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Just to expand and what Dan said about acoustic spaces: if we project songs from several populations into a low dimensional space (let's say 2 dimensions) representing variation in acoustic structure and in which each point is an individual (so points close to each other have similar songs), then, if dialects are present, we can expect to find clusters, and the individuals within a cluster should belong to the same population. This can be used as a decision rule if we add a statistical test (like a Mantel test of acoustic vs spatial distances). This approach can be pretty flexible given that the acoustic space can be estimated using pretty much anything: measured features, pairwise similarity measures, repertoire composition, syntax, etc.