Someone asked a similar question recently regarding "a lot of them are..." Here is a link: http://english.stackexchange.com/questions/44942/a-variety-of-x-is-vs-a-variety-of-x-are "Both sentences are grammatical." You could call it something of an anomaly of English grammar (but then, what isn't? :)).

plural = exist singular = exists

exists = singular unit of meaning, either one person or one group of things (eg this disease only exists in Africa) exist = plural unit, either people or things eg 'large groups of people exist in harmony' or 'a wide variety of wetlands exist'