Multi-isotopes in human hair: A tool to initiate cross-border collaboration in international cold-cases

Unidentified human remains have historically been investigated nationally by law enforcement authorities. However, this approach is outdated in a globalized world with rapid transportation means, where humans easily move long distances across borders. Cross-border cooperation in solving cold-cases is rare due to political, administrative or technical challenges. It is fundamental to develop new tools to provide rapid and cost-effective leads for international cooperation. In this work, we demonstrate that isotopic measurements are effective screening tools to help identify cold-cases with potential international ramifications. We first complete existing databases of hydrogen and sulfur isotopes in human hair from residents across North America by compiling or analyzing hair from Canada, the United States (US) and Mexico. Using these databases, we develop maps predicting isotope variations in human hair across North America. We demonstrate that both δ2H and δ34S values of human hair are highly predictable and display strong spatial patterns. Multi-isotope analysis combined with dual δ2H and δ34S geographic probability maps provide evidence for international travel in two case studies. In the first, we demonstrate that multi-isotope analysis in bulk hair of deceased border crossers found in the US, close to the Mexico-US border, help trace their last place of residence or travel back to specific regions of Mexico. These findings were validated by the subsequent identification of these individuals through the Pima County Office of the Medical Examiner in Tucson, Arizona. In the second case study, we demonstrate that sequential multi-isotope analysis along the hair strands of an unidentified individual found in Canada provides detailed insights into the international mobility of this individual during the last year of life. In both cases, isotope data provide strong leads towards international travel.


