DOI: 10.5061/dryad.vt4b8gtn0
title: An analysis of avian vocal performance at the note and song levels

description: Sexual displays that require extreme feats of physiological performance
 have the potential to reliably indicate the signaller’s skill or
 motivation. We tested for evidence of performance constraints in
 Adelaide’s warblers (Setophaga adelaidae) songs. At the note level, we
 identified three trade-offs with well-defined limits. At the song level,
 we identified two trade-offs, but their limits were less well-defined than
 the note-level limits. Trade-offs at both levels suggest that song
 structure is constrained by limits to the speed of both frequency
 modulation (while vocalizing and between notes) and respiration. 
 Performance metrics derived from the observed limits to performance varied
 moderately among individuals and strongly among song types. Note-level
 performance metrics were positively skewed, as predicted by the hypothesis
 that performance is constrained. We conclude that physiological limits on
 frequency modulation and respiration constrain song structure in male
 Adelaide’s warblers. Further work is needed to determine whether receivers
 respond to natural levels of variation in performance, and whether
 performance correlates with singer quality or motivation.
description: Study species Adelaide’s warbler is a
 socially monogamous insectivore endemic to Puerto Rico and Vieques. Mated
 pairs maintain all-purpose territories throughout the year (Toms 2010).
 Male songs are frequency modulated trills (Fig. 2). Individual males sing
 repertoires of song types (avg. ≈ 23 songs), many of which are shared with
 other males (Staicer 1991; Kaluthota et al. 2019). Each male’s repertoire
 comprises two categories, A and B, which are characterized by distinct
 times of delivery, song rates, and song switching frequencies (Staicer
 1991; Kaluthota et al. 2019). The individual notes comprising songs are
 structurally simple, with almost all of the energy concentrated in the
 fundamental frequency. There exists considerable among-note variation in
 duration, frequency, and frequency modulation (Fig. 2).
 Ethics This research was approved by the
 Institutional Animal Care and Use Committee at the University of Puerto
 Rico, Mayagüez (17 September, 2010). It adheres to the ASAB/ABS Guidelines
 for the use of animals in research. Birds were captured under D.M.L.’s
 federal bird banding permit (no. 23696). The U.S. Fish and Wildlife
 Service granted permission to work at the Cabo Rojo Wildlife Refuge
 (permit 2012-01). Recording and scoring
 We recorded nine mated male Adelaide’s Warblers at the Cabo Rojo
 National Wildlife Refuge (US Fish and Wildlife Service) during the
 breeding season between March and June, 2012. All subjects wore unique
 combinations of coloured leg bands, allowing recordists to unambiguously
 identify individuals. Each male was recorded on four days, from 45 minutes
 before sunrise until 2 hours and 45 minutes after sunrise. Consecutive
 recordings of a given male were separated by at least four days, except on
 two occasions when recordings were made on consecutive days because of
 logistical constraints. Recordings were made with Marantz PMD 661 digital
 recorders and Sennheisser ME67 shotgun microphones (file format = wav,
 sampling rate = 44.1KHz, bit depth = 16 bits). This is the same set of
 recordings used in a previous study of short-term variation in song
 performance (Schraft et al. 2017), a methods paper on song sequences
 (Hedley et al. 2018), and an analysis of singing modes (Kaluthota et al.
 2019). We visualized recordings as sound spectrograms
 in Syrinx PC v.2.6 (J. Burt, Seattle, WA; Settings: Blackman window,
 transform size = 1024 points). Each song recording from a focal male was
 assessed for recording quality. One person (D.M.L.) assigned song
 recordings to song types. A previous study that used the same recordings
 estimated the inter-rater reliability of song type scoring to be 100%
 within an individual bird, and 87% among individuals (Kaluthota et al.
