Correction to: Nature Ecology & Evolution https://doi.org/10.1038/s41559-018-0743-8, published online 17 December 2018.

In the version of this Article originally published, the description of equation 1 in the Methods subsection ‘Biodiversity conservation benefits’ was incorrect.

The following sentence:

‘On the basis of a previous study10, the change in extinction risk (r) for each individual species as a function of habitat area was modelled as follows:

$$r = 1-\left( {x/A_0} \right)^z$$
(1)

where A0 is the current habitat area, x is additional habitat area that would arise from habitat restoration, and the power z describes the rate of diminishing returns in value of additional area at reducing extinction risk.’

should have read as follows:

‘On the basis of a previous study10, the extinction risk (r) for each individual species as a function of habitat area was modelled as follows:

$$r = 1-\left( {x/A_0} \right)^z$$
(1)

where A0 is the original habitat area, x is the current habitat area (that could be increased through habitat restoration), and the power z describes the rate of diminishing returns in value of additional area at reducing extinction risk.’

This error has now been corrected.