Correction to: Nature Reviews Earth & Environment https://doi.org/10.1038/s43017-023-00431-y. Published online 27 June 2023.

In the version of this article initially published, the red trace for MLP-causal was missing from the graph in Fig. 4i. In addition, in the text directly following equation (2), now reading “where denotes independence,” the symbol for “dependent with” appeared instead. The errors have been corrected in the HTML and PDF versions of the article.