 2019). We only used high-quality recordings (high signal-to-noise ratio,
 minimal overlap with other sounds) for song measurements. High quality
 song recordings were analysed in Luscinia v2.14 (max. freq. = 10kHz, frame
 length = 5ms, time step = 1ms, dynamic range = 35 dB, dynamic equalization
 = 100ms, de-reverberation = 100%, de-reverberation range = 100ms, high
 pass threshold = 1.0kHz, noise removal = 10dB; Lachlan 2007). We loosely
 outlined the trace of each note with a stylus on a touchscreen monitor,
 and Luscinia’s algorithms identified the signal and rejected background
 noise. The following note-level acoustic variables were output to a
 spreadsheet: start time, end time, maximum peak frequency, and minimum
 peak frequency. Luscinia offers several frequency metrics. We chose peak
 frequency because visual inspection of spectrograms showed that it tracked
 the fundamental frequency better than the fundamental frequency
 metric. Analysis: trade-offs The
 note-level analysis omitted the one or two low-amplitude notes that began
 some songs and the final note of all songs. We omitted final notes because
 it was impossible to define the duration of the silent gap following the
 last note. For the note-level analyses, we analysed the frequency
 bandwidths and durations (based on note start and end times) of both notes
 and silent gaps (Fig. 3). Following Cardoso (2013), we measure frequency
 bandwidth (BW) as the ratio of the maximum frequency to the minimum
 frequency. Gap duration and gap BW are taken from the silent gap after the
 focal note. Gap BW is based on the end of the focal note and the beginning
 of the subsequent note. We tested three comparisons at the note level that
 might reveal trade-offs indicative of performance constraints: note
 duration vs. gap duration (respiratory), note BW vs. note duration (voiced
 FM), and gap BW vs. gap duration (unvoiced FM). We
 chose four parameters for the song-level analyses: trill rate, average
 frequency bandwidth, percent of sound, and duration. Trill rate (TR) was
 calculated as the number of notes in the song minus one, divided by the
 time from the beginning of the first note to the beginning of the last
 note. We excluded the final note from this calculation because TRs based
 on the full song necessarily omit the ‘gap’ after the last note, biasing
 estimates upward for songs with fewer notes. Adelaide’s warbler songs are
 frequency modulated trills (Fig. 2), so the total frequency bandwidth of a
 song is only weakly related to the amount of FM in the song. We therefore
 calculated a song’s BW as the average BW of the notes in the song. Percent
 of sound (PoS) is the percent of the song that is voiced. It was
 calculated as the sum of note durations, divided by the total duration of
 the song, multiplied by 100. Lastly, we measured song duration because
 many kinds of performance increase in difficulty with increasing duration
 (Byers et al. 2010). We tested four comparisons that might reveal
 trade-offs at the song level: TR vs. mean BW (FM, respiratory), duration
 vs. TR (respiratory endurance), duration vs. PoS (respiratory endurance),
 and TR vs. PoS (respiratory). Wilson et al. (2014)
 recommend quantile regression to test for acoustic trade-offs. Quantile
 regression produces a linear function to estimate a defined quantile Y
 over a range of X (Cade and Noon 2003). Standard quantile regression,
 however, fails to account for the non-independence of multiple data points
 from a given subject, raising concerns about pseudoreplication. Unlike
 standard quantile regression, mixed quantile regression includes one or
 more random variables (Geraci 2014). We ran mixed quantile regression with
 the random variable “individual identity” to account for the
 non-independence of acoustic units from the same individual. To the best
 of our knowledge, this is the first study to use mixed quantile regression
 to test for acoustic trade-offs. Initially, we ran all models with both
 random intercepts and random slopes (Barr et al. 2013). The random slope
 estimates proved unstable for the note level models, so we ran random
 intercepts models for the note-level analyses and verified the absence of
 Simpson’s paradox (see Results). For those analyses, we report the sum of
 the overall intercept estimate and the average individual intercept
 adjustment, because that value represents a population-level estimate of
 the intercept (Table ESM-1). The song-level models include both random
 intercepts and random slopes. We predicted positively
 sloping lower boundaries for all note-level analyses, because higher
 values of acoustic variable X were predicted to constrain the minimum
 values of variable Y (as in Geberzahn and Aubin 2014a). The term
 “trade-off” often implies a negative relationship, so readers may question
 whether it is appropriate to describe a positive relationship as evidence
 of a trade-off <i>per se</i>. We applied the term to both
 positive and negative relationships because a negative correlation can be
 functionally identical to a positive one (e.g., a positive relationship
 between note duration and gap duration is the same as a negative
 relationship between note duration and gap <i>shortness</i>),
 and both can result from constrained resource allocation.
