The application of a CART model for forensic human geolocation using stable hydrogen and oxygen isotopes

The isotopic spread for each study site

The overall linear relationship between δ²H and δ¹⁸O values for hair (n = 81) and toenails (n = 39), respectively, were (Fig. 2):

δ²H and δ¹⁸O values in hair samples collected from individuals residing in Site 4 had the most positive values, and Site 1 had the most negative values (Table 2, Fig. 3). For toenails, the most positive δ²H and δ¹⁸O values were also observed for individuals from Site 4; however, the most negative δ²H and δ¹⁸O values were observed for Site 1 and Site 3, respectively. This is an interesting result as Site 3, Iqaluit, was expected to produce the lowest values for δ²H and δ¹⁸O values in both hair and toenails, given that it is located on a much higher latitude compared to the other sites, including Site 1 of Metro Vancouver (see Supplementary Fig. S1 online). However, such a pattern could not be observed for Iqaluit, except for δ¹⁸O values in toenails.

MANOVA results (differences in δ²H and δ¹⁸O in tissues between study areas)

An outlier was detected for one hair sample (H2) with δ²H = − 58.3‰ and δ¹⁸O = 6.4‰ using the Mahalanobis distance ⁵⁵. When MANOVA was run on the original dataset, including the outlier, mean δ²H and mean δ¹⁸O values differed between the four sampling sites as measured by the MANOVA test [F(3, 77) = 14.07, p < 0.01] and [F(3, 77) = 7.43, p < 0.01], respectively. MANOVA was also run on the dataset with the outlier removed but resulted in a similar result where δ²H and δ¹⁸O values of hair differed across the study sites at [F(3, 76) = 22.093, p < 0.01] and [F(3, 76) = 6.90, p < 0.01], respectively. Thus, the presence of the outlier did not influence the overall results for hair. Mean δ²H values and mean δ¹⁸O values in toenails differed between the four sampling sites as measured by the MANOVA test [F(3, 35) = 8.26, p < 0.01] and [F(3, 35) = 6.34, p < 0.01], respectively.

Results from the Tukey post-hoc test indicated that δ²H values in hair samples collected from Site 1 differed significantly from those collected from Sites 2 (p < 0.01) as well as from Site 4 (p < 0.01) (See Supplementary Table S2. online). Site 3, on the other hand, was more similar to Site 1; however, it was distinct from Site 4 (p < 0.05). Hair δ¹⁸O values also differed significantly between Sites 1 and 2, and between Sites 1 and 4. For toenails, samples from Site 1 showed δ²H values that were distinct from all other sites, whereas δ¹⁸O values in samples from Site 4 differed significantly from the other three sites.

Human tissue and drinking water

δ²H and δ¹⁸O values of tap water from Wolfville, NS were − 61.8‰ and − 9.4‰, respectively. These data are also true for all cities in Site 4 as they are all supplied by the same Cornwallis watershed^42,43. For the remaining study sites, isotopic data were collected from existing publications. Actual tap water data were retrieved for all cities in Site 1 from Ueda and Bell’s⁷ extensive tap water study covering the entire regional district of Metro Vancouver, BC (Table 3). The tap water value for the city of Barrie, ON in Site 2, was downloaded from the Waterisotope Database⁴⁶. Although the source water information was not provided, it was assumed that the data are sufficient as Barrie is mainly supplied by a single water source, the Kempenfelt Bay²⁹, and thus has a high likelihood that this particular tap water sample came from the main drinking water source.

Surface water data were retrieved for locations where actual tap water data could not be found. Isotopic data of the Black River near Washago, ON⁵⁶ were chosen as the most representative data for Lake Couchiching as no isotopic data on water samples collected directly from Lake Couchiching were found. Another city in Site 2, Gravenhurst, ON, primarily draws drinking water from Lake Muskoka. Untreated water from Lake Muskoka is drawn proximate to Brydon’s Bay for treatment and distribution to residents across Gravenhurst. Thus data from the drainage area identified as MA3BA in James et al.’s⁵⁷ study, which covered the entire area of Brydon’s Bay, was determined to best represent drinking water isotope values for Gravenhurst. Finally, the Online Isotope Precipitation Calculator was used to estimate drinking water values for the remaining cities of Horseshoe Valley, ON and Midland, ON in Site 2, and Iqaluit, NU in Site 3.

