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Figure S1  Examples of Stipa tenacissima grasslands without and with shrubs.

Figure S2  Photographs of some of the study sites in 1946, 1975 and 2006.

Figure S3  Richness and evenness of fatty acids measured in plots with and without shrubs.

Figure S4  Values of the surrogates of soil fertility and ecosystem functioning measured in plots with and without shrubs.

Table S1  Main characteristics of the study sites.

Table S2  Nested permanova for main treatment effects and interactions on the surrogates of soil fertility and ecosystem functioning measured from the tussock and open microsites across all sites.

Table S3  Correlation matrix between shrub effect size and both the proportion of total cover accounted by sprouting shrubs and the main abiotic features of the study sites.

Table S4  Summary of nested permanova for main treatment effects and interactions on the composition of vascular plants, biological soil crusts and microbial communities.

Table S5  Summary of nested permanova for main treatment effects and interactions on the relative abundance of particular biological soil crust and fatty acid groups.

Table S6  Likely effects of plant traits on the functional outcome of shrub encroachment.

Appendix S1  Detailed materials and methods.

Appendix S2  Discussion on the importance of the traits of the encroaching woody vegetation relative to those of the grasses as a desertification driver.

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