Journal of Insect Biotechnology and Sericology 82, 00-00 (2013)

Shape of Silkworm cocoon changes with size in some races
Takahiko Nishioka1＊, Keisuke Mase2, Zenta Kajiura3, Mika Morishima1, Takashi Kudoh4
21
Department of Textile System Engineering, Faculty of Textile Science & Technology, Shinshu University, 3-15-1, Tokida, Ueda 386-8567, Japan,Nihon University, College of Humanities and Sciences Department of General Studies, 3-25-40, Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan,
3
Department of Applied Biology, Faculty of Textile Science & Technology, Shinshu University, 3-15-1, Tokida, Ueda 386-8567, Japan,
Hitachi Plant Technologies, Ltd. 603, Kandatsu-machi, Tsuchiura Ibaraki, 300-0013, Japan(Received ★★★★★, ★★★★; Accepted ★★★★★, ★★★★)

In general, the basic shape of Silkworm (Bombyx mori) cocoons is thought to depend upon race and not thesize of the cocoon. That is, it is thought that within species, changes in the size of cocoons are proportional. The
ratio of cocoon length to width is commonly used to numerically express the shape of cocoons. In the presentstudy, we employed a Fourier coefficient in order to express the cocoon shape in detail. We found that in some
Chinese silkworm races, the basic shape of the cocoon changed with size. The shapes of the geographical silkworm races have been precisely reported by Enokijima et al. through the ratio of the length to the width of thecocoon.
Key words: cocoon shape, cocoon size, Fourier coefficient, regression analysis

INTRODUCTION
The author et al. been investigating whether changes inthe breeding environment of silkworms (Bombyx mori) affect the shape of the cocoons. The shape of cocoons does
not always conform to the basic cocoon shape that is associated with a given silkworm race. Enokijima et al.
(1985) described cocoon shapes for 268 geographicallyclassified races. The report included the length, width, volume and the ratio of the length to the width for cocoonsfrom each race. However, the report did not indicate why
the length-to-width ratio was significantly correlated tothe cocoon volume only for the Chinese race. We attempted to describe characteristics of the cocoon shape using
Fourier coefficients from measured images of cocoons.
When Fourier coefficients were used to describe the cocoon shape, it became apparent that the cocoon shapes ofmost silkworm races were distributed within a certain
range, with the exception of some Chinese races.
We attempted to express the reason for the wide rangeof cocoon shapes observed for some Chinese races using
the a0/2 and a2 Fourier coefficients.

We examined the shape of the cocoons spun by thesilkworm larvae and analyzed the ways in which the basic
shape of the cocoons varied with cocoon size using thecoefficients of a Fourier expansion. The basic shape of thecocoon was defined by a constant and two or three cosine
terms of the Fourier series, as previously reported (Nishiokaet al., 2001).
Because the Fourier series can contain an arbitrary
number of terms, the shape of cocoons can be represented
in more detail when the Fourier series is used than when
the ratio of the cocoon length to cocoon width is used.
To obtain the cocoon shape, we measured the length inmillimeters from the center to 128 points along the outer
contour of each cocoon (Fig. 1). These measurements
were plotted in a Cartesian coordinate system, as indicated by the wide line in Fig. 2. The thin line shown in Fig. 2is the cocoon shape calculated from the mean term a0/2

MATERIALS AND METHODS
1. Cocoon shape measurement
We reared silkworm larvae on mulberry leaves donatedby Laboratory of Agricultural Science, School of Textile
Science and Technology, Shinshu University. Larvae werekept at 25°C ± 2°C and cocooned in 5 cm3 cardboard boxes.
*To whom correspondence should be addressed.
Tel: +81-268-21-5381.
Email: tntecha@shinshu-u.ac.jp

Fig. 1.  Measurement method for Bombyx mori cocoons.
The distance from the center of the cocoon to 128 separatepoints along the cocoon contour was measured in millimeters.

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Nishioka et al.

Fig. 2.  The waves representing the shape of Bombyx moricocoons. The wide line indicates the measured cocoon shapewhile the thin line indicates the shape calculated from Fourier
coefficients a0/2, a2, a4, and a6. The mean circle refers to themean distance from the center of the cocoon.

and cosine terms a2, a4, and a6. In this figure, the alternating long-and-short dashed line indicates the average distance from the center to the contour of the cocoon (meancircle). Figure 3 shows the individual waves that compose
the cocoon shape. Of course, if all of the obtained coefficients were included in the calculation, the calculated
wave might completely correspond to the measured cocoon shape.
2. Analysis
As can be seen in figs 2 and 3, the a2 Fourier coefficient indicates the basic shape of the cocoon. That is, theshape of the cocoon is characterized mainly by coefficienta2. We previously reported that there was a high correlation between the cocoon volume and the a0/2 coefficient(Nishioka et al., 1998). Therefore, we examined the relationship between the a0/2 and a2 Fourier coefficients.
If the basic shape of the cocoon is similar, regardless ofcocoon size, then the length and width should remain proportional over a range of cocoon sizes. That is, each silkworm race would have an inherent ratio of cocoon length
to width. If this is true, the cocoon length-to-width ratio
would not be significantly correlated with the cocoon volume.
The elements used to describe the basic shape of cocoons are included in a Fourier series, as shown in thefollowing expression.
f (t) =a0263+ Σ (ak coskωt + bk sinkωt)
k=1(1)

