The issue of whether language is the result of mechanisms that are specifically human, and specific to language, has been publicly discussed in a recent series of papers in Science and in Cognition. Hauser, Chomsky and Fitch (2002) and again in Fitch, Hauser and Chomsky (2005) argue that recursion is the only mechanism that qualifies on both counts, and they call this the Faculty of Language in the Narrow sense (FLN), in contrast to the Faculty of Language in the Broad sense (FLB). In the later 2005 paper, they say (p.200): "much of phonology is likely part of FLB, not FLN, either because phonological mechanisms are shared with other cognitive domains (notably music and dance), or because the relevant phenomena appear in other species, particularly bird and whale 'song'."
My goal in this squib is to ponder on what it is, as a phonologist, I would take to be core properties of phonological systems, and then ask which, if any, are known to be found outside humans, and which are known to be absent in at least some non-human animals.