Introduction
The establishment of Interpol many decades ago came from the necessity for international police cooperation in response to the rise of international crime organizations. Nevertheless, such international cooperation usually remains restricted to organized crime while significant barriers impede cooperation in the resolution of cold cases [1]. Countries lack a universal language, funding and the political will to harmonize law enforcement practices and facilitate cross-border cold case investigations [1]. A significant and increasing number of cold-cases are international, particularly in areas located close to land borders where remains of migrants or trafficking victims are common [2]. The remains of individuals with a foreign origin often stay unidentified due to the absence of documents, evidence and cooperation between law enforcement agencies [2]. When DNA or fingerprint databases are available (e.g., EU, North America), they strongly favor cross-border collaboration for those cases with potential international origin [3]. However, while DNA is considered the holy grail of identification, it is often inapplicable either because the DNA is too degraded for analysis, too costly or simply not useful because there is no known reference sample (e.g., family reference sample or the decedent's DNA profile in a database) to compare the sample of the deceased individual to. It has been found that the more socially marginalized the family of the missing is, the more obstacles the family has to face to obtain information about the loved one's whereabouts and to submit data to the appropriate authorities [4]. The administrative, technical, and cultural barriers that limit cooperation between law enforcement agencies are unlikely to disappear in the short term. There is therefore an urgent need to develop tools that provide robust leads to facilitate cross-border implications in the resolution of cold-cases [5].
Stable isotopes are ubiquitous intrinsic markers with the potential to contribute new and actionable evidence in cold-cases, even those involving long-term unidentified individuals [6][7][8][9][10][11][12][13]. Isotopes compose all organic molecules and their abundances in human tissues inform about a person's diet, health, or mobility history providing critical information about human remains [6,8,[14][15][16][17][18][19]. Isotope data from hair have been increasingly used in investigating coldcases because hair is easily collected and resistant [20], and isotope data in hair is usually preserved post-mortem [21,22]. While bulk isotope data is often used in forensic cases, sequential isotope profiles along human hair can provide chronological information about the diet and location changes of an unidentified decedent at approximately monthly to bi-monthly resolutions as hair grows at ~7-10 mm/month, though not continuously [6,10,16,[23][24][25][26][27][28][29][30]. Isotope data in hair could provide a key screening tool to identify those cold-cases that have a potential international outlook. However, the application of this isotope geolocation technology at the international scale requires the development of cross-border databases of isotope composition in hair and models predicting the isotope patterns in the tissue of interest.
Many isotopes have the potential to trace individual mobility. However, some (e.g., metals) are not directly integrated within the hair structure and are easily exchanged or contaminated by exogenous sources (e.g., bathing water, aerosols, post-mortem exposure) [19,22]. Consequently, when measured in hair, those isotopes reflect local contamination by soil and water at the site where human remains were found and are not useful for solving cold cases [31,32]. Hydrogen/oxygen and sulfur, however, compose keratin [33], are resistant to postmortem exposure [34] and are thus the ideal candidate for multi-isotope geolocation of humans from their hair. The 2 H and 18 O abundances (δ 2 H and δ 18 O values respectively) in humans reflect primarily the isotopic variability in drinking water which follows systematic spatiotemporal patterns along latitude, elevation, and continentality [28]. When an individual moves through the landscape, its hair inherits the isotopic composition of the drinking water consumed along the way and can thus be used to reconstruct origin and movements [32]. Though limited in the geographic resolution of the information it can provide, δ 2 H in human hair has been used for decades in isotope geolocation studies [6,10,16,[24][25][26][27][28][29][30] and data is available from many countries to develop continental-scale maps of isotope variations (or isoscapes) [35].
The S isotope composition (δ 34 S) in human hair is inherited from the isotopic composition of the food consumed with little isotopic fractionation [36]. Plants and crops, at the base of food systems, uptake S from two main sources: S-containing bedrock minerals or inorganic fertilizers, which generally have low but variable  34 S, and marine aerosols which have high  34 S values [37]. The mixing of these two isotopically distinct S sources controls a large part of  34 S variations observed in ecosystems and ancient human societies with high  34 S values in coastal environments and progressively lower  34 S moving inland [37][38][39]. In modern times, however, the supermarket human diet mixes products from multiple distant locations and sources, complicating the interpretation of  34 S values [36,[40][41][42][43]. But even in modern societies, the  34 S values in resident human hair display clear differences between countries and continents [36,[40][41][42][43]. For example, hair of North American residents have distinctively lower  34 S values than those of Asians or Europeans [36,[40][41][42][43]. Bataille et al. (2020) further demonstrated that, within a country, systematic and predictable  34 S gradients were present [41]. The predicted  34 S values in hair of Canadian residents could unambiguously distinguish "true" residents from "snowbirds" traveling to the tropics to escape the Canadian winter.
Carbon and nitrogen isotope compositions ( 13 C and  15 N) in human hair are also composing keratin and resistant to post-mortem exposure [34]. Both carbon and nitrogen come primarily from diet but can, in certain cases, bring some geolocation information [44].  13 C values in human hair primarily track dietary habits of an individual, particularly the proportion of C4 vs. C3 plant-derived products consumed [20,21,44]. This is because C3 crops including beet, barley, rice, potato, or wheat have in average much lower  13 C values (~-25‰) [45] than C4 plants including corn, soybean, millet, and cane sugar (~-12‰) [45]. However, some δ 13 C trends, independent of personal dietary choices, also exist at the regional up to the global scales due to the distinct mix of C4 vs. C3 products in food systems [11]. For example, in North America, more C3 crops (e.g., wheat, barley, beats) are cultivated in the North and dry continental interiors whereas more C4 crops (e.g., corn, sugar cane) are cultivated in the South and coastal regions. This spatial organization of food systems leads to distinct  13 C values in human hair transmitted through the preferential consumption of local food [41,42,46]. Similar spatial patterns exist for the  15 N in hair at the regional to global scale due to differences in agricultural practises [11]. However,  15 N values in human hair are mostly controlled by dietary choices with more positive δ 15 N values for individuals eating more seafood in coastal regions [47].
The main objective of this study is to develop a framework to use multi-isotope geolocation from modern human hair to assist in solving international cold cases. We first analyze and/or compile δ 2 H and  34 S values from hair of residents of Canada, the United States and Mexico. We use these databases to generate maps predicting δ 2 H and  34 S values in hair across North America. We then analyze the δ 2 H,  34 S, δ 13 C and  15 N values in bulk hair of undocumented border-crossers (UBCs) that died at the Mexico-US border and were later identified through the Pima County Office of the Medical Examiner. We compare the predicted geographic origins from bulk hair dual H and S isotope analysis with their known-origin. We finally run a sequential analysis of δ 2 H,  34 S, δ 13 C and  15 N values along the length of a Canadian cold case. We assess the potential mobility of the individual and the possibility of cross-border traveling.

