One small branch of this five year old avocado tree is covered in black cones that resemble barnacle shells. Ants are clearly interested in them. What is going on here? Has something other than the ants colonized the tree?
Yes - you have a scale infestation. The shield shaped objects attached to the branches are adult scales - there may be crawlers on the soft parts such as leaves and stems. The ants are attracted by the honeydew the scale produce, so they aren't a problem; get rid of the scale and the ants will disappear.
You may be able to remove the ones on the twiggy parts by using either a disposable cloth moistened with methylated spirits and rubbing it firmly over the branch, or by using a cotton bud dipped in 70% isopropyl alcohol, but it depends how large your tree is - this kind of treatment isn't really practical on large trees. It is not advisable to use this treatment on the foliage. Where possible, severely infested branches can be pruned out. Otherwise, horticultural oil sprays when crawlers are present provide some control, or seek out a suitable insecticide intended for use on scale infestation. Further info here https://www.planetnatural.com/pest-problem-solver/houseplant-pests/scale-control/
If you have more than one avocado tree, or you live in California, the information here http://ipm.ucanr.edu/PMG/r8300211.html may be of interest, though its really aimed at professional growers producing avocados as a crop.