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Figure S1 Illustration of computer simulation experiments testing the effects of linear and sinusoidal spatial structures on isolation of species suitable habitat.

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Figure S2 Examples of spatial eigenvector maps of each region.

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Figure S3 Examples of correlograms for spatial eigenvectors maps of each region.

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Figure S4 Mantel correlograms for redundancy analysis residuals.

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Figure S5 Correlograms for regression residuals corresponding to western North America, eastern North America and eastern Asia.

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Figure S6 Correlograms for regression residuals corresponding to the Cape Floristic Region and south-west Australia.

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Figure S7 Simulation results show contrasting effects of spatial heterogeneity in precipitation of the driest month and annual mean precipitation on isolation of species suitable habitat in eastern North America and eastern Asia.

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Figure S8 Proportion of variation in multivariate climate explained by sinusoidal spatial structures at different spatial scales across western North America, eastern North America, eastern Asia, the Cape Floristic Region and south-west Australia.

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Table S1 Central tendency and variation in 17 climatic variables across western North America, eastern North America and eastern Asia.

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Table S2 Central tendency and variation in 17 climatic variables across the Cape Floristic Region and south-west Australia.

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Table S3 Results of tests for differences in climate heterogeneity that preserve spatial structure.

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Appendix S1 Computer simulation experiments testing the effect of linear and sinusoidal spatial structures on isolation of species suitable habitat.

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Appendix S2 Testing for differences in climate heterogeneity while preserving spatial structure.

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Appendix S3 Standardization of dispersion matrices.

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Appendix S4 Computer simulation experiments comparing the effects of spatial heterogeneity in precipitation of the driest month and annual mean precipitation on isolation of species suitable habitat in eastern North America and eastern Asia.

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