The introduction of livestock to an area leads to over-grazing that removes native grasse

That livestock is a invasive species.

Invasive species. Native grasses have evolved with the normally-occurring grazing organisms to achieve a level of reproduction which sustains the grasses despite the grazing. An invasive species disrupts this ecological balance that took millions of years to develop by eating the grass at a rate that exceeds the rate for the grass to re-seed itself and maintain its own population. The invasive species easily decimates the grass population.