Does Zipf's law of abbreviation shape birdsong?

In human languages, words that are used more frequently tend to be shorter than words that are used less frequently. This pattern is known as Zipf's law of abbreviation. It has been attributed to the principle of least effort - communication is more efficient when words that are used more frequently are easier to produce. Zipf's law of abbreviation appears to hold in all human languages, and recently attention has turned to whether it also holds in animal communication. In birdsong, which has been used as a model for human language learning and development, researchers have focused on whether more frequently used notes or phrases are shorter than those that are used less frequently. Because birdsong can be highly stereotyped, have high interindividual variation, and have phrase repertoires that are small relative to human language lexicons, studying Zipf's law of abbreviation in birdsong presents challenges that do not arise when studying human languages. In this paper, we describe a new method for assessing evidence for Zipf's law of abbreviation in birdsong, and we introduce the R package ZLAvian to implement this method. We used ZLAvian to study Zipf's law of abbreviation in the songs of 11 bird populations archived in the open-access repository Bird-DB. We did not find strong evidence for Zipf's law of abbreviation in any population when studied alone, but we found evidence for Zipf's law in a synthetic analysis across all populations. Overall, the negative concordance between phrase length and frequency of use in birdsong was several times weaker than the negative concordance between word length and frequency of use in written human languages. The method and the results we present here offer a new foundation for researchers studying if or how the principle of least effort shapes animal communication.