Ask Mr. Smarty Plants

Your black walnut tree (Juglans nigra) is defending its space—that's why you are having trouble getting any other plants to grow underneath it. With this defense mechanism, called allelopathy, the tree makes and releases a chemical called juglone that adversely affects many other (but not all) plants. Juglone can be found in all parts of the black walnut tree. If the roots of another plant come within 1/2 inch of the walnuts roots, they can absorb the juglone and sicken and die. Also, walnut leaf litter and walnut fruit on the ground leach juglone into the soil.

Virginia Extension Service has an excellent discussion of the black walnut and its allelopathic effects. Additionally, the article lists common plants that are affected by the juglone of the walnut. There is also a list of plants that will grow near the black walnut. Here are a few attractive native plants that will grow underneath your tree in Tyler:

Black-eyed susan (Rudbeckia hirta)
Pink evening primrose (Oenothera speciosa)
Cardinal flower (Lobelia cardinalis)
Virginia creeper (Parthenocissus quinquefolia)
Inland sea oats (Chasmanthium latifolium)

By the way, allelopathy is one of the reasons some invasive plants, such as spotted knapweed (Centaurea biebersteinii), are so successful.