Adherence to Menzerath's Law is the exception (not the rule) in three duetting primate species

Across diverse systems including language, music and genomes, there is a tendency for longer sequences to contain shorter constituents; this phenomenon is known as Menzerath's Law. Whether Menzerath's Law is a universal in biological systems, is the result of compression (wherein shortest possible strings represent the maximum amount of information) or emerges from an inevitable relationship between sequence and constituent length remains a topic of debate. In non-human primates, the vocalizations of geladas, male gibbons and chimpanzees exhibit patterns consistent with Menzerath's Law. Here, we use existing datasets of three duetting primate species (tarsiers, titi monkeys and gibbons) to examine the wide-scale applicability of Menzerath's Law. Primate duets provide a useful comparative model to test for the broad-scale applicability of Menzerath's Law, as they evolved independently under presumably similar selection pressures and are emitted under the same context(s) across taxa. Only four out of the eight call types we examined were consistent with Menzerath's Law. Two of these call types exhibited a negative relationship between the position of the note in the call and note duration, indicating that adherence to Menzerath's Law in these call types may be related to breathing constraints. Exceptions to Menzerath's Law occur when notes are relatively homogeneous, or when species-specific call structure leads to a deterministic decrease in note duration. We show that adherence to Menzerath's Law is the exception rather than the rule in duetting primates. It is possible that selection pressures for long-range signals that can travel effectively over large distances was stronger than that of compression in primate duets. Future studies investigating adherence to Menzerath's Law across the vocal repertoires of these species will help us better elucidate the pressures that shape both short- and long-distance acoustic signals.