Supplementary Materials for Akçay, Campbell and Beecher (2013). Individual differences affect honest
signaling in a songbird
Table S1. Loading coefficients for the Principal Component Analyses (PCA). The first component of PCA
on aggressive behaviors (the top three variables) explained 67.9% of variance and was taken as
aggression score. The first component of PCA on signaling behaviors (the bottom two variables)
explained 68.3% of variance and was taken as signaling score. n=219 trials, 69 subjects.
variable
Rate of flights
Time spent within 5 m
Closest approach
Rate of soft songs
Rate of wing waves
Coefficients
Aggression PCA
0.81
0.87
-0.79
Signaling PCA
0.83
0.83
Validation of measures of aggression as a replacement for physical attack
In this section we report additional analyses on data published in Akcay et al. [1] that validates
our measures of aggression (PCA scores as reported in Table S1). In Akcay et al., we confronted each
subject (n=48) with a taxi-dermic mount at the center of their territory and subjects were given 15
minutes to attack the mount or not. 31 out of 48 subjects attacked (see ref [1] for the details of the
experimental design). In order to validate our current measures of aggression, we extracted the same
variables we use for aggression scores here (rate of flights, time spent within 5m, closest approach) and
carried out a PCA analysis. The first component of PCA explained 69.3% of variance.
Table S2. Loading coefficients of the behavioral measures in the PCA carried out on the data from Akcay
et al. [1].
variable
Rate of flights
Time spent within 5 m
Closest approach
Coefficients
PCA1
0.77
0.84
-0.89
When we entered the PCA1 scores into a discriminant function analysis, the PCA1 scores were
able to classify all but 4 of the subjects (91.7%) correctly as attackers and non-attackers. The 4 subjects
that were misclassified had high scores but did not attack. It is important to note that the 15 minute
limit on attacks is arbitrary (but necessary to carry out a large number of trials in a reasonable amount
of time), and it is possible these 4 subjects would have attacked had we kept the trial duration longer. In
any case, the PCA scores were a remarkably good proxy of whether or not the bird will physically attack
the mount. This result thus validates the PCA scores used in the current experiment.
An alternative method of calculating repeatability of signaling scores controlling for aggression.
In this section, we report an alternative method of calculating repeatability of signaling scores
while controlling for aggression that uses the General Linear Mixed Model (LMM) approach suggested
recently by Nakagawa and Schielzeth [2]. In this method, the adjusted repeatability (repeatability
controlling for a confounding factor) is calculated by partitioning the observed variance in the variable of
interest (here, the signaling levels) into three components: the variance accounted by the fixed factor
(σϒ2; individual aggression), between-subject variance (σα2) and within-subject (error) variance (σε2). The
adjusted repeatability then can be calculated as the following ratio: σα2/ (σα2+ σε2), as in a simple
repeatability. Thus, adjusted repeatability is akin to calculating residuals in signaling scores after
accounting for aggression and calculating the repeatability of these residuals. If, after removing the
variance due to the effect of aggression, a significant portion of the variance in signaling scores can still
be attributed to between-subject variance, than signaling levels can be said to be repeatable after
controlling for aggression. This would be evidence for a repeatable personality trait that, along with
aggressiveness, drives observed signaling levels (Figure 1c). On the other hand, if after removing the
variance due to aggression levels, the remaining variance is mostly due to within-subject (error)
variance, than there would be no evidence for this hypothesis (Figure 1b).
We calculated the adjusted repeatability scores controlling for aggression scores from a
random-intercept LMM (using R package ‘lme4’) where signaling score was the dependent variable,
aggression scores the fixed effect and subject identity the random factor. We tested whether the effect
of the random variable (subject identity) was significant with a restricted likelihood ratio test using the
R-package RLRsim[3].
The mixed model analysis showed that aggression scores were a significant predictor of
signaling scores (effect size± SE = 0.39± 0.06, t= 6.59, n = 219, p< 0.000001). Figure S1 shows the
portions of variance in the LMM model that was explained by the fixed effect of aggression scores,
individual (subject) and residual error variance.
We then calculated the repeatability of signaling scores, adjusted for aggression scores. As
explained above, we divided the estimated variance of between-subject variance (σα2= 0.33) by the sum
of between-subject variance and residual variance (σε2= 0.42) to calculate the repeatability: r= 0.44, p<
0.0001 (the p-value was determined from a likelihood-ratio test for the significance of the random
effect). This finding suggests that individuals consistently signaled above or below the expected level of
signaling for any given level of aggression, corroborating the finding of the analysis on signaling residuals
reported in the main text. Note that the estimate of the repeatability, although somewhat higher than
the estimate of repeatability from the residuals (0.39), is well within the range of confidence intervals
we found for the repeatability of residuals (0.24- 0.54).
