Good afternoon Kim, 

Thank you for Ask Extension question about a large hole in your yard.

Based on your picture, I believe that is a rabbit burrow. However, it is very difficult to identify the exact animal based only on pictures, and it could also be caused by a skunk or a fox. For accurate identification, you will need to look around the hole for prints or debris like bones, or set up a trail cam. 

I don't believe any of these animals will harm the roots of your tree, though rabbits will damage the trunks of trees and eat nearby plants. Skunks can cause other damage by digging for food. 

Please don't hesitate to contact us again with any further questions. 

Best Regards, 
Michelle D

Colorado Master Gardener Volunteer Apprentice