Ethics statement
The Office of Research Ethics and Integrity of the University of Ottawa approved this research program under protocol number [05-08 -19]. Specifically, all sampling and analytical methods used to collect samples and information were in accordance with these regulations. Informed consent was obtained from all subjects or from their legal guardians in accordance with, and maintained under, IRB regulations.

Hair samples 2.2.1 Residents' hair samples from across North America:
We analyzed or compiled 692 δ 34 S (Database_S1) and 846 δ 2 H (Database_S2) from hair of North American residents. Out of these samples 649 sites have both δ 2 H and δ 34 S data (Database_S3). We obtained 101 Mexican residents' hair samples collected by Dr. Ammer in 2019 following protocols described in [42]. These samples were analysed for δ 2 H values at the Jan Veizer Stable Isotope Laboratory. These samples had already been analyzed for δ 34 S values [42]. We compiled 210 δ 2 H and 60 δ 34 S data from American residents' hair samples analyzed in [28] and [36], respectively. The data generated by Ehleringer et al. (2008) were analyzed using older protocols and calibration standards. We transformed the hair δ 2 H values using the function refTrans in the assignR package to place them on the same calibration scale as the rest of the hair data described in [35]. We obtained 592 Canadian residents' hair samples collected by Dr. Chartrand between 2007 and 2012. 531 of these samples were previously analyzed for δ 34 S values [41]. 535 samples were analyzed for δ 2 H in 2013 though the results are only available in a non-peer-reviewed report [48]. The data generated by Chartrand were analyzed using older protocols and calibration standards. We transformed the hair δ 2 H values using the function refTrans in the assignR package to place them on the same calibration scale as the rest of the hair data as described in [35].

United States -Mexico undocumented border crosser hair samples
The remains of undocumented border crossers are often found by border patrol, nongovernmental institutions or private citizens in the rural regions along the Mexico-US border. Remains found throughout most of southern Arizona are then transported to the Pima County Office of the Medical Examiner (PCOME). As part of Dr. Ammer's doctoral thesis, hair samples from four undocumented border crossers were collected by pulling the hair with the roots (Table 1). These individuals were found relatively rapidly after their death (<5 weeks) limiting potential effect of decomposition on the isotope values [34]. Additionally, the individuals have been tentatively identified by authorities through various means and await final confirmation. Those identifications can be used, with caution, as a mean to validate isotope-based geographic assignments. All hair samples were approximately 4 cm long, thus representing the last few months of these individuals' lives. We analyzed the bulk hair for δ 2 H, δ 13 C, δ 15 N and δ 34 S (Table 2 and Data_S1). It is assumed that the bulk analysis of isotope in hair of those UBCs, by and large, reflect the region of last residence. However, the journey to the border can sometimes take up to months and in rare cases, even years as some reside close to the border awaiting their chance to cross. Further, some of the individuals might have crossed the border multiple times after living in the US and being deported. Based on the investigative work and contact with the potential family of the deceased, it is thought that UBC#2 lived in the US for a few months and was subsequently deported and died during his subsequent crossing back into the US. The metadata on the four undocumented border crossers can be found in Table 1.  [32]. However, the hair of this individual was extremely brittle which made alignment challenging. Consequently, individual locks of hair were used as the basis for alignment, combination and segmentation. We prepared a total of 27, 0.5 cm samples, each representing about half a month timeframe. Due to the difficulty in aligning the dreadlocks, the time uncertainty and averaging represented by the isotope time-series are probably higher than in previous studies causing, in this case, a more "elastic" timeframe than usual [31,32]. We analyzed each segment for δ 2 H, δ 13 C, δ 15 N and δ 34 S (Data_S2).

