See:
Algae, Lichens, and Mosses on Plants
Cause A number of mosses and lichens grow on hazelnut, walnut, and fruit trees. None are parasitic. Control may be desirable because ice or snow may accumulate on mosses and lichens and break branches. If orchards are regularly pruned or sprayed, usually mosses or lichens are few or nonexistent. If plantings are not sprayed regularly for other reasons, spray thoroughly every 4 to 5 years to control mosses and lichens. Dead mosses and lichens will stay on trees for a time but gradually weather away.
Symptoms Nonvascular plants cover or hang from small twigs or larger branches. Mosses have leaves that are only one cell thick but they do not have true roots, flowers, or fruit; instead of seeds, they have spores. They may form green carpets and cushions. Lichens do not have a stem-and-leaf structure, and few of them are bright or deep green. Rather, lichens come in shades of gray, cream, pale green, olive green, yellow, and orange.
Chemical control Spray when moss and lichens are actively growing. Application of copper-based materials in the fall after harvest may help provide some bacterial blight control. Application of copper-based materials in late February or early March may help provide some protection from Eastern Filbert Blight.
- Basic copper 53 at 6 lb/100 gal. Group M1 fungicide. 24-hr reentry. O
- Bordeaux 6-6-100. Group M1 fungicide. O
- C-O-C-S WDG at 11.6 lb/A plus 1 pint superior-type oil/100 gal water. Can be used only after harvest. Group M1 fungicide. 48-hr reentry.
- Cuprofix Ultra 40 Disperss at 10 to 15 lb/A. Oregon and Washington only. Group M1 fungicide. 48-hr reentry.
- Kocide 50 DF at 8 to 12 lb/A plus 1 pint superior-type oil/100 gal water. Can be used only after harvest. Group M1 fungicide. 48-hr reentry.
- Monterey Liqui-Cop at 1 to 2 Tbsp/gal water. H
- Nordox 75 WG at 8 to 13 lb/A. Can be used only after harvest. Group M1 fungicide. 12-hr reentry. O
- Nu-Cop 50 DF at 8 to 12 lb/A with 1 pint superior-type oil/100 gal water. Can be used only after harvest. Group M1 fungicide. 48-hr reentry. O
- Rex Lime sulfur (28%) at 6 to 12 gal/100 gal water after harvest but prior to winter bloom (flowering). 48-hr reentry. O
Reference Living with Mosses. http://bryophytes.science.oregonstate.edu/mosses.htm