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Appendix S1 Maps of distribution of occurrence points used for constructing the models.

Figure S1.1 Occurrence records of Amphibalanus improvisus that were used in the ecological niche models.

Figure S1.2 Occurrence records of Carcinus maenas used in the ecological niche models.

Figure S1.3 Occurrence records of Littorina saxatilis used in the ecological niche models.

Figure S1.4 Occurrence records of Styela clava used in the ecological niche models.

Appendix S2 Table of the relative influence of the parameters on the models and global maps of the Maxent output for the potential distribution of the four invasive species given current conditions or predicted future warming.

Appendix Table S2.1. Relative influence of the parameters on the models for the training gain, test gain, and the AUC of the models.

Appendix Figure S2.1 Global projected potential distribution from the cumulative output of Maxent for Amphibalanus improvisus.

Appendix Figure S2.2 Global projected potential distribution of Carcinus maenas.

Appendix Figure S2.3 Global projected potential distribution of Littorina saxatilis.

Appendix Figure S2.4 Global projected potential distribution of Styela clava.

Appendix Figure S2.5 Global projected potential distribution for Amphibalanus improvisus given the annual mean surface warming predicted by the IPCC A2 scenario.

Appendix Figure S2.6 Global projected potential distribution for Carcinus maenas given predicted warming.

Appendix Figure S2.7 Global projected potential distribution for Littorina saxatilis given predicted warming.

Appendix Figure S2.8 Global projected potential distribution for Styela clava given predicted warming.

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