Weed-trees can be controlled without dangerous chemicals, but more time, patience, and understanding of tree anatomy is needed.
Xylem carries water and minerals from the roots to the leaves. Phloem carries manufactured food (sugars) from the leaves to the roots. The cambium (a watery layer only a few cells thick) is the generative layer, giving rise to both xylem and phloem. If the phloem is severed all the way around the tree (girdling the tree), food cannot be carried to the roots and they will eventually die, causing death of the tree. A tree can be girdled at any time, but some times are better in terms of ease and effectiveness. At a time of rapid growth (usually from March till June), the bark "slips". This means the phloem and cork layer will easily peel free, leaving the cambium and xylem. Just slipping a ring of bark is inadequate. If the cambium is left, it will heal. Slip as wide as wide a section of bark as convenient, then scrape the surface of the xylem to remove the cambium. (Some vines, such as Wisteria, develop an internal phloem, so do not respond well to this technique.) The best time to girdle is before the trees leaf out. The process of leafing out will deplete energy stores from the roots, which stores cannot be renewed if the phloem conduit has been interrupted.
Many trees will send off adventitious sprouts near an injury. Sprouts coming out below the girdle have to be removed regularly (probably every three weeks) before they contribute a significant quantity of food to the roots. When removing sprouts, it is a good idea to check the girdled strip and remove any bark which has begun to form in areas where the cambium was inadvertantly left intact.
Although not as rapid as proper treatment with herbicide, girdling is an effective way of killing unwanted trees. A completely girdled tree will die in one to three years, depending on the species, size, and time of girdling. In most riparian areas, dead trees do not have to be removed. In fact, they provide feeding perches for raptors and flycatchers, feeding and nesting sites for woodpeckers and, secondarily, nest holes for titmice, tree swalows, and house finches.