Electronic Supplementary Material
Spontaneous female flash calls in an Asian firefly
Hideo Takatsu, Mihoko Minami, Kei-ichi Tainaka, and Jin Yoshimura
Statistical Inferences
1. Regression analysis of flash duration on temperature (Figure 2, Fig. S1)
In this section, F and T denote flash duration and temperature, respectively. The
detailed statistics were shown in Table S1 for all the regression models.
For male (n = 298), the ordinary linear regression model was used for the
relationship of F on T. The linear regression equation was: F = 0.190 – 0.0072T. The
standard deviation of residuals was 0.025 and the adjusted R-square was 0.408. For
female (n =225), the weighted linear regression model was used because the residual
variance seemed to vary with temperature. We used the inverse of the squared estimated
standard deviation (i.e. the estimated variance for given temperatures) as weights (Fig.
S1). The linear regression equation for female was given by F = 0.753 – 0.0252T. The
standard deviation of residuals was 0.1533 and the adjusted R-square was 0.337.
2. Discrimination between male and female by the logistic regression model
(Figure 2)
For the discrimination between male and female, we used the logistic regression model.
We employed the model with flash duration and temperature as explanatory variables,
because the AIC (Akaike’s information criteria) value was 21.2 with flash duration and
temperature, while it was 74.5 with flash duration only. The estimated linear predictor
was log (p/ (1-p)) = -39.05 + 1.38T + 103.15F, where p denotes the probability of being
female. Equating the predictor to zero (i.e. p = 0.5) gives the discriminant boundary.
The deviance explained by the model was 90.13%. The leave-one-out cross validation
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estimate for the prediction error was 0.574% (3 out of 523). The densities of linear
predictor scores (Inserted graph) were estimated with the kernel density estimation
method with Gaussian kernel using function “density” in the statistical software R.
3. Discrimination between the success and the failure of the male attraction to the
electronic firefly (Figure 3)
To find the lower discriminant boundary of successful male attraction, we excluded the
data in the area {F  -0.066T + 1.91}, because we considered that the failures in this
area were not due to confusion with the male flashes. We employed the logistic
regression model with flash duration only as explanatory variables, because the AIC
value was 104.5 with flash duration only, while it was 105.7 with flash duration and
temperature. The estimated linear predictor was log (p/ (1-p)) = -4.77 + 29.79F, where p
denotes the probability of successful male attraction. Equating the predictor to zero (i.e.
p = 0.5) gives the lower discriminant boundary.
To find the upper discriminant boundary, we excluded the data in the area {F  0.2},
because we considered that the failures in this area were due to confusion with the male
flashes. We employed the logistic regression model with flash duration and temperature
as explanatory variables, because the AIC value was 86.9 with flash duration and
temperature, while it was 110.4 with flash duration only. The estimated linear predictor
was log (p/ (1-p)) = 14.91 – 0.594T – 4.047F. Equating the predictor to zero (i.e. p =
0.5) gives the upper discriminant boundary of the successful male attraction.
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Table S1. Some statistical values for the distributions of flash duration along ambient
temperatures in L. parvula. For entries, Target, EC and SE denote a target factor, the
estimated coefficients and the standard errors, respectively. Ob-M (Ob-F) denotes the
(weighted) linear regression model for the observed males (females) in Fig.2. M-F-B
denotes the logistic regression model for the discrimination between sexes in Fig.2. LS-B (U-S-B) denotes the logistic regression model for the lower (upper) discrimination
boundary for successful male attractions in Fig.3. For targets, Ic, Tm and FD denote the
intercept, temperature and flash duration, respectively.
Model
Target
EC
SE
t-value
Ob-M
Ic
0.190
0.008
23.63
<2e-16
Tm
-0.0072
0.0005
-14.35
<2e-16
Ic
0.753
0.041
18.29
<2e-16
Tm
-0.0252
0.0024
-10.71
<2e-16
Ic
-39.05
12.50
-3.124
0.001785
Tm
1.38
0.51
2.690
0.007152
FD
103.15
28.50
3.619
0.000295
Ic
-4.77
0.88
-5.449
5.6e-08
FD
29.79
5.59
5.326
1.01e-07
Ic
14.91
3.05
4.885
1.03e-06
Tm
-0.594
0.143
-4.169
3.06e-05
FD
-4.047
0.795
-5.091
3.56e-07
Ob-F
M-F-B
L-S-B
U-S-B
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z-value
Pr(>|t|)
0.25
0.15
0.05
moving standard deviation
12
14
16
18
20
temperature
Fig. S1 The estimated residual variances for the weighted linear regression
model. The circles are the 41-term moving standard deviations of flash duration
with respect to temperature. The solid line is the estimated standard deviation of
flash duration for given temperatures (max (0.83 – 0.048T, 0.083)).
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