If, for example, the size of Cocoon A were 80% of thesize of Cocoon B, but both had the same shape, multiplying each term on right hand side of the equation for Cocoon B by the constant 0.8 would provide the term of theequation for Cocoon A (1). Similarly, to obtain the terms
for a cocoon that is 120% the size of Cocoon B, eachterm in the expression for Cocoon B would be multipliedFig. 3.  The three significant waves and a constant term
used to describe the Bombyx mori cocoon shape. a0/2 is theaverage length (the mean circle) from the center to the contour of the cocoon and akcoskωt represents the k times cosine terms against the fundamental period.

by 1.2 (1). Thus, in cocoons that are of different sizes butof the same shape, the ratio of any two arbitrarily chosencoefficients that are included in expression (1) remains
constant. To examine whether the shape of cocoonschanged with size, we performed a regression analysis ofcoefficient a2 against coefficient a0/2. If the basic shape ofthe cocoon changes to similar figures by varying in size, arestricted regression line that passes through the origin
may be obtained. We used the following restricted regression model,
y = cx + εi(2)where c is the ratio of Fourier coefficient a2 against a0/2.
This variable also represents the slope of the regression
line. The estimate of coefficient c was obtained using thestandard least square method through the following formula:ĉ = Σ xi yii/Σixi2.

This regression model has no constant term and can beused to test the hypothesis that the regression line passes
through the origin. Although this model does not attainthe minimum variance assumed by mathematical statistics,
this coefficient can be compared to the coefficient obtained by usual regression.

RESULTS
1. Japanese silkworm cocoon
Figure 4 shows a plot of the a2 against the a0/2 for race
N01. Here, the coefficient a0/2 is a constant term of a
Fourier series that has been previously called the mean
circle of the cocoon. In this figure, the solid line showsShape of Silkworm cocoon

3Fig. 6. Regression lines of a2 against a0/2 for race N603.
Fig. 4. Regression lines of a2 against a0/2 for race N01.
Table 1. Intercepts obtained from general regression and its
upper and lower limits in the Japanese Bombyx mori cocoons
races
N01
N124
N137
N511
N512
N603
SAWA-J
TN26
TN38Fig. 5. Regression lines of a2 against a0/2 for race N511.

the usual linear regression line, and the broken line shows
the restricted regression line. These two lines have nearly
equal characteristics, indicating that the basic shape of cocoon did not vary with cocoon size. Figure 5 shows asimilar plot for race N511. This figure indicates that race
N511 had the same characteristics as race N01. Although
the restricted regression line of race N603 shown in Figure 6 had a different slope than the usual regression line,
the hypothesis that the regression line passes through theorigin was not rejected. Table 1 shows the characteristicsof nine races of the so-called Japanese silkworm cocoonsthat were used in this experiment, including intercepts of
the regression equations. Zero is included in the 95% confidence interval for the estimated intercept value of all
Japanese silkworm cocoons. Therefore, the hypothesis thatthe regression line passes through the origin could not berejected. In other words, the basic shapes of all Japanesesilkworm cocoons may be similar for all cocoon sizes.
2. Chinese silkworm cocoon
Figure 7 shows a plot of the a2 against a0/2 for race
C505. This plot is similar to those for Japanese races, andn142016
6
913
815
15

95% confidence intervals
intercepts
lower limits upper limits
0.5885−2.2429
3.4198−0.8221−1.8320
0.18790.7983−1.10352.70010.5451−5.5347
6.6250−0.5686−2.8074
1.6703−6.0836−12.4501
0.28303.3977−0.2737
7.0691−0.5981−2.6150
1.41890.4775−5.1192
6.0741indicates that the cocoon shape did not vary with cocoon
size. Figure 8 shows a similar plot for race C514. In thisfigure, the regression line is different from those of theJapanese races. Similarly, Fig. 9 indicates that the regression lines for C108 (New) share the same characteristics
as those for race C514. This means that, unlike the cocoons of Japanese races, the cocoon shapes of these otherraces varied with size. The intercepts of the regressions
for Chinese silkworm races can be found in Table 2. Zero
was not included in the 95% confidence interval for theintercept of regression lines for races C108 and C514.
That is, the hypothesis that the regression line passes
through the origin was rejected. The measured cocoon
shapes of C514 and N01 are provided in Fig. 10 for comparison. This figure indicates that the size of race C514
cocoons depends primarily on their width (Fig. 10a).
Thus, the basic shape of cocoons in this race changed
with cocoon size because cocoon size variation was mainly due to cocoon width. The basic shape of race N01 cocoons (Fig. 10b) did not change with cocoon size because
the ratio of the cocoon’s length to width was similar for
all cocoon sizes. A significant regression was not found,though an analogous characteristic of races C514 andC108 appears in C149. Some Chinese silkworm cocoons
had large positive correlation coefficients, while others

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Nishioka et al.

