Phrase-type use, bigram occurrence, and transition probabilities observed in training sets and corresponding testing sets.

<p>Each point represents a phrase type <b>(a)</b>, bigram <b>(b)</b>, or transition probability <b>(c)</b> in a bird’s repertoire, and different individuals are represented by different colors. Individuals recorded in both 2013 and 2014 (n = 6 individuals) are denoted by circles, while those recorded in only a single year are denoted by triangles. Transition probabilities <b>(c)</b> were only calculated for probabilities conditioned upon at least 50 observations. Dotted lines have the equation y = x.</p

Complexity, Predictability and Time Homogeneity of Syntax in the Songs of Cassin’s Vireo (<i>Vireo cassinii</i>)

<div><p>Many species of animals deliver vocalizations in sequences presumed to be governed by internal rules, though the nature and complexity of these syntactical rules have been investigated in relatively few species. Here I present an investigation into the song syntax of fourteen male Cassin’s Vireos (<i>Vireo cassinii</i>), a species whose song sequences are highly temporally structured. I compare their song sequences to three candidate models of varying levels of complexity–zero-order, first-order and second-order Markov models–and employ novel methods to interpolate between these three models. A variety of analyses, including sequence simulations, Fisher’s exact tests, and model likelihood analyses, showed that the songs of this species are too complex to be described by a zero-order or first-order Markov model. The model that best fit the data was intermediate in complexity between a first- and second-order model, though I also present evidence that some transition probabilities are conditioned on up to three preceding phrases. In addition, sequences were shown to be predictable with more than 54% accuracy overall, and predictability was positively correlated with the rate of song delivery. An assessment of the time homogeneity of syntax showed that transition probabilities between phrase types are largely stable over time, but that there was some evidence for modest changes in syntax within and between breeding seasons, a finding that I interpret to represent changes in breeding stage and social context rather than irreversible, secular shifts in syntax over time. These findings constitute a valuable addition to our understanding of bird song syntax in free-living birds, and will contribute to future attempts to understand the evolutionary importance of bird song syntax in avian communication.</p></div

Comparison of L₁-distances observed (closed circles) to the L₁-distances expected under a second-order Markov model, which has the property of being time homogeneous (open circles).

<p>‘Observed’ points were calculated by comparing the training set with the testing set for each individual, while the ‘Time Homogeneous’ points are average L₁-distances from 100 simulated training and testing sets for each individual. Significant differences are denoted with asterisks (* = p<0.05, ** = p<0.01).</p

L₁-distances for the three candidate models compared with those of the training set.

<p>Lines connect results from a given individual for the first-order, second-order, and training results, but were not drawn from the zero-order model for clarity and because this model so clearly diverged from the rest. Values on the left represent the seven N-gram distributions, while the values on the right represent the recurrence interval (RI) distributions.</p

Spectrogram of four phrases from the songs of the ‘Gully’ individual.

<p>The sequence depicted shows the phrase types <i>ai</i>, <i>en</i>, <i>ds</i>, and <i>ai</i>. The clear resemblance of the first and last phrases illustrates the high levels of within-type stereotypy in the songs of the species.</p

Summary of each individual’s recording corpus, along with the results from the Fisher’s tests for second- and third-order dependencies.

<p>Summary of each individual’s recording corpus, along with the results from the Fisher’s tests for second- and third-order dependencies.</p

Illustration of the methodology and results of forward selection.

<p>Black lines show results for the individual ‘AGBk’; other individuals are shown in gray. <b>(a)</b> states were added to the model by selecting the state providing the largest improvement when applied to the training set (dotted line). The supplemented model was then tested on the testing set (solid line), and the method repeated until all second-order states had been added to the model. The best (interpolated) model was that which gave the minimum negative log-likelihood when applied to the testing set (solid circles). <b>(b)</b> structure of resulting interpolated models, showing the proportion of a bird’s repertoire exhibiting zero-order, first-order and second-order properties.</p

Results from likelihood and predictability analyses.

<p>L-0, L-1, L-2, and L-Int represent the average per-phrase negative log-likelihood under the zero-order, first-order, second-order, and interpolated Markov models, respectively. P-0, P-1, P-2 and P-Int indicated the prediction accuracy for the same models. Bolded values highlight the most likely model and the model with the best ability to predict upcoming phrases for each individual under the two evaluation paradigms.</p

The relationship between the predictability of upcoming phrases and singing rate of Cassin’s Vireos (gray bars).

<p>Predictions were derived from the ‘interpolated’ Markov model using the train-test paradigm. Sample sizes for each interval are shown (black circles).</p

Sensitivity of California Thrashers (<i>Toxostoma redivivum</i>) to song syntax

<p>Many birds have songs with variable structure and sequences. In earlier studies, we characterized some features from the song structures of California Thrashers (<i>Toxostoma redivivum</i>). In the Thrashers, there were a large number of phrase types, dozens to hundreds and the songs that were sequences of these many phrases were not random, but show some structure referred to as syntax. For example, a syntactic rule might be that phrase type A can be followed by phrase type B, but not type C. We, along with others, have assumed that syntax is an important feature of songs. This paper describes an experimental attempt to determine that syntax is important to California Thrashers by recording the reaction of territorial thrashers to playbacks of other thrasher songs, some of which obeyed the syntax rules we had discovered while others violated those rules. We also obtained video recordings of their behaviour near the playback speakers. We observed differences in the reactions to the birds that heard these two types of playbacks. Resident males reacted to either playback type, but more strongly when the original order was preserved. We observed difference in their behavioural response to correct or altered syntax. This indicates that the syntax of their songs is perceived in territorial defence by the birds.</p