The doves are the faithful Christians, who are safe from the devil as long as they remain in the church. Christ is the right side of the tree, the holy spirit the left side. The devil is afraid of the church and will not come near, but the Christian who leaves the church should beware.
The Aberdeen Bestiary has a slightly different interpretation: " Take the tree as God, the shadow as his son... Take the fruit to be the wisdom of God, that is, the Holy Spirit." The rest of the allegory is basically the same as usual.