Isotope analysis
The Mexican resident bulk hair, Mexico-US border migrant bulk hair and Canadian cold-case hair segments were all analyzed following the same procedure at the Jan Veizer Stable Isotope Laboratory at the University of Ottawa, Canada. Hair was first washed in a series of three baths of 2:1 solution of chloroform:methanol (CHCl3:MeOH). The hair was then dried, ground using a Retsch ball mill and stored in glass vials until analyzed.
The δ 2 H of the non-exchangeable hydrogen of hair was determined using the comparative analysis approach described by Wassenaar and Hobson [49] based on two USGS calibrated keratin hydrogen-isotope reference materials (CBS: −157‰, KHS: −35.3‰). We performed hydrogen isotopic measurements on H2 gas derived from high-temperature (1400 °C) flash pyrolysis (TCEA, Thermo) of 150 ± 10 ug hair subsamples and keratin standards loaded into silver capsules. Resultant separated H2 was analyzed on an interfaced Thermo Delta V Plus continuous-flow isotope-ratio mass spectrometer (Bremen, Germany). All δ 2 H values are reported to the international scale VSMOW-SLAP. Measurement of the two keratin laboratory reference materials corrected for linear instrumental drift were both accurate and precise with typical within-run measurement error < 2‰. Two USGS human hair standards, USGS 42 (δ 2 H= -72.9 ± 2.2 ‰) and USGS 43 (δ 2 H= -44.4 ± 2.0 ‰), were used as quality checks. Analytical precision is based on the reproducibility of the USGS hair standards is better than ± 2‰. For δ 34 S analyses, the samples and standards were weighed into tin capsules, loaded onto an Elementar Isotope Cube Elemental Analyser, and flash combusted at 1800°C. The EA method was optimized for SO2, where N2 and CO2 were not retained. SO2 was trapped and released to the Conflo IV (Thermo, Germany) interfaced to the IRMS (DeltaPlus XP, with a special 6 collector sulfur cups array (SO-SO2), Thermo, Germany). Standards used for calibration were silver sulphides: IAEA-S-1 (δ 34 S= -0.3‰), IAEA-S-2 (δ 34 S= 22.7‰), and an internal standard S-6 (δ 34 S= -0.7‰). All δ 34 S values were reported to the international scale VCDT. Two USGS human hair standards, USGS 42 (δ 34 S= 7.84 ± 0.25 ‰) and USGS 43 (δ 34 S=10.46 ± 0.22 ‰) were used as quality checks. Analytical precision is based on the reproducibility of the USGS hair standards is better than ± 0.3‰.

Isoscapes
Geographic probability maps compare the observed isotopic value for a biological tissue (e.g., hair) with that predicted by an isoscape [50].

Sulfur hair isoscape
Bataille et al. (2020) predicted the δ 34 S trends of modern human hair across Canada demonstrating a strong gradient from coast to more inland provinces reflecting the influence of local food systems [41]. Similar trends are observed in the δ 34 S in hair of residents of the United States [36] and, to a lesser extent, Mexico [42]. Based on these observations, we used an existing framework to generate a δ 34 S isoscape from hair of North American residents [38,41]. We assembled data on selected covariates that represent the main factors that impact variability in δ 34 S values, including country of residence (Canada, USA or Mexico), geology (age), climate (e.g., precipitation, temperature), soil proprieties (e.g., pH, clay content, organic matter), aerosol deposition (e.g., sea salt) and distance to the coast. We resampled and reprojected all the selected environmental geospatial products into WGS84-Eckert IV 1km 2 resolution and used the latitude and longitude of each sampling site to extract the local values for each raster. We combined the δ 34 S hair compilation and the extracted covariate values at each site into a regression matrix and used generalized linear model (GLM) regression kriging to predict δ 34 S in hair across North America using the "caret" package [51]. We first use the Akaike information criterion (AIC) to estimate prediction error and rank the relative quality of GLM models. We then used simple kriging to map the remaining variance of the residuals (Script_S1).

Hydrogen hair isoscape
We generated a δ 2 H isoscape for human hair following the procedure described in the assignR package [52]. The process requires a tissue-specific isotope dataset of known-origin individuals to develop a transfer function between an isoscape and the tissue of interest. We used the compiled dataset of δ 2 H in hair combining the δ 2 H in hair of Canadian and Mexican residents analyzed in this study with published δ 2 H in hair of US residents and incorporated this dataset to the known origin sample database in the assignR package. We calibrated the hair δ 2 H isoscape using the calRaster function in the assignR package.

Probability maps
We used the metrics generated by the QA function in assignR to compare the quality of probability maps generated from each isoscape. We then used the continuous-surface probability framework from the assignR package [52] (i.e., pdRaster function) to estimate the most likely locations of origin of each individual from the bulk hair single (δ 2 H or δ 34 S) and dual (δ 2 H and δ 34 S) isotope data from Mexican-US border crossers and from each segment of the Canadian cold-case (Script_S2).

