Materials, methods, and analysis
The data analyzed here were obtained from
Mitsuishi’s data (3–6) published
in Zenkoku Hotaru Kenkyukai-shi (Proceedings of the Japan Association
for Fireflies Research). These articles are freely available on the
website of the Japan Association for Fireflies Research
(http://zenhoken-std.sakura.ne.jp/). Mitsuishi (3–6) recorded his
measurement data as the mean values of body length (length from anterior
margin of pronotum to posterior margin of elytra), body width (width
across both elytra covering mesonotum) and pronotum width at 41 sites in
Nagano Prefecture.
In the present study, cluster analysis was first performed to classify
the measurement data into two groups using Ward’s method with Euclidean
distance. Then, allometric equations were applied to the two groups
using standardized major axis
regression with the smatr package in R version 4.2.2 (14). The data were
log10 transformed and thereby the
log-log relationship between
pronotum width (x ) and
body length (y ), the log10-transformed allometric equation was
expressed as:
\begin{equation}
\operatorname{}\mathbf{y}\mathbf{=}\operatorname{}{\mathbf{a+b}\operatorname{}\mathbf{x}}\nonumber \\
\end{equation}where a and b are constants. The constant b is the
slope of the line, also known as the allometric coefficient.
This allometric equation was fitted to each of the two groups identified
by the cluster analysis. As shown in Figure 1, the two allometric lines
representing the two groups did not differ significantly in slope
(χ 2 = 0.077, df = 1, p = 0.78), but did differ
significantly in elevation (χ 2 = 229.6, df = 1, p< 0.001). The two allometric lines were found to be parallel
and share a common slope of 0.34.