greater extent than today. Historical consumption data on beef, pork and cheese show that in the 1970s, imports of these groceries amounted to 7.8%, 8% and 20.4% of the total consumption in Sweden. Less than a decade ago (2013), the import of these products had increased to 49.1%, 33.2% and 63.1% (Lööv et al. 2015). Consequently, if one was born in the 1970s and if one's parents did not only visit local farms for their food purchases, the diet would end up being a mix of the food farmed and produced at a large variety of places, albeit less so than today and often from elsewhere within the country.
Through interviews with the person who lent his tooth to the study, it is known that his parents bought most of their food at the local grocery store (Konsum Sölvesborg). He also states that he ate a diet consisting of mostly potatoes and meat, with occasional pasta or rice to substitute for the potatoes and, on occasions, fish and chicken would substitute the meat. He seldom ate vegetables, such as tomatoes, salad and cucumber, but he ate bread, cereals (cornflakes, etc.) and porridge for breakfast and drank milk to all his meals. Water was more seldom drunk and only in between meals. It is also known that the town of Sölvesborg, where he grew up, received its water from the local groundwater. During the 1980s, Sölvesborg municipally did major changes to their water supply system by modernizing it and reducing the number of hydropower plants. The groundwater abstractions are roughly the same today as in the 1980s 1 . Due to the major reconstructions, it is not possible to exactly determine the strontium isotope ratio in the Sölvesborg tap water for the 1970s. Hence, no analyses have been performed on modern tap water. Instead, data from two natural springs (Barnakälla and Skönabäckskällan), both within 10 km from Sölvesborg and on the same Table 6 R-squared values for linear and 2 nd to 5 th orders of polynomial trendlines for a modern tooth. Calculations were made in chronological, following the initial sweep of the enamel formation from the tip to the cervix, and randomized order. No correlation is indicated (r 2 ≤ 30)

Tooth
Linear (%) 2 nd -order (%) 3 rd -order (%) 4 th -order (%) 5 th -order (%)  . 6 The measured 87 Sr/ 86 Sr ratio data, as obtained by LA-MC-ICP-MS, from a modern man from Sölvesborg put in a chronological sequence, following the initial sweep of the enamel formation from the tip to the cervix, and b randomized order. Linear and polynomial trendlines of the 2 nd to 5 th orders were added to each tooth to illustrate the R-squared data presented in Table 6; red = no correlation: r 2 ≤ 30. Mean Sr ratio is 0.71251, and mean ablation variance is 0.000000088 geological bedrock with 87 Sr/ 86 Sr isotope ratios at 0.712687 and 0.713100 (Boethius et al. 2021), is here used as a proxy for the 1970 tap water strontium isotope ratios.
To understand the observed LA-MC-ICP-MS pattern from the modern man, it could also be important to know the subject's travelling habits during childhood. The subject states very little childhood mobility and did, to his or his mother's recollection, not undertake more than two separate trips outside the local area between 1974 and 1981 (his analysed tooth formed between 1975 and 1979 (see Table 3) and would have mineralized with a delay in relation to this period). One of these two trips went to Dalarna, in mid-Sweden, which has a significantly older bedrock and elevated 87 Sr/ 86 Sr ratios compared to the sandstone bedrock of Sölvesborg. This trip lasted about a week, and food was likely (he does not remember what they ate) purchased at local grocery stores in Dalarna. His other trip lasted about a week and went to Öland, which has a bioavailable baseline similar to Sölvesborg (Fig. 7). Considering that the archaeological human teeth had a distinguished chronological strontium pattern (Figs. 3, 4 and 5), and a completely random human enamel mineralization can likely be excluded, the measurement fluctuations observed in the chronologically sequenced measurements on the modern man are likely connected to a diet from different isotope regions.
Delving further into the matter, the tap water proxy for 1970 Sölvesborg does fit well with the enamel data from the modern man. However, this can be a function of similarities in the most fertile areas in southern Sweden, which are often on similar bedrock with similar 87 Sr/ 86 Sr ranges as the town of Sölvesborg (cf. e.g. bioavailable baseline in southern Scania Fig. 7), and likely not related to drinking tap water. The subject also states that he rarely drank tap water, preferring milk, which would make a significant input of tap water to his strontium ratios even more unlikely.

