It needs fire to reproduce* and takes over the landscape after a fire, outcompeting many other species. This is not unique to eucalyptus. Some pines also need fire to reproduce and redwoods tend to survive fire better than other trees and thrive in the aftermath.

But it sounds like eucalyptus may actively promote fire in a way I haven't heard of other trees doing.

* http://learnline.cdu.edu.au/units/env207/ecology/individual....