Sulfur isoscape
The 692 compiled and analysed δ 34 S data from hair of North American residents are normally distributed (Shapiro Test, p-value<0.05). δ 34 S values range from -1.4‰ to 8‰ and average 2.3‰. Some geographical regions of North America are underrepresented in the dataset: the eastern USA, western USA and southern USA. The best GLM model (AIC=556) used latitude, longitude, country of origin, and distance to the coast as the dominant predictors of the δ 34 S values (Fig 1A). This GLM explained 66% of the variance with a Root Mean Square Error (RMSE) of 0.79‰ (Fig 1A). After kriging the residuals using a Gaussian variogram model (Fig. 1B), the resulting regression kriging model explains 77% of the variance with a RMSE of 0.65 ‰ (Fig 1C). The value of 0.65‰ represents ~8% of the full range of measured δ 34 S values over the dataset. Latitude and country of origin are the strongest predictor of δ 34 S values. Going north to south, Canadian samples, on average, have lower δ 34 S values than Americans and Mexicans. Distance to the coast and longitude are also key predictors with individuals living close to the coast having higher δ 34 S values than those living more inland.
The regression kriging produced a δ 34 S isoscape in human hair that displays strong spatial patterns associated with country and distance to the coast. Sites located in coastal North America have higher δ 34 S values (Fig. 1D). The highest values are found in western coastal Mexico. Conversely, sites located in interior regions of Canada have the lowest δ 34 S values.

Hydrogen isoscape
The 846 compiled and analysed δ 2 H data from hair of North American residents are normally distributed (Shapiro Test, p-value<0.05). δ 2 H values range from -119.8‰ to -37.4‰ and average -79‰. We observed a strong correlation between δ 2 H values in hair and δ 2 H values in precipitation ( Fig. 2A). The produced δ 2 H isoscape in human hair displays strong spatial patterns (Fig. 2B).

Figure 2. Hydrogen isoscape generated in the assignR package. A:
Map of δ 2 H in hair of residents from North America with locations of collection sites from residents (including individuals from this study as well as published data) and B: Calibration equation between modeled δ 2 H in precipitation and hair from North American residents (including individuals from this study as well as published data).

Figure 3. Quality evaluation of hydrogen, sulfur and dual-isotope probability maps.
These plots were generated using the QA function in the assignR package. A. Proportion of the study area excluded from the assignments as a function of probability threshold. Higher values indicate a potential for more specific assignments. B. Proportion of validation samples correctly assigned as a function of the probability threshold. If accurate posterior probabilities are estimated for each sample, these values should fall along the 1:1 line. C. Proportion of validation samples correctly assigned as a function of the area quantile, providing an integrated measure of assignment sensitivity. D. The distribution of odds ratios for the known origins of the validation samples relative to random quantifies the strength of isotopic support for one location relative to another. Higher odds ratios indicate more specific assignments.
Quality metrics for the single-and dual-isotope analyses suggest strong potential for this method to provide accurate and specific information on the origin of human hair samples, and highlight the added power of the dual-isotope method (Fig. 3). The area-exclusion plot (Fig.  3A) shows that the spatial distribution of posterior probabilities is very uneven, particularly for the dual-isotope analysis. This implies that the isotopic information strongly discriminates between more-and less-likely regions and could be used to eliminate large parts of North America as a potential origin for a sample at a high level of certainty. The validation plot (Fig.  3B) shows that, for hydrogen isotopes, the proportion of samples correctly assigned to origin mostly scales as expected with the probability threshold adopted for assignment, implying that this isoscape and its uncertainty appropriately represent the human hair data. The validation plots show slight deviation from the expected proportion of samples correctly assigned for δ 34 S and for dual isotopes (Fig. 3B). For δ 34 S the proportion of stations included are overestimated relative to the probability quantile likely indicating that the modeled uncertainty is lower than represented in the isoscape. Surprisingly, however, the dual isotope show the opposite trend with the proportion of validation stations underestimated relative to the probability quantile indicating that the model misses the true origin of known-origin individuals more than expected (Fig. 3B). This could reflect some bias in the sulfur isotope predictions associated with the regression kriging approach and/or the validation approach. This bias would be accounted for in the univariate uncertainty but leads to incorrect predictions in the multivariate case. With larger dataset with more complete spatial coverage, it might be useful to test new modeling approach to predict δ 34 S variations (e.g., random forest regression). The assignment power plot (Fig. 3C) uses the known origin data to test the ability of the method to correctly assign sample origin across a range of exclusion area thresholds. It shows that both single-and dual-isotope analyses have high power, though the δ 2 H and dual-isotope method give substantial increase in power across all area thresholds relative to δ 34 S. Finally, the odds ratios for the known locations of sample origin are substantially higher than the random value for all methods, but are approximately 5 time greater for the dual-isotope method than either single-isotope analysis (Fig. 3D). Collectively, these results support the validity of the isoscapes as a template for interpreting human hair isotope data and suggest that assignments made using the isotopic data, particularly in the case of dual-isotope analysis, can provide accurate and specific information on the geographic origin of samples.

