The example I’m thinking of is New Zealand, where there’s endless studies into causes of erosion most of which mention the introduction of grazing game animals(e.g. deer) as a contributing factor.

deforestation and overgrazing by livestock and introduced game animal

https://doi.org/10.1002/ldr.3400060202

introduction of exotic plants and animals (e.g. rabbits, deer) resulted in obvious signs of land depletion and erosion

https://www.mpi.govt.nz/dmsdocument/81/direct

By the 1930’s the deer population in New Zealand was out of control and causing serious environmental damage through grazing, severe soil erosion and slips from the thousands of hooves ripping up the ground

https://www.rnz.co.nz/programmes/deer-wars/story/2018906408/e01-the-last-great-adventure