Table 1.
Glossary.
Fig 1.
Which methods to use depending on the level of analysis: A first evaluation of whether a signal is periodic or aperiodic relies on IOI and visual assessment of the data.
Whether an acoustic signal sequence might be isochronous or heterochronous can be inferred from IOIs and nPVI calculations. To find exact beat frequencies a GAT approach, FFTs or again an assessment of IOIs can be used, and the detection of simple or complex heterochronous patterns is guided visually by recurrence plots. Exact beat frequencies are only interpretable if accompanied by a goodness-of-fit value. The figure was adjusted after [28].
Fig 2.
Visual representation of the different sequences.
Different colors indicate different element types. (A) An exemplary sequence of C. perspicillata isolation calls. (B) An exemplary sequence of S. bilineata isolation calls. (C) An exemplary sequence of P. macrocephalus echolocation clicks as used for orientation and foraging. Click trains can be up to 200 elements long.
Fig 3.
Visual explanation of the internal reference: The mean of the binary sequence that serves as input for the Fourier analysis determines the amplitude of the zero-bin-component (DC-term).
This amplitude will always be the highest in this kind of analysis serving as an internal reference for the second highest peak that determines the best fitting exact beat frequency.
Table 2.
Summary of IOI results.
Fig 4.
Analysis of the datasets per method: The first column shows the distribution of IOIs for all datasets.
The second to fourth column depict exact beat frequency distributions for the three datasets (1. C. perspicillata, 2. S. bilineata, 3. P. macrocephalus) and different methods.
Table 3.
Overview of exact beat frequencies found for three datasets with three methods.
Table 4.
Comparison of Goodness-of-Fit values for all datasets and methods.
Fig 5.
Individual Beat Clusters in C. perspicillata pups confirm the results of other methods: Exact beat frequencies as analyzed with the three different methods are shown with clusters in the data.
One individual is depicted per column, all exact beat frequencies found are shown as dots. Depicted in red are the sequences falling into the largest cluster of sequences sharing a similar beat. Percentages at the bottom indicate the percentage of sequences per individual in the largest cluster. (a) Exact beat frequencies and individual clusters as obtained by the GAT approach. (b) Exact beat frequencies and individual clusters as obtained by the FFT method. (c) Exact beat frequencies and individual clusters as obtained by IOI analysis.
Fig 6.
Recurrence plots of two sequences.
No difference is indicated by white; the darker the color, the bigger the difference. Note that absolute differences are depicted and colors represent different differences in both plots, as shown in the legend. A) Echolocation click train of P. macrocephalus: a very isochronous pattern is visible by only white and light grey colors. B) The multisyllabic structure of an isolation call of S. bilineata is visible in the differences in IOIs: a subsequence of very similar IOIs is followed by an alternating sequence of two more element types.
Fig 7.
Deciding on a method depending on the dataset and results.
The workflow starts with simple distributional measures such as IOI analysis and nPVI calculations. Questions to be answered in subsequent order are: 1) Is a dataset periodic? 2) If so, can we infer isochrony? 3) Assuming an isochronous pattern, how to analyze exact beat frequencies best, depending on the data at hand? The sequences we analyzed fall in three of the decision paths: S. bilineata isolation calls would be best to analyze with IOI or FFT; C. perspicillata would be best to analyze with the GAT approach, while P. macrocephalus echolocation click trains should be analyzed with IOI and FFT as well.