There are few simple rules to count on. The stability of grasslands depends on circumstances, usually including a range of herbivores to prevent forestation. Mega-fauna, like mammoths used to contribute to grove and prairie creation by eating trees, before humans dominated.
I wrote this to dereke in another comment, I think it is relevant to understanding the present situation:
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Two hundred years ago about 60% of the earth surface was covered in mature and native forest. The figure is less than 30% today. Most of the worlds fertile crops are grown on deforested land, on the soil which native forests developed through ecological diversity and lack of erosion. Most of the grasslands which are used for grazing, don't have the soil quality to support demanding crops.
https://www.britannica.com/science/deforestation