US-Mexico border crossers cold cases results
The hair samples of the undocumented border crossers were bulk-analyzed, thus not segmented. Table 2 presents the δ 2 H, δ 34 S, δ 13 C and δ 15 N isotope values for each of the four individuals. The values are the average of three measurements. The δ 13 C and δ 15 N isotope values of the four UBCs were compared to the values previously published for residents of North America [36,41,42]. Based on the available δ 15 N data from North America, an origin from the United States can be excluded for UBC #1, all other individuals fall within the ranges reported for all three countries ( Table 2). The δ 13 C values reported for two of the UBCs (UBC #3 and UBC #4) would exclude both the United States and Canada as potential countries of origin ( Table 2). The δ 13 C values for UBC #1 and UBC #2 fall within the higher end of the range of values found in the United States and Canada but would not allow for a clear distinction. The δ 34 S values of UBCs #2 and #4 fall within the ranges reported for all three countries, while #1 and #3's values are too high to have originated from Canada ( Table 2). The δ 2 H values of all UBCs fall within the ranges reported for Mexico and the United States but are not compatible with Canada (Table 2).

Figure 4
Probabilistic maps of provenance for Mexico-USA border crossers estimated from δ 2 H and δ 34 S values for bulk hair. Locations where the human remains were discovered, are indicated by white circles. Locations where the remains are thought to have originated, based in independent evidence, are marked with red circles. Colours on the maps depict the predicted probability of origin based on isotopic evidence.
We generated single and dual isotopes probabilistic maps of provenance for each individual and compared them to the location of origin tentatively identified by authorities (Fig. 4). UBC #1 probably originated from Jitzamuri, Sinaloa, Mexico. Only a few coastal regions of western Mexico are compatible with the isotope data from this individual's hair. Among those, the region around Jitzamuri shows high probability. UBC #2 probably originates from Tlacatecpa, Tlaxcala, Mexico. The dual isotopes probabilistic maps show low probability of origin in the purported region of origin except for some coastal regions along the Gulf of Mexico. Probable regions of origin include most of the southeastern USA, and coastal region around the Gulf of Mexico. UBC #3 probably originates from Ayulta de los Libres, Guerrero, Mexico. The dual isotope probabilistic maps show a high probability from this city but are not very specific as all the western coast of Mexico shows a high probability of origin with highest probability in northwestern Mexico. Most of northern Mexico and the southern USA regions are also compatible with the isotope values of this individual. UBC #4 most likely originated from San Ildefonso, Huehuetenango, Guatemala. Unfortunately, our map does not extend to Guatemala. The most probable regions of potential origin within our study areas is the south-central USA along the Mississippi river valley.  However, the δ 13 C values are higher between 5-12 months PTD and would be compatible with eastern Canada or the eastern USA during this interval (Fig. 5B) (Table 2). Except for one very low value at 5 months PTD, the δ 2 H values from Mr. Halifax's hair become more positive between 5-12 months PTD (Fig. 5C).
We used these isotope values to generate single and dual-isotope probabilistic geographic maps from each segment of hair. We summarized in Fig. 6

Isocapes
Since the seminal work of Ehleringer et al. (2008), country-scale studies analyzing isotopes in human hair of residents and/or tap water have become increasingly available providing the basis to develop isoscapes in many regions of the world [28,[41][42][43][53][54][55][56]. Efforts to harmonize isotope analyses have also facilitated the integration of data generated from different laboratories, countries and times [35].

