Sounds like you are growing it well. You need to make an enclosure using hardware cloth and a secure access to it to keep out animals. Birds will also dig around in your growing area looking for something to eat or for nesting materials.

If your roof is located in the sun, you have probably found Entodon, Ceratodon, Hedwigia or Bryum growing on the shingles. There could be additional species if your roof is in a shady spot. Mosses that grow on roofs can be transplanted to soil or rocks. Often as a moss landscape specialist, I utilize these "roof" species in the creation of moss and stone walkways or to enhance stone walls. Several years ago, I designed and installed an intentional moss green roof at the NC Arboretum featuring some of these moss species.

Dealing with critter damage is a dilemma that all moss gardeners must face eventually. It could be your own dog running in a frenzy; birds seeking a tasty worm (or even stealing moss fragments for their nests); diggers like squirrels or armadillos can dislodge moss colonies. The good news is that the mosses can easily be put back in place totally unharmed. Water and walk on the spot to help rhizoids re-attach to the soil. If you continue to have critter visitors, wildlife netting can be placed tightly over your moss garden to prevent digging with the side benefit that newly distributed moss fragments or colonies won't blow away. You don't need a physical barrier, fence or enclosure to safeguard your moss features. Other methods for discouraging critters include motion sensor lights and mothballs. Good Luck and enjoy the beauty of year-round green mosses! -- Mossin' Annie, Owner, Mountain Moss and author, The Magical World of Moss Gardening