Black walnut will stunt the growth or even kill tomatoes, blackberry, alfalfa, asparagus, chrysanthemum,dock, potatoes, cereal grains, pine trees and apple trees.
On the other hand, Russian olive, black raspberries, ferns, goldenrod, asters, mints, violets, wild grape, clovers, buckwheat, peach trees, pear trees, plum trees and Kentucky bluegrass all have been
found to grow fairly well either beneath or near black walnut trees 
plants such as tomato, potato, blackberry, blueberry, azalea, mountain laurel, rhododendron, red pine and apple may be injured or killed within one to two months of growth within the root zone of these trees.
Jimbo Mathews wrote:Finding this makes me feel much much better about my dismal tomato crop, as they were planted pretty close to a bit black walnut tree. What is a REAL mystery to me however is my crop of golden giant grain amaranth. The ones that are by far the tallest and best (7 ft now) are the ones most directly in line with the root radius of another black walnut tree. Maybe its coincidence, maybe weeds were suppressed and the lawn I busted up to plant these was somehow conserving nutrients better than the grass outside the radius of said walnut tree. It'll be really interesting if I can replicate this, or if similar results happen with my wicked late crop of corn in the same area. Any ideas on some possible symbiosis here?