The precision of LA-MC-ICP-MS on archaeological data
The results indicate that the strontium isotope bulk measurements through TIMS correspond well with the average, weighted average and median laser ablation data from each tooth ( Table 4). The results are somewhat elevated compared to previous comparisons between solution and laser ablation-based analyses, from which a study on modern rodents indicates an average measurement difference of 0.0003 ± 0.0002 (Copeland et al. 2008) and another study on fossil rodent teeth indicates an average measurement difference of 0.0005 ± 0.0010 (Copeland et al. 2010b). On these previous comparisons, both bulk and laser ablation analyses targeted comparable areas of the same teeth when evaluating the use of laser ablation as a tool for strontium isotope provenance. On the majority of the teeth in the former of the two studies, the ablations were done with one ablation line and in the latter with two ablations, and efforts to secure comparability were taken. This is a contrast to this study, where the bulk analyses had been made for other purposes without any intention to compare with data obtained through LA-MC-ICP-MS and the exact part of the analysed enamel is unknown, whereby an increased discrepancy may be expected as a result. In addition, small rodents are known for their limited mobility, making their inclusion in archaeological deposits optimal for creating bioavailable baseline ranges (Kootker et al. 2016). Humans have both varied feeding habits and may have long-distance mobility, whereby a slight difference in areas of sampling might result in elevated discrepancies between two different methods of analysis.
The TIMS and LA datasets show a high correlation in average/median data, with the added gain of LA-MC-ICP-MS analyses being able to provide more information on the measurement variation within the tooth. There are a few exceptions of increased measurement differences between the two datasets and to understand these discrepancies, the data needs to be considered in context. The bedrock in the area around Norje Sunnansund is highly varied, which is not the case for the areas around Skateholm and Västerbjers (Fig. 7). The bioavailable 87 Sr/ 86 Sr ratio diversity around Norje Sunnansund is further enhanced by a complicated water catchment route to the ancient Lake Vesan, which gave much higher strontium ratios in the lake compared to the immediate surrounding terrestrial landscape (Boethius et al. 2021).
On the two teeth from Norje Sunnansund with > 0.2% difference between the two datasets (NS:99 and NS:101), most of the enamel was removed during the TIMS analyses and the later laser ablations had very little remaining enamel to target. The LA-MC-ICP-MS analyses on these two teeth were measuring enamel from a significantly smaller area than what was sampled for the TIMS analyses (Fig. 8), which implies that the bulk measurements, on the teeth with diverging strontium ratios, also included strontium signals from regions that were unaccounted for by the ablations. The tooth with the largest discrepancy between TIMS and laser ablation analyses also had the most elevated internal precision uncertainty (standard error) of all archaeological teeth in the study. Furthermore, on both of the teeth with elevated measurement differences, the enamel had been coloured black by the depositional environment, which may suggest diagenesis. A third tooth from Norje Sunnansund (NS:103) also had blackened enamel but did not show any measurement difference between the two methods of analysis. Since it was possible to ablate NS:103 on the entire enamel tooth side, i.e. corresponding to the section removed for TIMS, it may suggest that differences in sampling location are mainly responsible for the measurement discrepancies seen in NS:99 and NS:101. Diagenetic effects can, however, not be completely ruled out as they might have affected both TIMS and laser ablation analyses on the three black teeth. Uranium and thorium concentrations measured in tooth enamel have previously been used to identify zones that were diagenetically overprinted (Willmes et al. 2016). However, the experimental setup in this study does not allow for simultaneous collection of Sr isotopes and U and/or Th elemental concentrations and this can therefore not be used in this case. Large amounts of incorporated rubidium could also point towards diagenetic overprinting. While this is not observed in the archaeological teeth here, the absence of proof is not a proof of absence and low Rb concentrations cannot be used to rule out diagenetic overprinting. However, if diagenesis affects the strontium ratios in the enamel from the black teeth, it is not correlated to the soil deposition environments, which displays higher values than NS:99 and NS:103 and significantly lower values than NS:101 (cf. Boethius et al. 2021). This suggests that, if present, diagenetic overprints have not been uniformly incorporated in the enamel and have likely only contributed to parts of the measured strontium isotope data.
