Ecological modellers have shown how reducing wild rabbit numbers helps maintain small native mammals.
Benefits for small mammals occur when 30-40% of rabbits are removed through a mix of biological and physical controls. Higher rates of rabbit removal can lead to a decline in small mammals in the short term, but with subsequent long term recovery under continued high rates of rabbit control. Field research has previously shown that higher rates of control can be needed for the sustained regeneration of highly palatable native plant species.
For more information see the article in The Conversation, or the Journal of Applied Ecology.