Correction to: Nature Communications https://doi.org/10.1038/s41467-023-37194-5, published online 05 May 2023

The original version of this Article contained errors in the Methods section ‘Target causal effect’, in which terms were omitted from the mathematical definitions of the causal effect and average causal effect. These sentences incorrectly read “The causal effect of a change in richness from R′ to R″ on productivity P in plot i is defined as [(R″) − (R′)], where Pi(R″) is the potential productivity outcome when R = R″ and P(R′) is the potential productivity outcome when R = R′ (R′ ≠ R″).” and “The average causal effect of a change in biodiversity from R′ to R″ across all plots is [(R″) − P(R′)], where E[·] is the expectation operator.”. The correct version states “[Pi(R′′) − Pi(R′)]” in place of “[(R″) − (R′)]”, “Pi (R′)” in place of “P (R′)”, and “E[Pi(R′′) − Pi(R′)]” in place of “[(R″) − P(R′)]”. This has been corrected in both the PDF and HTML versions of the Article.