The third tooth with > 0.2% difference between the two datasets (VB:34) did not show discoloured enamel and did not have an elevated standard error on the laser ablation measurements, and unlike the diverging teeth from Norje Sunnansund, it was ablated from the crown to the cementum-enamel junction. However, similar to all other teeth in the study, it is not possible to specify exactly which parts of the enamel were analysed with TIMS. The ablations on the first formed areas of the VB:34 tooth, i.e. closest to the occlusal surface, gave ratios that were most deviant from the bulk measurement (cf. Figs. 2A and 5), with values higher than any other human measurements from Västerbjers. If only the enamel closest to the cervix was analysed with TIMS, an increased discrepancy between the two datasets may be expected.

Assessing the value of LA-MC-ICP-MS for mobility studies on archaeological teeth
Strontium isotope ratios obtained through LA-MC-ICP-MS are less precise than the data obtained through TIMS, and a slight discrepancy between TIMS and averaged data of the compiled LA-MC-ICP-MS measurement is evident in this study. However, the LA-MC-ICP-MS measurements are accurate enough to study mobility and provenance and the margin of error is well within what is required to interpret the geographic bioavailable origins and does not affect the archaeological interpretation. Indeed, LA-MC-ICP-MS precision, as shown here for human teeth, was demonstrated more than a decade ago for both modern and fossil rodents (Copeland et al. 2008;Copeland et al. 2010a) and the margins and sources of error have, through technological development and advancements of in situ laser ablation analytical techniques (Benson et al. 2013;Le Roux et al. 2014;Lewis et al. 2014;Willmes et al. 2016), narrowed since then.
Technological developments in LA-MC-ICP-MS are relevant when e.g. assessing the data where Montgomery et al. (2010) concluded that the decrease in sample volume does not increase the resolution of the measured strontium signals and that the processes involved do not increase the temporal resolution of the measured signal. They built their arguments on the laser ablation data from Horstwood et al. (2008) who had an error margin for each ablation at around 0.1-0.15% (2 SD). The data obtained with more recent LA-MC-ICP-MS measurements are more precise and show a 0.015-0.05% 2 SD error margin (median 0.03%), i.e. an up to 10 times decreased uncertainty (Boethius et al., Submitted). It is conceivable that with increasing precision, along with measures taken to ensure that the enamel is targeted at equal depths, it also becomes possible to better distinguish changes in temporal resolution. This may be the reason why the end-member mixing results seen in previous bovine enamel analyses  are not evident Fig. 8 Pictures of the three teeth with black enamel from Norje Sunnansund. NS:99 and NS:101 have > 0.2% discrepancies between TIMS and LA measurements while NS:103 has < 0.06% measurement discrepancy here. A high spatio-temporal resolution further suggests that the ablation measurement span itself is a good representation of the variability of 87 Sr/ 86 Sr ratios in the analysed human enamel. Converting the data from the individual ablation into e.g. boxplots ( Fig. 2A) thus provides a good base for understanding the various baseline signals incorporated in the enamel from a tooth, i.e. compared to if the same area of the tooth was bulk sampled (where only one averaged measurement would become available).
Although TIMS provide more precise, low-error margin averaged data, LA-MC-ICP-MS has other advantages that, depending on the purpose of the study, offer a wide range of possibilities. These include cost efficiency and being close to non-destructive: LA-MC-ICP-MS can be used on rare or unique specimens and barely causes any visible damage. The greatest potential in micro-sampling methods of archaeological biological remains lies in the prospects of obtaining data from limited strontium averaging time slices and by being able to follow the enamel mineralization pattern and thus trace the mobility of the subject within the period of strontium incorporation in a specific tooth.

Addressing strontium incorporation in enamel
There is a clear contrast between the chronological and the randomized data for the archaeological teeth. Polynomial trendlines were able to illustrate a strong correlation with the data sequence for most teeth when analysed in chronological order, whereas it was, in general, not possible to find a pattern in the randomized data sequence (cf. Figs. 3, 4 and 5, Table 5). While the mineralization process, where the main strontium deposition occurs, is not fully synchronized with the initial matrix deposition, a non-random strontium deposition pattern suggests a spatio-temporal resolution and a traceable chronological order, from the tip to the cervix, of strontium incorporation in human enamel.
The various functional stages in the life cycle of the ameloblasts have been suggested to follow the enamel deposition pattern during maturation, by reaching its final maturation stage in a sweeping motion from the tip of the tooth towards the cervix (Nanci 2017:131). Thereby, it may be suggested that human enamel mineralization is, in this regard, similar to the enamel mineralization of sheep; see Fig. 1 as adapted from Green et al. (2017). This means that even though the process of complete enamel mineralization is extended, limited areas of the enamel surface appear to mineralize rapidly and thus contain temporally limited data.
