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Appendix S1 Description of Models.

Appendix S2 Derivation of effective potential.

Appendix S3 Mean first passage time calculations.

Appendix S4 Results for the two-variable vegetation model.

Appendix S5 Results for the parameterized lake model.

Appendix S6 Analysis of real data sets.

Appendix S7 Asymmetric arguments for multivariable models.

Appendix S8 Relative merits of indicators.

Appendix S9 Analysis of failure of skewness.

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