 We predicted negative upper
 boundaries for all song-level analyses, because higher values of variable
 X were predicted to constrain the maximum values of variable Y as in (as
 in Podos 1997). For the note-level dataset, we tested lower boundaries
 with 10<sup>th</sup> quantile regressions (tau = 0.10),
 following advice in Wilson et al. (2014). Similarly, we ran
 90<sup>th</sup> quantile regressions (tau = 0.90) to estimates
 upper boundaries in the song-level dataset (Wilson et al. 2014).
 Population-level performance limits could arise from a pooled
 analysis of individuals that do not themselves exhibit trade-offs. For
 example, some individuals might sing high-trill-rate, low-bandwidth songs
 while others sing low-trill-rate, high-bandwidth songs, resulting in a
 sloping limit to the population’s distribution when individuals’ data are
 pooled. Alternatively, different individuals may be subject to similar
 trade-offs, which combine to produce a population-wide trade-off. We
 therefore examined data from individual birds for evidence of
 trade-offs. In addition to the hypothesis tests
 described above, we offer several visual representations of our data. We
 graphed the whole distributions with semi-transparent points and quantile
 regression lines. To show individual variation near the boundaries, we
 also present zoomed-in views of the boundary regions with separate colours
 for each individual and polygons that mark the limit of each individual’s
 distribution. Polygons were generated with the
 <i>geom_encircle</i> command in the <i>ggalt
 </i>package (Rudis et al. 2017), with settings s_shape =1 (no added
 curvature) and expand = 0 (polygon edges intersect extreme points).
 Finally, we present separate distributions for each individual in the
 electronic supplementary material. Analysis:
 Performance metrics Deviation scores were calculated
 as the orthogonal distance from the quantile regression lines, such that
 higher (more positive) values indicate lower putative performance (Podos
 2001). We estimated intra-class correlations (ICCs) to test how repeatable
 individuals were with respect to note-level deviation scores averaged over
 songs and song-level deviation scores. We calculated ICCs for individuals
 using both the entire sample and the average scores for each song type
 within individual (see Introduction). We also tested whether note-level
 deviation scores averaged over songs and song-level deviation scores were
 significantly repeatable among song types. We conducted likelihood ratio
 tests to test whether ICC’s were statistically distinguishable from 0
 (Stoffel et al. 2017). We generated Pearson’s
 correlation matrices of deviation scores for notes and songs. The
 song-level correlation matrix included song-level deviations, note-level
 deviations averaged over songs, and FEX. We calculated the skewness of the
 deviation scores to test competing predictions of the constrained
 performance and constrained learning hypotheses. All
 statistics were conducted in R Studio (Team 2015). Mixed quantile
 regressions relied on the <i>lqmm</i> package (Geraci 2014).
 Intra-class correlations were assessed with the <i>rptR</i>
 package (Stoffel et al. 2017). Data visualizations relied on the package
 <i>ggplot2</i> (Wickham and Chang 2008). Data and R code are
 available at DRYAD (doi:10.5061/dryad.vt4b8gtn0).
description: The rmd files are Markdown files for use in R. 
 "PerfConst17.3.rmd" is the note-level analysis and
 "SongPerfConst7.1.rmd" is the song-level analysis. The current
 versions of the .rmd files correct minor errors in previous versions,
 including versions that were previously posted to Dryad. These errors were
 corrected before publication, so the paper is based on the corrected
 version of the R code. Feel free to contact me about these data at
 david.logue@uleth.ca.