Sulfur isoscape
As observed in previous studies [36,40,41,43], the δ 34 [41]. Within countries, particularly Canada and the USA, we observe a trend between δ 34 Shair values and distance to the coast. δ 34 S in North American crops should reflect the mixture of isotopically light sulfates from the soil solution, and isotopically heavy marine aerosols [36,41,43,57,58]. As food systems become more distant from the coast, bedrock S or anthropogenic sources dominate decreasing δ 34 S values. The δ 34 Shair variability in North American residents closely follows this isotopic pattern in food systems likely because customers obtain a large part of their S from locally sourced high-protein food items (e.g., meat, yogurt, cheese, eggs). Even though North American residents have a supermarket diet and homogenized dietary habits, the regional patterns in δ 34 S in ecosystems are transmitted to human hair through the importance of regional food supply in sulfur intake. Eating locally has become a more powerful movement in the last decade where locally produced foods have become more available and prized. The difference in sea salt aerosol deposition between North American countries might also explain their distinct average hair δ 34 S values and the trend in δ 34 S values with latitude. Mexico receives more marine sulfate than the United States and Canada because populations are on average closer to the coast in Mexico. The δ 34 S isoscape developed from this regression kriging approach shows excellent predictive power and strong spatial patterns that are promising for identifying cross-border cold cases.

Hydrogen isoscape
As observed in previous studies [28,53,59], the δ 2 H values in human hair follow a continuous gradient across North America ( Fig. 2A). When δ 2 H hair data is corrected to be on the same reference scale [35], we can explain 80% of the variations in δ 2 H hair across North America using only the isotopic signal from modeled precipitation (Fig. 2B). This strong relationship between local water and hair δ 2 H values reflects the local nature of water sources in human societies [28]. Drinking water has usually local to regional origin depending on the source [54][55][56]. Similarly, most beverages are derived from local to regional water sources including bottled water, coffee, tea or even soft drinks and milk [60]. Some of the residuals between precipitation and δ 2 H values in hair probably derive from differences between the δ 2 H of local precipitation and that of the consumed tap water. Tap water from different sources at one location might have different isotopic compositions. For example, tap water from shallow groundwater usually reflects an average of local precipitation δ 2 H [61] whereas tap water from deep aquifers, lakes or river waters might have more distant or fossil sources (e.g., glacial water) and/or might have been evaporated [54,61]. This isotopic difference between water sources is exacerbated at the continental scale because different countries and regions rely on different water sources. For example, in North America, Mexico supplies the majority of its tap water from groundwater sources whereas Canada and the USA use primarily surface water sources. Differences in dietary choices, tap water sources and beverage inputs between participants living in a single location can also contribute to distinct hair δ 2 H values at a single location [60]. Many other factors can influence the relationship between precipitation δ 2 H and δ 2 H in human hair including the consumption of imported drinks with non-local δ 2 H values, the presence of non-local study participants or uncertainties in the predicted precipitation δ 2 H values. Despite those limitations, the continental δ 2 H isoscape shows excellent predictive power and strong spatial patterns that are promising for identifying cross-border cold cases.