The LA-MC-ICP-MS investigations for this study targeted the rapidly mineralizing surface enamel in human teeth, which, due to large differences in the sample preparation process, might be the most significant dissimilarity between this study and the study of Montgomery et al. (2010). Here, we remove ~ 10 μm of the outer enamel surface by pre-ablating the analysis spot using a slightly wider laser beam (150 μm) than what is used when running the strontium analyses (130 μm), whereas Montgomery et al. (2010) used a tungsten carbide dental burr to remove the entire outer enamel surface layer. Surface enamel appears to mineralize slightly faster than enamel further towards the EDJ, which suggest a shorter average time, but the precise pre-ablations used to remove the outer surface enamel layer before measurements were taken is also important for studying chronological patterns.
The ability to target enamel at comparable depths might, considering how enamel mineralizes (Fig. 1), narrow the margin of error related to temporally depth-dependent mineralization and permit sampling in a chronological sequence. This might also be a reason why it was possible to follow and correlate the strontium ratios of Mongolian sheep enamel to the bioavailable strontium signatures of their actual GPS-tracked mobility (Lazzerini et al. 2021), as the measurements were done at an equal distance from the EDJ. Rapidly mineralizing enamel at equal depths may therefore be a key in obtaining chronologically differentiated measurements.
Regarding the averaging effect of strontium residence time in the body, we suggested that if a high spatio-temporal resolution is present in enamel and if it is related to enamel mineralizing from the tip to the cervix, the pattern generated by the ablations should follow a distinct and gradually changing order when measured in a consecutive sequence. The gradual change was suggested to come from a combination of the averaging effect of residence strontium and a diet mainly consisting of animals and plants from a limited geographical region, corresponding to where in the landscape food was gathered, hunted or fished. Comparing this hypothesis to the outcome of the data, it is precisely what we can observe in the chronologically ordered measurement sequence from the archaeological teeth (Figs. 3a, 4 and 5a). This suggests that while strontium residing in the human body does affect its incorporation in enamel, by smoothing the transition between different isotope ranges, the averaging effect is still temporally limited, allowing a chronological resolution in human enamel to be distinguished.
The smoothening effect by residence strontium further suggests that an absolute relation to a specific diet during a more limited period, e.g. after a successful hunt of a large animal and extensive consumption of this animal for some days in a row, will not be traceable. However, if diagenetic alterations can be ruled out, periodic shifts in diet extending for a couple of weeks or more would be traceable in the isotopic enamel record with the resolution obtained from laser ablations. Examples of this, as based on a huntergatherer-fisher perspective, could include residential mobility between resource patches situated in different isotopic regions. It could be caused by periodic diets stemming from a temporally limited abundance of one resource type, e.g. fish, during fish migrations and spawning, and the consumption of winter storages from one main food supply, e.g. fermented fish (Boethius 2016) or roasted hazelnuts (Holst 2010). It could also include periodic dietary shifts caused by foraging parties gathering plants from one isotopic region, which were brought back to the main settlement to be consumed over some weeks, after which the foraging party went to a different isotopic region to repeat the process.

Inferences from modern man tooth data
The strontium ratios from the modern man provide a frame, which can be used to interpret the archaeological data. Through interviews with the subject, we know that he did not travel for any extended periods during the mineralization of his tooth. We also know that he ate a diet based on what was available at the local grocery store. Strontium ratios in enamel are largely dependent on the ratios from plants (Bentley 2006) as their strontium concentrations are several times higher than concentrations in flesh. The subject states that his plant diet was mainly derived from cereals and potatoes, which, in the 1970s, mostly came from national farms. In the area around Sölvesborg, where he grew up, most crops ending up at the local grocery store would have been farmed in fertile areas of southern Sweden. The strontium ratios from these regions match with the range of ratios measured in the subject tooth (cf. modern man data with strontium ranges from southernmost Sweden in Fig. 7), suggesting it is possible to infer from where a modern person obtained the main part of the diet.
The subjects' strontium ratios also match fairly well with the proxy data for local tap water. Due to low strontium concentration in freshwater, this is, however, not likely to have a major impact on the strontium ratios of the subject if other more strontium-rich food sources are consumed, e.g. plants (Bentley 2006). Results from the Netherlands also show that the correlation between tap water and geographic origin lacks connection to modern human enamel, suggesting the strontium intake has become detached from the local geological strontium isotope composition due to a globalised diet (Kootker et al. 2020). Consequently, the strontium range in the modern man is likely unrelated to the tap water where he grew up, making the overlapping strontium ratios more of a coincidence. As suggested by the interviews, a strontium input from freshwater also seem unlikely considering that the subject states that he rarely drank tap water, preferring milk.