Ruling out alternative explanations of consistent individual differences.
In this section we deal with two alternative explanations raised by reviewers that may explain
the presence of individual differences. The first alternative explanation is that individual differences may
be not due to some individual trait but due to age differences in aggression. If age is responsible for
most of the individual differences, controlling for age should decrease the repeatabilities of aggression
and signaling behaviors significantly. To answer this question, we carried out LMM-based adjusted
repeatability analyses as described above on the 34 subjects (108 trials) for whom we had age
information. We carried out two LMM analyses (using lmer in R package lme4) on the signaling and
aggression scores with age as a fixed covariate and bird identity as a random effect, and the significance
of the fixed effect was tested with a likelihood-ratio test (anova function in R). Age had a significant
effect on aggression scores (β+SE = -0.19+0.10, t=2.00, p=0.046, n=108 trials) but not on signaling scores
(β+SE: -0.11+0.08, t= -1.45, p=0.14, n=108). In these models, age explained 7.5% and 4.3% of variance
respectively (R2 were calculated according to the formulae in [4]) . This is a fraction of the variance
explained by the random effect of bird identity in same models (50.7% and 50.4%, respectively).
Adjusted repeatability after controlling for age for aggression scores was r= 0.55 and the
adjusted repeatability for signaling scores was r=0.52. For the same 34 males, simple repeatabilities
calculated from LMMs that did not include age as a factor were r=0.57, and r=0.53, for aggression and
signaling scores respectively. Thus, the effect of age did not have a profound effect on the estimates of
repeatabilities.
We also calculated the adjusted repeatability scores for signaling, controlling simultaneously for
age of the bird and aggression scores in an LMM. This repeatability score also is very similar to the ones
reported in the manuscript and above; r= 0.38. These results all point to the fact that individual’s age,
although having a weak negative effect on aggression scores (but not signaling scores), is not a primary
driver of individual consistency in either aggression or signaling or signaling strategies.
Another alternative explanation for individual differences raised by one reviewer is that (1) if
observation durations are consistently different between birds because of the fact that birds had
different latencies to respond, and (2) if birds switch from signaling to aggressive behaviors at a certain
threshold, we would detect what looks like individually consistent differences in signaling levels. We can
rule these two assumptions out with current dataset: First of all, observation durations (mean± SD: 547
± 99.9 seconds) were not repeatable (r= -0.005, F(4,214)= 0.78, p=0.54).
The second point above assumes that there is a distinct switch from primarily signaling
behaviors to primarily aggressive behaviors. This is not the case in song sparrows. For instance Searcy et
al. [5] showed a minute by minute breakdown of soft song rates in the period leading up to an attack
and found that soft song rates do not change significantly from early to late trial; i.e. the birds do not
stop signaling. This is consistent with the detailed descriptions of natural interactions between song
sparrows described by Nice [6].
We can also rule out that song sparrows do not stop signaling later in our current dataset. To
this aim, we looked at behaviors in the first 5 minutes vs. second last minutes of the trial and ran a LMM
model for each of the following behaviors (again converted to rates per minutes to account for unequal
durations of observations within these halves): rate of flights, rate of soft songs, rate of wing waves,
time spent within 5m, and closest approach distance. For each of these measures we ran a LMM with
trial period (first vs. second) as a fixed factor and the month of testing and bird identity as random
factors. We used likelihood ratio tests to compare the LMM with a null model that did not have trial
period in the model (this model only has month and bird as random factors). We used lmer function in
lme4 package for the LMM and the anova function in base R for the likelihood ratio tests. The results are
presented in the table below (Table S3). With the exception of time spent within 5 m, the effect of trial
period was not significant. Time spent within 5 m showed a slight but significant increase between the
first and second of the trial which is probably due to the fact that at the start of the trial, birds tend to
be far away from the speaker. The difference between early vs. late in time spent close to the speaker
therefore does not correspond to a switch from a mostly signaling to mostly aggressive behavior.
Table S3. Coefficients from the LMM models and χ2 values and associated p-values from the likelihood
ratio tests.
Variable
flights
time spent within 5m
closest approach
soft songs
wing waves
Coefficient
0.94
0.07
-0.67
0.03
-0.26
St. Error
1.29
0.03
0.65
0.11
0.16
t
0.73
2.56
-1.04
0.31
-1.56
χ2
0.52
6.31
1.08
0.09
2.44
p
0.47
0.01
0.30
0.76
0.12
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