Interest in multi-isotope provenancing in international forensic studies
Stable isotopes have shown promise for provenancing unidentified decedents from cold-cases investigated by local jurisdictions [6,31,[62][63][64] or to identify remains recovered from the sites of past wars and conflicts [7,38,39,62,65]. However, the development of international isotope baselines from modern residents offers new possibilities to use isotopes for contemporary cross-border forensic applications [7,8,65]. In our globalized world, many forensic questions have international components. Through two case studies, we show that using dual S and H isotope provenancing provides critical leads to facilitate international forensic collaborations.
Lack of documents, fingerprint, dental, medical records and family members to obtain family reference samples or antemortem samples for DNA comparison makes it very challenging to identify UBCs at the US-Mexico border. These difficulties are further enhanced by the inability to narrow down the search area to more probable options. The four individuals studied here were recently tentatively identified and serve as a basis to test the use of dualisotope provenancing for identification purposes. Out of the 4 UBC studied, none showed a local origin in the western US. All the individuals have dual-isotope values that place their origin in more southern regions of North America. As we only analysed isotope values in bulk hair for these individuals, we were not expecting precise provenancing because the isotope data in hair could reflect a mixture of isotope values from their last location of reference with isotope values inherited during their journey to the border. Specifically, the durations of travel can vary greatly, from merely days to up to months, and in rare cases even years. This largely depends on the availability of funds, previous extortions through cartels, previous (negative) experiences, place of origin, health status and, among many other variables personal decisionmaking. Even with this temporal resolution limitation, the dual-isotope data show promising results. The individuals UBC #1 and UBC #4 show high isotope-based probabilities in the city/region of inferred origin of the UBC. UBC #2 likely resided for several months in the U.S. before being deported, re-entering and perishing in the US, explaining the strong signal from the southern USA. The origin of UBC #3 could not be properly inferred because our predictions did not include Guatemala. Analyzing isotope data sequentially along the hair and from other tissues (e.g., teeth and bones) could thus substantially help reconstruct a more detailed travel history for those individuals.
While Mr. Halifax was found near an international airport, the forensic inquiry around this cold-case has remained national. The dual S and H isotope provenancing reveal that this individual traveled across large distances in the year prior to his death (PTD). During the few months PTD, the individual lived either somewhere in eastern Canada, very likely in a municipality along the shore of the Great Lakes such as Sudbury, Sault-Saint-Marie or Winnipeg or in the northern US Midwest region. However, earlier in his life (i.e., 5 to 14 months PTD), the dual-isotope provenancing indicate travel and/or residence in the southeastern USA. During the 5 to 12 months PTD interval, some probability maps of provenance are incompatible with any region in Canada. Dual isotope probability maps between 12 to 14 months PTD show some potential Canadian origin in coastal Nova Scotia or Newfoundland but are mostly compatible with the southeastern USA. The carbon isotope data further support the proposed dual-isotope geographic assignments. While it is challenging to use carbon isotope for producing probabilistic maps of provenance because of fractionation associated with individual physiology and diet, the δ 13 C trend within a hair profile does record mobility [32]. In the case of Mr. Halifax, carbon isotope trends strongly validate the dual S and H isotope geographic assignments. Extremely low δ 13 C values (~ -19 ‰), a few months PTD, are compatible with regions of Ontario around the Great Lakes (i.e., western Ontario and Manitoba). However, between 5 to 14 months PTD, a shift towards higher δ 13 C values culminating at -18 ‰ is more typical of the USA. Even the δ 15 N values, which are usually not sensitive to mobility within a given country [32], appear to record a shift from lower to higher δ 15 N values around 5 months PTD. The higher δ 15 N values a year PTD possibly reflect a shift in dietary habits between places of residence (e.g., more fish consumption in the southeastern USA leading to higher δ 15 N values).
This study demonstrates the potential of using multi-isotope analyses, and isotope-based geographic assignments as a rapid response tool in international cold-cases. The power of isotope provenancing increases several folds when multiple isotope systems are combined. The precision of dual-isotope results varies, but in some cases, the potential areas of origin that are identified are very specific. Reconstructing the movement history and origin with isotope data provides critical leads to law enforcement agencies for cross-border collaborations. The case of UBC #4 demonstrates the importance of large-scale and continuous isoscapes that are as spatially extensive as possible. This not only applies to undocumented border crossers at the US-Mexico border but also to any other case of unidentified human remains with a potentially international outlook. Incomplete isoscapes bear the risk of exclusion or inclusion of regions that may otherwise be ex/included. This can severely affect the investigative work and thus slow down the identification process.

Conclusion
In this work, we demonstrated that developing continental-scale isoscapes for sulfur and hydrogen in hair is feasible and yields accurate models with strong predictive potential for isotope-based provenancing. As more isotope data from human tissues are published and integrated, those models will become increasingly accurate and useful for provenance. We then show how those isoscapes are particularly useful to provide evidence for cross-border mobility in unidentified individuals. Through a first case study, we show that probabilistic maps of provenance derived from bulk isotope analysis of UBC at the US-Mexico border help identify their country/region of origin. Through a second case study, we show that sequential multi-isotope analysis along a hair strand combined with continuous probabilistic maps of provenance yields a detailed travel history of an unidentified individual between eastern Canada and the southeastern USA. This type of evidence indicating international travel is essential to engage collaborations between law enforcement agencies. Now that the isotope baselines are established, we argue that multi-isotope profiling in human hair combined with isotope-based probabilistic provenancing provide a rapid, practical, inexpensive and powerful tool to screen cold-cases for potential international leads.