It was initially suggested that because a modern diet primarily derives from grocery stores, it would not be possible to detect a chronological pattern in the data even if spatio-temporally limited strontium ratios could be obtained through LA-MC-ICP-MS. This has proven true for the investigated modern subject. Not all ablations fall on the end-member gradient, suggesting that there is a measurable spatio-temporal resolution, but it is not possible to detect a pattern in the sequence of the measurements. This suggests that it is not possible to track childhood mobility using 87 Sr/ 86 Sr LA-MC-ICP-MS on modern human teeth.
The data from the individual ablations of the modern man oscillate, without any traceable pattern, around an averaged value of 0.71251 (SD=0.0003, variance=0.000000088). The overall similar strontium ranges are likely related to the main strontium input stemming from similar isotope regions (e.g. potatoes and cereals mainly from fertile areas of southern Sweden). The oscillations may, thereby, be caused by the randomness of the exact origin of each product, the inclusion of meat from various isotopic regions and the consumption of occasional imports, such as rice.
This has implications for our understanding of data patterns seen in archaeological enamel. As suggested by the data from the modern man, if particular strontium ranges dominate the daily dietary intake in combination with parts of the diet providing completely different Sr ranges, it appears as if it will result in an oscillating pattern in the enamel, if measured from the tip to the cervix along the side of a tooth. While the archaeological teeth, in general, display a clear pattern and a high correlation with the individual measurement sequence, there is some data oscillation. Part of the oscillations may be explained by measurement analytical errors or undetected diagenesis, but some may also have similar causes for intraindividual isotopic variation as suggested for the modern man.
If plants were gathered from specific resource patches and these changed over the year and across seasons, it would provide a pattern with a high correlation with the individual measurement sequence. If at the same time, the diet also consisted largely of fish and the fish were caught in a water body with different strontium isotope ranges than the terrestrial resource patches, the measurements pattern may, to some degree, mimic the oscillating order observed in the modern man. Depending on the seasonal or yearly subsistence base, there might even be different patterns on the same tooth. Increased oscillation in the ablation data pattern from a specific part of the enamel could indicate a diet from multiple and varied strontium regions (e.g. Baltic Sea fish and terrestrial plants). Enamel sections with relative homogenous measurements could indicate a diet from similar strontium regions (e.g. terrestrial plants and terrestrial mammals from the same area combined with fish from a local freshwater lake). Lastly, enamel sections of elevated strontium isotope differences might, consequently, not only be caused by mobility from one strontium region to another but also by seasonal diet shifts, e.g. a winter diet consisting mainly of stored fish when the summer and autumn diet mainly consisted of various plants. By understanding how the diet of a modern man affects the strontium signals in minor parts of the enamel, it becomes possible to better interpret the isotope ratios and their measurement patterns on archaeological teeth as well.

Conclusions
The averaged LA-MC-ICP-MS measurements investigated here indicate a strong correlation with TIMS data and are therefore able to provide archaeological provenance information. In addition, and more importantly, temporally limited and chronologically deposited strontium is evident in enamel when measured at an equal distance from the outer surface of the investigated archaeological human teeth. The results show a spatio-temporally limited strontium incorporation pattern unrelated to a long-term averaging effect. The individual ablation measurements, sampled along the side of the tooth, show data unrelated to the strontium values obtained from the ablation end-members. By decreasing the enamel sampling area, we show that it is possible to increase the spatio-temporal resolution and provide more detailed data corresponding to strontium incorporation during a limited period of the spot-specific enamel mineralization. This suggests that the main parts of the strontium signals incorporated close to the enamel surface are not from a long-term averaged strontium reservoir. Thereby, if the majority of the strontium in small sections of human enamel are averaged over a limited period of weeks and not years, these values may be relatable to the isotope regions where the main strontium came from during these specific weeks, i.e. to the bioavailable strontium ratios in the landscape.
