This really seem to be the defining characteristic:
"Most species of cacti have lost true leaves, retaining only spines, which are highly modified leaves. As well as defending against herbivores, spines help prevent water loss by reducing air flow close to the cactus and providing some shade. Cactus spines are produced from specialized structures called areoles, a kind of highly reduced branch.
Areoles are an identifying feature of cacti."
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http://en.wikipedia.org/wiki/C...
