Construction of radiogenic isotopic datasets
The filtered DC20 dataset3 comprises six oceanic hotspots (Fig. 1), i.e., Iceland, Tristan, Reunion, Hawaii, Easter and Galapagos, and two plateaus, i.e., Kerguelen and Louisville. A total of 1,809 samples with complete 87Sr/86Sr, 143Nd/144Nd, 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb data were selected. 207Pb*/206Pb* and 208Pb*/206Pb* are calculated using Equation (1) for both datasets to assess the time-integrated growth of 206Pb, 207Pb and 208Pb since the Earth’s formation.
207Pb*/206Pb* = (207Pb/204Pb – 10.294)/(206Pb/204Pb – 9.307)
208Pb*/206Pb*= (208Pb/204Pb – 29.476)/(206Pb/204Pb – 9.307)25 (Eq. 1)
The expanded isotopic dataset consists of 1,809 samples from the DC20 dataset and 1,655 additional samples from all 26 oceanic hotspots compiled in the EarthChem portal (http://portal.earthchem.org). The expanded dataset includes hotspots situated around and within the African LLSVP or the Pacific LLSVP (Fig. 1). All the samples have complete records of 87Sr/86Sr, 143Nd/144Nd, 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb, and calculated 207Pb*/206Pb* and 208Pb*/206Pb* (Supplementary Data).
The definition of the DUPAL domain follows that of Jackson and Macdonald2, with primary characterization of 143Nd/144Nd. The DUPAL domain comprises 11 hotspots (Fig. 1): Tristan, Discovery, Samoa, Pitcairn, Meteor/Shona, Tasmantid, Kerguelen, Hawaii, San Felix, Societies and Amsterdam/St. Paul. The non-DUPAL domain comprises the remaining 23 hotspots. The geographic distribution of the DUPAL domain closely aligns with the distribution of the DUPAL hotspots reported by Hart1, who focused on the deviations of 207Pb/204Pb and 208Pb/204Pb from the NHRL1 and absolute values of 87Sr/86Sr.
Random forest classifications of geochemical data
The random forest algorithm23 is an ensemble learning algorithm that consists of multiple decision trees. Each decision tree starts at the root node and progresses toward the leaves. At each node, a split is made based on a single feature. This process continues until it reaches one of the leaf nodes at the top of the tree. Each decision tree predicts a class, and the class receiving the most votes from the decision trees becomes the model's final prediction. A random forest repeatedly subsamples both the data and features to train decision trees43,44, which mitigates potential overfitting and enhances model generalizability.
Four random forest classifiers are constructed to test two dichotomies using two datasets: (a) classification between the LLSVPs using the DC20 dataset; (b) classification between the LLSVPs using the expanded dataset; (c) classification between the DUPAL and non-DUPAL domains using the DC20 dataset; and (d) classification between the DUPAL and non-DUPAL domains using the expanded dataset. The isotopic ratios include 87Sr/86Sr, 143Nd/144Nd, 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb, 207Pb*/206Pb* and 208Pb*/206Pb*.
To avoid data leakage, we divide the training and test datasets at the geographical location level rather than into individual samples. That is, all samples from the same geographical location are either in the training set or in the test set. In each run, 70% of the locations are randomly selected for training, and the remaining 30% are used for testing. The number of locations for two classes remains equal during training and testing to ensure that the classification accuracy is not affected by imbalanced data. This procedure is repeated 1,000 times to determine the optimal hyperparameter pair (tree depth and forest size) for each classifier. The average accuracy and standard deviation of the four classifiers are calculated using the searched optimal tree depth and forest size: 6 and 95 for the LLSVP dichotomy using the DC20 dataset, 15 and 95 for the LLSVP dichotomy using the expanded dataset, 13 and 100 for the DUPAL dichotomy using the DC20 dataset, and 15 and 95 for the DUPAL dichotomy using the expanded dataset (Supplementary Fig. S11).
Feature importance of geochemical measurements
Feature importance, i.e., the relative importance of each isotopic ratio in classification, is evaluated by the Shapley value. The Shapley value is measured with the Shapley additive explanation approach27,28, which is defined as follows:
![](data:image/png;base64,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)
Data-driven decision boundaries for separating geochemical regimes
To map the decision boundaries of the two dichotomies, we retrain the random forest classifiers with only the two most important isotopic ratios as inputs: 87Sr/86Sr and 206Pb/204Pb for the DUPAL dichotomy and 87Sr/86Sr and 208Pb*/206Pb* for the LLSVP dichotomy. The trained classifiers predict the possibilities of virtual grid points across the 87Sr/86Sr-206Pb/204Pb or 87Sr/86Sr-208Pb*/206Pb* diagrams. These predicted possibilities are plotted as heatmaps. Each heatmap is generated from a random data split of training and testing sets. This process is repeated 1,000 times, and the decision boundary is the contour with a predicted probability of approximately 0.5 in the average heatmap.