The intra-tooth measurement arrangement changes from following a distinct pattern when ordered in a chronological sequence to becoming random when the sequence of the individual measurements from a tooth is randomized. This suggests that the individual ablations represent temporally limited strontium incorporation in enamel and that the 87 Sr/ 86 Sr ratios from the ablations, ordered from the tip to the cervix, represent a transition corresponding to temporal movement, or diet changes, within or between different isotope regions. Temporal changes in strontium ratios are dependent on specific circumstances for the investigated subject. Considering the hunter-gatherer-fishers studied here, these changes may be related to mobility through the landscape and to food from different areas of the local home ranges having been brought back to the settlements to be consumed by the children, or because dietary patterns vary seasonally or based on availability or a combination of these scenarios.
While LA-MC-ICP-MS analyses provide information of the investigated archaeological foragers during enamel mineralization, about provenance, mobility and origin of the consumed food, the same is not true when applied to a modern human. This is likely due to modern food consumption patterns where the diet is both of varied origin and, most often, unrelated to the area where one lives. Despite the detachment from local geological strontium isotope ranges, there is valuable data in modern human enamel when dietary and travel background is known during mineralization. This information has been used in this study to interpret archaeological human strontium isotope ratios. Comparisons of the information from archaeological and modern human enamel suggest that for shifts in strontium isotope measurements to be traceable as a gradually changing chronological pattern, the dietary changes must last for some weeks in a row. If food constantly came from various isotopic regions, the strontium isotope ratios would be averaged towards the diet with the highest strontium concentrations, there would not be a traceable chronological pattern in the ablation sequence and the measurements would be oscillating around the averaged value without a clearly ordered pattern.

Limitations and future considerations
LA-MC-ICP-MS analyses have recently proven to be capable of tracking animal mobility by showing a correlation between the location of the animal as tracked by GPS, the bioavailable strontium along the movement route and the strontium isotope ratios in caprine tooth enamel (Lazzerini et al. 2021). For obvious ethical reasons, similar studies cannot be made on human children, whereby the same level of accuracy cannot be obtained. It is possible to keep a record of the diet of pregnant women and continue this record during the first years of life to, after the deciduous teeth have fallen out, analyse the teeth. However, a human diet is omnivorous and, despite the efforts to secure this data, the result would still be far from what can be achieved when analysing the teeth of young herbivores herded through a landscape of shifting isoscapes.
Despite this, there are areas from which more research could expand the gain of applying LA-MC-ICP-MS analyses. Synchrotron analyses on enamel mineralization could be applied to human teeth, e.g. using material from archaeological excavations and bioarchaeological analyses to estimate the age of death for the children whose teeth were selected for analysis. This could provide detailed information on human enamel mineralization, enabling spot-specific age correlation. Furthermore, e.g. using high-intensity synchrotron light or neutron diffraction, it could also be valuable to investigate the possibilities of mapping the elements in archaeological enamel specimens before strontium isotope analyses were conducted. This would potentially allow one to avoid areas of elevated REE levels and thus minimize the risk of analysing diagenetic specimens.
More modern teeth from different countries and geographic regions could also be analysed to establish if the pattern seen in the modern man analysed here is valid and widely applicable. The present study also suffers from the inability to target the same areas of the enamel when assessing the accuracy of LA-MC-ICP-MS analyses. Consequently, it would be interesting to see if the correlation between the TIMS and the LA-MC-ICP-MS datasets would be further strengthened if enamel sampled at the same distance from the cusp and comparable depths on the same tooth were analysed.
Further investigations are also needed to study the averaging effect of body strontium reservoirs. The timeframe of what constitutes "the most recent diet" remains unclear, and more data is needed to determine the time it takes for an averaged strontium content plateau to be reached and incorporated during human tooth enamel mineralization. Moreover, it is important to establish what timespan each ablation line represents, i.e. how many days, weeks or months of averaging strontium ratios each ablation line embodies. It is also important to obtain data on how deep the enamel can be sampled before the averaging time changes (if it changes), and how much variation in analysis depth is acceptable to still obtain data from the same mineralization horizon (i.e. chronologically ordered data).
As more information on the bioavailable baseline from new areas becomes available and as technological developments advance, further increasing the accuracy of the measurements, new areas and materials will be open for research. More research is needed to confirm and elaborate on the results presented here. However, the ability to show a chronologically ordered strontium uptake in human enamel, along with an increasing need for non-destructive methods when analysing rare and unique parts of our common cultural heritage, is likely to further increase the use of LA-MC-ICP-MS analyses in archaeological research.