All good advice above here and I agree, the best way to control ants is to bait for them. You can make a sweet bait with sugar syrup, bottled water and boric acid, or, as Tee suggested above, buy some ant stakes. As far as non-chemical control, the only thing is probably DE (diatomaceous earth). It's a non-toxic powder that is abrasive to the ants so they are killed if they walk over or through it. You can buy it in 10lb. bags at Home Depot and just 'dust' it around the trees where the ants' trails are. Bait is better and works faster though, but don't make the bait too strong for small ants. You want the ants to take it home to mama and kill the whole nest. Sometimes it takes several refills of bait, and a couple of weeks for it to work but baiting is the most effective thing.
But, along with everyone else, I'll caution you that the ants are most likely there for another reason and you should keep looking for the other reason. Ants do not feed on trees or damage them. Even Carpenter Ants make tunnels in wood, but do not eat the wood and rarely do enough damage to be seen, especially to living trees.
Your best source of information might be an entomologist at your local Ag university. They are bug geeks and love to talk about bug problems. Sometimes they will have an e-mail address on the university site where you can send a question.