Table 2. Intercepts obtained from general regression and its
upper and lower limits in the Chinese Bombyx mori cocoons
races
C108
C149C505
C512
C513
C514
PCG

n
14
14
9
7
7
11
12

95% confidence intervals
intercepts
lower limits upper limits
5.56091.68329.4386
4.1462−0.4766
8.7691−1.2055−2.7372
0.32611.2170−2.1915
4.6255−3.1635−8.95212.62519.6701
6.064313.2760
1.5872−4.0278
7.2022

Fig. 7. Regression lines of a2 against a0/2 for race C505.

Fig. 10.  Example of changes in the basic Bombyx mori cocoon shape with cocoon size.
(a) Measured cocoon shapes for silkworm race C514
(b) Measured cocoon shapes for silkworm race N01

Fig. 8. Regression lines of a2 against a0/2 for race C514.

Fig. 11.  Regression lines of a2 against a0/2 for race PCG ×N124.

Fig. 9. Regression lines of a2 against a0/2 for race C108.

had large negative correlation coefficients. Positive correlation coefficients imply that the slope of the regression ispositive, and cocoon shapes did not vary with size, as theJapanese silkworm cocoons. Negative correlation coefficients imply that the slope of the regression is negative,
and the basic cocoon shape varied with size. It should be
noted that not all Chinese races have cocoons that varywith size. as C514 and C108 do.

3. Hybrid-type cocoon
Figure 11 shows a plot of the a2 against a0/2 for the result of a cross between race PCG and N124 (PCG × N124).
The regression line for this race indicates that the basic
shape of PCG × N124 did not vary with size. Figure 12
shows a similar plot for race N510 × C512. In this case,the basic shape of the cocoon did not vary with size, either. The intercepts of regression for hybridized races areshown in Table 3. The correlation between coefficient a0/2
and a2 for these races, with the exception of races PCG ×
N124 and N510 × C512, was poor. In general, most of theShape of Silkworm cocoon

5

described a similar correlation to those in the present
study between the ratio of the cocoon’s length to width
and the cocoon’s volume for each race. However, nothing
had been mentioned about it at that time.
We have been studying changes in the basic shapes ofcocoons that are associated with a variation in cocoon
size within races in order to evaluate the silkworm-breeding environment. We conclude that this phenomenon isevidence that cocoons are generated by living things rather than by machines.

ACKNOWLEDGMENTS
Fig. 12.  Regression lines of a2 against a0/2 for race N510 ×C512.
Table 3. Intercepts obtained from general regression and its
upper and lower limits in the hybridized-race Bombyx moricocoons
racesAKEBONON137C146
HONOBONO
PCG × N124
N510 × C512
PNG × PCSGPNY × PCSY

n121110910101095% confidence intervals
intercept
lower limit
upper limit
2.1875−5.1315
9.50642.5808−1.3474
6.50892.1875−5.1315
9.50640.0748−2.27112.4207−0.8833−3.9223
2.15573.2491−1.59158.0896
3.69550.6971
6.6938hybrid cocoon shapes did not noticeably vary with size.

DISCUSSION
The basic shapes of the Japanese silkworm cocoons did
not change with cocoon size, as indicated by the length
and width coefficients, with the same ratio for various cocoon sizes. However, the basic shapes of some Chinesesilkworm cocoons (C108 and C514) change with size, according to the difference in the variation of the length andwidth of the cocoon.
It should be noted that not all of the Chinese races necessarily have an inherent basic cocoon shape. Enokijima

We would like to express our gratitude to Dr. T.
Yamamoto, the chief of the former National Institute ofAgrobiological Sciences Silk Technology Unit for his advice as to the handling and techniques for silkworm rearing. The silkworm strains used in this study were donatedby the National Institute of Agrobiological Sciences, andwe wish to express our gratitude. The National Biosource
Project (RR2002) and NIAAS Genebank supported therearing of silkworm larvae.
We would like to thank Editage for providing editorialassistance.

REFERENCES
Enokijima, M., Yamamoto, T., Shimiz, K. and Shimizu, F.
(1985) Racial specificity of several quantitative characters inthe silkworm stocks (3) Relationship between the cocoon
shape and some quantitative characters. Tech. Bull. Sericul.
Exp. Sta., 124, 35-45.
Nishioka, T., Satoh, H. and Liew, K. (1998) Numerical representation for cocoon shapes by principal component analysis
that uses Fourier coefficients. J. Sericult. Sci. Jpn., 67, 479484 (in Japanese with English summary)
Nishioka, T., Nakazawa, K. and Chow, K. (2001) Decision of
number of the order of Fourier series by Akaike Information
Criterion of basic shape of the cocoon J. Sericult. Sci. Jpn.,
70, 11-15 (in Japanese with English summary)
Nishioka, T. Mase, K. and Kajiura, Z. (2010) The dispersion of
the cocoon shape and its Mahalanobis’s generalized-distance
between races. Journal of Insect Biotechnology and Sericology., 79, 9-13.