How do you eradicate alders?

Alder is a common name of a genus of flowering plants belonging to the birch family

Any of various deciduous shrubs or trees of the genus Alnus, native chiefly to northern temperate regions and having alternate simple toothed leaves and tiny fruits in woody, conelike catkins. The...

Yes most 'Alders' are trees, the black Alder and Red Alder grow to 30mtr tall deciduous trees however the Green Alder is classed as a large 'shrub' normally growing to about 5mtr tall.

Kurt Alder (1902-1958)