Quantifying similarity in animal vocal sequences: Which metric performs best?

1. Many animals communicate using sequences of discrete acoustic elements which can be complex, vary in their degree of stereotypy, and are potentially open-ended. Variation in sequences can provide important ecological, behavioural, or evolutionary information about the structure and connectivity of populations, mechanisms for vocal cultural evolution, and the underlying drivers responsible for these processes. Various mathematical techniques have been used to form a realistic approximation of sequence similarity for such tasks. 2. Here, we use both simulated and empirical datasets from animal vocal sequences (rock hyrax, Procavia capensis; humpback whale, Megaptera novaeangliae; bottlenose dolphin, Tursiops truncatus; and Carolina chickadee, Poecile carolinensis) to test which of eight sequence analysis metrics are more likely to reconstruct the information encoded in the sequences, and to test the fidelity of estimation of model parameters, when the sequences are assumed to conform to particular statistical models. 3. Results from the simulated data indicated that multiple metrics were equally successful in reconstructing the information encoded in the sequences of simulated individuals (Markov chains, n-gram models, repeat distribution, and edit distance), and data generated by different stochastic processes (entropy rate and n-grams). However, the string edit (Levenshtein) distance performed consistently and significantly better than all other tested metrics (including entropy, Markov chains, n-grams, mutual information) for all empirical datasets, despite being less commonly used in the field of animal acoustic communication. 4. The Levenshtein distance metric provides a robust analytical approach that should be considered in the comparison of animal acoustic sequences in preference to other commonly employed techniques (such as Markov chains, hidden Markov models, or Shannon entropy). The recent discovery that non-Markovian vocal sequences may be more common in animal communication than previously thought, provides a rich area for future research that requires non-Markovian based analysis techniques to investigate animal grammars and potentially the origin of human language.We thank Melinda Rekdahl, Todd Freeberg and his graduate students, Amiyaal Ilany, Elizabeth Hobson, and Jessica Crance for providing comments of on a previous version of this manuscript. We thank Mike Noad, Melinda Rekdahl, and Claire Garrigue for assistance with humpback whale song collection and initial categorisation of the song, Vincent Janik and Laela Sayigh for assistance with signature whistle collection, Todd Freeberg with chickadee recordings, and Eli Geffen and Amiyaal Ilany for assistance with hyrax song collection and analysis. E.C.G is supported by a Newton International Fellowship. Part of this work was conducted while E.C.G. was supported by a National Research Council (National Academy of Sciences) Postdoctoral Fellowship at the National Marine Mammal Laboratory, AFSC, NMFS, NOAA. The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Marine Fisheries Service. We would also like to thank Randall Wells and the Sarasota Dolphin Research Program for the opportunity to record the Sarasota dolphins, where data were collected under a series of National Marine Fisheries Service Scientific Research Permits issued to Randall Wells. A.K. is supported by the Herchel Smith Postdoctoral Fellowship Fund. Part of this work was conducted while A.K. was a Postdoctoral Fellow at the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1111/2041-210X.1243