Answer: It is hard for me to analyse what disease (if it is a disease) that your tree has without being able to see it myself.
In general, the Mesquite (Prosopis) requires a warm, dry climate and can only tolerate very light frosts. It must be grown in full sunshine, and you should also ensure that the tree is not waterlogged (which could also be the source of the problem) - the soil should be light and well-drained with moisture at depth. The Mesquite species tolerate dry conditions very well and prefer alkaline soil.
There is a disease common to mesquites, called Ganoderma root rot, which is caused by the soil borne fungus Ganoderma. The Ganoderma that infects mesquite and acacia differs from the Ganoderma lucidum that infects other trees and shrubs in Arizona, and its species is still under investigation. The fungus is soil borne and infects mesquite roots, particularly at wound sites. It rots the roots causing a slow decline and death of mature trees and can move from tree to tree via root contact. The fungus has not been found in upper parts of the tree, but it could be responsible for dying branches at the top. The only distinguishing sign of disease is the appearance of fruiting bodies at the base of the tree. These growths are most common during the summer rainy season, and start out as white bulbous structures at soil level. If they continue to grow, the fruiting bodies become shelf-like structures that are reddish brown and glossy on the top and brown on the bottom. Spores released from the bottom may leave a reddish brown dust on the soil and trunk nearby.
There is no recommended treatment for infected trees; infections may be prevented by preventing wounds to roots and to the trunk at the soil level.
For a positive diagnosis, you may want to take a sample of the problem to your local Cooperative Extension office or Master Gardener clinic. Best wishes with your mesquite!
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