A couple of years ago I'd planted a row of tomatoes under our cottonwood tree, and they did not do well at all. Many died, those that lived produced very few tomatoes. I blamed it on the variety I had chosen, and have not planted those since. Then I realized that the strawberries I'd planted near that tree have never done well. I've replanted the same area with strawberries for 3 years, and just couldn't get them to grow. I got to wondering if maybe the cottonwood had something to do with these problems. I did some research, and the answer is YES!
Cottonwood trees, like the Black Walnut, produce the chemical, juglone. Juglone is very toxic to some vegetables and fruits including: tomato, pepper, potato, eggplant, blackberry, blueberry, apple. These plants will yellow, wilt and die. I didn't see anything about strawberries not growing there, but in my experience, they didn't. There are also several ornamental plants that won't grow near them, but I don't do those. Vegetables that are tolerant to juglone include: beans, corn, melons, squash, beets, onions, parsnips, carrots.
I will no longer be planting tomatoes, peppers or potatoes or strawberries near these trees. I also try to remove all leaves and twigs that fall onto the beds. Apparently it's ok to compost the leaves and twigs, but they should not be left on fresh. It is best to add additional organic matter/compost to these beds, which will lessen the effect of the juglone.
This year I planted several perennial herbs in the area which had been my strawberry bed. They'll just sit there and I won't worry about what to plant there in the future. These did quite fine. One of the things I planted directly under the tree was mint. I know that mint is quite invasive, and I thought that if it would grow there, it would be just fine! I've read that mint leaves are good to repel squash bugs, so rather than planting the invasive mint among the squash, I will let it grow by the cottonwood if it can, then cut the leaves and scatter them around the squash. The mint grew there quite well, along with some chives, lemon balm, marjoram, lovage, thyme and salad burnet. In the spring I will discover what survived the winter.
For more information, read these articles: