Fire ants use trees as nesting places because little or no soil disturbance or mowing occurs around trees. Also moisture and food resources are plentiful on and around trees and shrubs.
Ants in mounds at the base of trees are probably not causing any damage to well-established trees. They may actually help by preying on other insects that feed on parts of the tree and may reduce compaction by tunneling in the soil.
However, very young, tender trees can be damaged by the ants girdling the plants and allowing roots to be exposed to the air, thus drying out root systems. For example, this has been observed in newly planted crepe myrtles and citrus trees, so use fire ant control methods in such areas.
Find more information about fire ants in eXtension's Imported Fire Ant Resource Area.