How reliable are the methods for estimating repertoire size?

Abstract

Quantifying signal repertoire size is a critical first step towards understanding the evolution of signal complexity. However, counting signal types can be so complicated and time consuming when repertoire size is large, that this trait is often estimated rather than measured directly. We studied how three common methods for repertoire size quantification (i.e., simple enumeration, curve-fitting and capture-recapture analysis) are affected by sample size and presentation style using simulated repertoires of known sizes. As expected, estimation error decreased with increasing sample size and varied among presentation styles. More surprisingly, for all but one of the presentation styles studied, curve-fitting and capture-recapture analysis yielded errors of similar or greater magnitude than the errors researchers would make by simply assuming that the number of types in an incomplete sample is the true repertoire size. Our results also indicate that studies based on incomplete samples are likely to yield incorrect ranking of individuals and spurious correlations with other parameters regardless of the technique of choice. Finally, we argue that biological receivers face similar difficulties in quantifying repertoire size than human observers and we explore some of the biological implications of this hypothesis.

Figure 1

Effect of trapping occasion size (i.e., number of elements included in each trapping occasion) on capture-recapture estimation. The estimates shown are based on a simulated sequence with completely random presentation of elements for an individual with 200 element types (true repertoire = dotted line). Data are not available for all trapping occasion sizes at all sampling levels because the maximum number of trapping occasions that can be currently analyzed with the program CAPTURE is 80.

Figure 2

Examples of inter-type and inter-individual variation in the syllable types of the tropical mockingbird. Types are identified by capital letters and singers are presented in parentheses.

Figure 3

Estimated repertoire size as a function of estimation technique, sample size and singing style. Five simulated individuals are identified by the size of their repertoire (e.g., Rep200 = Individual with 200 types in its repertoire). The abbreviations for the different presentation styles follow Table 1.

Figure 4

Relative ranking of five individuals based on estimated repertoire size as a function of estimation technique, sample size and singing style. The five simulated individuals are identified by the size of their repertoire (e.g., Rep200 = Individual with 200 types in its repertoire). The abbreviations for the different presentation styles follow Table 1.

Figure 5

Least squares means for the mean relative error of the different estimation techniques as a function of presentation style. Errors were ranked from lowest to highest and these ranks were natural log transformed to insure normally distributed residuals in our model. Larger Y-values imply larger errors in the estimation. SE=Simple Enumeration; CF=Curve-fitting; CR=Capture-recapture; Abbreviations for presentation styles follow Table 1.

Figure 6

Syllable type use in the tropical mockingbird. All the types present in the population are listed in the same order for every bird.

Figure 7

Estimated repertoire size and relative ranking for six male tropical mockingbirds as a function of sample size and estimation technique.