The retrieval of drinking water isotope data allowed the determination of the relationship between stable hydrogen and oxygen isotopes in modern human tissues and drinking water. The linear regression results between δ²H of hair (δ²H_hair) and drinking water (δ²H_dw) for all study sites with drinking water values (n = 81) were (Fig. 4):

δ²H of toenails (δ²H_toenails) and drinking water gave a relationship of:

δ¹⁸O of hair (δ¹⁸O_hair) and drinking water (δ¹⁸O_dw):

And finally, δ¹⁸O of toenails (δ¹⁸O_toenails) and drinking water

Tissue values from all study sites were also regressed against OIPC values that were calculated from latitudinal, longitudinal, and altitude data (Fig. 4):

Actual tap water data could not be retrieved for Iqaluit and given that higher-than-expected stable hydrogen and oxygen isotope values were measured for individuals from Iqaluit, these samples were removed as it was unclear whether the OIPC generated values were appropriate estimates for Iqaluit drinking water. Below are the relationships between human tissue values and drinking water values where Iqaluit samples were excluded from the analysis (Fig. 4).

And for OIPC values (Fig. 4):

The R² values increased for all four equations when Iqaluit samples were removed. Overall, stable hydrogen and oxygen isotope values in modern human tissues are weakly related to those in drinking water as measured by tap water. The R² value showed a slight increase for δ¹⁸O values in toenails when the OIPC precipitation data were used instead of tap and surface water values; however still on the lower end at R² = 0.2. Therefore, there is no clear evidence from this dataset that a latitudinal gradient exists for hydrogen and oxygen values in human tissues for Canada as measured by the stable isotope values of drinking water.

The CART model

The first CART decision tree model was built for hair samples with stable hydrogen and oxygen isotope values (Model 1) (Fig. 5a). The split cut-off for node 1 was determined by hydrogen values where any samples with δ²H_hair values less than − 82‰ were predicted as Site 1. Samples with δ²H_hair > − 82‰ were then split further where any samples with δ²H_hair values less than − 73‰ were initially classified as Site 2. These samples were then split again to either Site 2 (δ²H_hair ≥ 76‰) or Site 4 (δ²H_hair < 76‰). Hair samples classified as Site 4 at this stage were further classified into Site 2 or 4 depending next on the δ¹⁸O values. Finally, all samples with δ²H_hair > − 73‰ were classified as Site 4. No samples could be classified as originating from Site 3. The second CART model was built for stable hydrogen and oxygen isotopes of toenails (Model 2) (Fig. 5b). The model included only two decision nodes in which the first predictor variable was δ²H_toenail value, where samples with values less than − 93‰ were predicted to be from Site 1. For toenail samples with hydrogen values greater than − 93‰, oxygen values were used to determine whether they could be classified as Site 2 or Site 4. Those samples with δ¹⁸O_toenail values less than 9.6‰ were classified as Site 2 and those with values greater than 9.6‰ were predicted as Site 4. No samples were predicted to be from Site 3 purely from stable hydrogen and oxygen isotopes in toenails. Finally, the third model consisted of stable hydrogen and oxygen isotope values in both hair and toenail samples (Model 3) (Fig. 5c). Model 3 selected toenails as the best attribute for classification, which indicates that toenail isotope values are the better predictor when both hair and toenail samples are present for analysis from Sites 1–4. The model was similar to that of Model 2.

Confusion matrices (Table 1) were constructed for all three models to evaluate the performance of the classification models. Of the three models, Model 3 proved to be the most accurate model with an overall accuracy of 71.4% (see Supplementary Fig S2. online). The performance evaluation summary, including measures for sensitivity, specificity, positive predictive value, and negative predictive value for all three models, is provided in (see Supplementary Table S3. online).

Intra-individual differences

Both hair and toenail samples were retrieved from 35 of the 86 individuals. The paired difference between δ²H values in hair and toenails of the same individual was tested using the Wilcoxon Signed Rank’s test for non-normal data as the dataset failed the Shapiro–Wilk’s normality test at the α = 0.05 significance level. Significant differences were found between δ²H values of hair (n = 35, mean = − 78.0‰, s.d. = 3.06) and toenails (n = 35, mean = − 90.9‰, s.d. = 3.27) from the same individual (p < 0.05). The paired t-test was utilized to assess for similarities in δ¹⁸O values of hair and toenail from the same individual as the dataset was normally distributed. The results indicated that there were no significant differences between δ¹⁸O values of hair (n = 35, mean = 9.7‰, s.d. = 1.22) and toenails (n = 35, mean = 8.2‰, s.d. = 2.10) at the 0.05 significance level, t(34) = 1.92, p > 0.05. Overall, the isotopic values of δ²H in hair were higher than those of toenail from the same individual by 13.0‰, on average, with a standard deviation of 8.4‰. For δ¹⁸O, the average was 1.5‰ with a standard deviation of 4.6‰ (Fig. 6).

The linear relationships between δ²H in hair and toenails for all individuals were (see Supplementary Fig S3. online):

and for δ¹⁸O:

Overall, both equations showed a weak relationship, as seen by the small R² values.

Source: Ecology - nature.com