Genuine causal relationship between protection from harvesting and community structure.

Here we test the criterion for inferring genuine causal relationship between protection and community structure under the context of thermal stress anomalies (TSA), human density and the presence of coral reefs. Following Ref. [31], we test the statistical 3-step criterion (i-iii) required to infer a genuine cause-effect relationship, the highest-level of causal inference that can be achieved (see Methods for details). Note that steps ii and iii have six alternative routes [31, 52]. That is, Route 1: i-iia-iia.1-iiia. Route 2: i-iia-iia.2-iiia. Route 3: i-iib-iib.1-iiib. Route 4: i-iib-iib.2-iiib. Route 5: i-iic-iic.1-iiic. Route 6: i-iic-iic.2-iiic. The larger the number of routes, the stronger the support. We use G2 test of independence [53]. We reject independence when the p-value