The scientific name for reed cane is Arundo donax L. and commonly known as Giant Reed plant. It is found on all continents and has two distinct varieties. One variety is called Arundo donax Variegata, which is not suitable for reed cane. It is my opinion that there is some genetic variation between plants worldwide. One plant dictionary indicates a sub-variety in France which has been the traditional source of reed cane.
Bassoon cane is typically taken from tubes of Arundo donax measuring 24-25mm in diameter (the same diameter as used for clarinet cane). Contrabassoon cane uses the largest diameters: 26mm and larger. Saxophone reeds range from 24mm for soprano and up to the largest diameter for bass sax. Reed cane is harvested in the winter of its second year of growth. This is necessary for it to obtain ‘woodiness’ and density. It is also necessary that the cane is carefully dried and later sun cured.
Oboe cane typically is 10-11mm, English horn 11-12mm, and diameters between the extremes are found in other double reed instruments including Renaissance instruments, bagpipes, shawms, etc.
Arundo donax typically grows near rivers and streams and is considered a nuisance weed in California and other locations in the United States. It has traditionally been used by farmers as a windbreak hence the term ‘canebreak’.
Arundo donax for reeds can be harvested in the wild as is common for some California reed makers and was planted around the state in the early 20th century by an Italian woodwind musician (source: Don Christlieb). It is also commonly planted for erosion control as was the case in the Sacramento River delta (cane harvested by boat). Cane is also farmed for reed cane in locations around the world.
For more information, see the Wikipedia article on Arundo donax.