You can also put up small wire temporary fencing around the area you are designating for the vine so that the peafowl can't reach through and eat it.
I had to do a lot of testing to figure out what plants I could keep in my peafowl aviary.
Generally thicker plants or plants that grow quickly and spread work better. I've tried having some softer plants in the past and most didn't do well. I even bought a clump of pampas grass for the aviary thinking that the razor edges of the grass would prevent the birds from destroying it, but they trampled it and lay on top of it for some reason.
I have two evergreen trees that look kinda like a Christmas tree that popped up on their own in my pen and I left them alone and the peafowl left them alone as well. I have never seen them peck at one.
My main plants I use in the aviary are:
Grass, clumping bamboo, fatsia japonica, rice paper plant, cast iron plants, heavenly bamboo, elephant ears, and Japanese maple.
In this photo you can see my mass planting of cast iron plants to the right. They like to grow in shade and they provide great cover for the birds. A local church was throwing them out because they said the plants weren't growing at all for them. The problem was they planted them in a sunny location. They took a while to get started but they were worth it, and free!
The closest plant is the rice paper plant. It spreads by underground roots - similar to how running bamboo will spread, so only plant it if you are okay with it appearing all over. I'm fine with pulling up the extras I don't want. It is kinda fun to see where it appears.
Then the burgundy colored plant in the back left is the Japanese Maple. You can get them in different colors. This one changes color. Behind that is my evergreen that just grew on its own and then behind that is the clumping bamboo. In the back right you can see the other kind of clumping bamboo which is yellow with green stripes. Then the big bush to the right next to the roost is fatsia japonica. The leaves are really thick so the peafowl can't eat it and unlike the rice paper plant, which has similar shaped leaves, this plant DOES NOT spread all over.
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