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European Journal of Applied Sciences – Vol. 10, No. 4
Publication Date: August 25, 2022
DOI:10.14738/aivp.104.12722. Fujii, K. (2022). Examination of Universal Racial Differences in Biological Parameters: Analysis Based on Wavelet Interpolation
Model. European Journal of Applied Sciences, 10(4). 363-378.
Services for Science and Education – United Kingdom
Examination of Universal Racial Differences in Biological
Parameters: Analysis Based on Wavelet Interpolation Model
Katsunori Fujii
Graduate School of Business Administration and Computer
Science, Aichi Institute of Technology, Toyota-city, Japan
ABSTRACT
It is known that the human body is becoming larger, even when viewed historically.
Since around 1900 a remarkable trend has been seen globally. Genetically, this
phenomenon has been hypothesized to be a mini-evolutionary phenomenon
related to epigenetics, but that has not been clearly verified. However, human
growth patterns could be called a universal phenomenon. Even though bodies are
becoming larger, there have been no great changes in growth patterns. Eveleth and
Tanner [14] showed research trends on global physical growth, and provided
valuable findings. The physical growth data shown in that report were published in
the 1960s, and so their findings are from analysis of physical growth trends of more
than 50 years ago, from an aggregation of research performed with very traditional
analytical methods. Therefore, there are no detailed data from analyses of these
growth curves with objective methods. While they may be a little old as physical
growth data, it would seem foolish to neglect these global scale data without
subjecting them to an analysis using scientific methods. By applying the wavelet
interpolation model proposed by Fujii [10], we analyzed the global physical growth
data shown by Eveleth and Tanner [14], in particular identifying the age at MPV of
height as a biological parameter and examining the differences in biological
parameters among the human races (Caucasoid, Mongoloid, Negroid, and
Australoid).
Keywords: Biological parameters, age at MPV, race, economic conditions
INTRODUCTION
The adolescent growth spurt is a phenomenon that always occurs in the physical growth of
humans, and the pubertal peak in height and the age at that point are considered to be biological
parameters indicating level of maturity. The reason for this positioning as biological
parameters is that Tanner [1] showed a very high correlation between age at the emergence of
pubic hair and age at the pubertal peak for height. For girls, a correlation of about r = 0.7 was
also shown with age at menarche, which has been considered an indicator of maturity, and a
close relationship with maturity was noted. The pubertal peak in height has thus been shown
to be closely related with the level of maturity. However, in contrast to the level of maturity
shown with clear age of onset number called a peak, maturity shown with the age at the
emergence of pubic hair has been shown with numbers that vary considerably in observations,
and it is thought to be difficult to work with as an indicator. Meanwhile, menarche is a relatively
easy numerical value to identify, and its reliability does not seem to be that low. However, there
is a problem in that the mechanisms of menarche themselves are affected by external factors
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after birth, including nutrition and environment, so that it is difficult to adopt as an indicator.
Considering the investigations of Malina [2], Fujii [3], and Fujii [4] on delayed menarche in
female athletes, menarche in girls would seem to have little meaning in terms of level of
maturity. In addition to this, Malina [5] stated that no effects from external factors on the age
at the pubertal peak in height have been reported, and indicated its stability. Therefore, age at
the pubertal peak would seem to be a biological parameter that can be used as an indicator of
maturity.
Here, an exact number needs to be derived to use as an indicator. However, with the graphic
methods proposed by Tanner et al. [6] and Takaishi et al. [7], an objective and exact peak age
cannot be derived. Thus, we have attempted to describe growth curves for height with
numerical functions, and identify the maximum (peak) velocity by deriving those differentials
as velocity curves. Preecs and Baines [8] and Gasser et al. [9] applied compounds of logistic
functions and kernel functions in attempts to identify the age at the pubertal peak. Originally,
the age at the pubertal peak in height meant the age at which the maximum growth velocity
was shown during puberty, and it has long been used as the age of peak height velocity (PHV).
There is also the similarly named peak weight velocity (PWV) for weight growth. However, PHV
and PWV are derived from the maximum amount of annual growth, and are peaks with a span
of one year.
To overcome these drawbacks, Fujii [10] named the age at the pubertal peak in height the age
at maximum peak velocity (MPV). The name MPV is from the maximum growth velocity in
puberty derived from the growth velocity curve for physique with the wavelet interpolation
model. It is used similarly for physical attributes such as the MPV of height, MPV of weight, and
MPV of chest circumference. Of course, MPV age has been shown to be an exact value
guaranteed by a theoretical rationale, and it can be standardized as an indicator of maturity.
Fujii [11] analyzed the mid-growth spurt that emerges in early puberty in the height growth of
Japanese. Fujii [12] also examined the trends over time in the height growth of Japanese, and
showed that from before to after World War 2 the trend in age at MPV of height became
extremely delayed, and that the trend shifted to a younger age together with the trend for high
economic growth. That is, he verified a height growth acceleration phenomenon. He also
examined the trends over time in height growth in South Korea [13], and showed that similar
to Japan the age at MPV of height shifted younger and continues in that direction even today.
Thus, there is a close relationship between economic conditions in a country and height growth,
and with conditions of economic development ethnic differences are seen in the phase of
physical growth even among the same Mongoloid/Asian races.
Based on this background, the research trends in global physical growth shown by Eveleth and
Tanner [14] provide important findings. However, the height growth data shown there were
published in the 1960s and the findings are from an analysis of trends in physical growth at
that time. Many of those studies were performed with very traditional analytical methods,
which means that the growth curves were not analyzed with objective methods. Thus, while
they may be a little old as physical growth data, it would seem foolish to neglect these global
data without subjecting them to an analysis using scientific methods.
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365
Fujii, K. (2022). Examination of Universal Racial Differences in Biological Parameters: Analysis Based on Wavelet Interpolation Model. European
Journal of Applied Sciences, 10(4). 363-378.
URL: http://dx.doi.org/10.14738/aivp.104.12722
Applying the wavelet interpolation model proposed by Fujii [10], the global physical growth
data shown by Eveleth and Tanner [14] were analyzed, the age at MPV of height was identified
as a biological parameter, and the differences between the four races (Caucasoid, Mongoloid,
Negroid, and Australoid) were analyzed. Differences due to ethnic and regional environmental
factors were then examined on a global scale. In particular, while the relationship between
biological parameters and economic conditions makes it possible to determine that
relationship from the trends over time in a single country, in this study it is difficult to extract
only the relationship between economic conditions and biological parameters between many
countries. Consequently, by analyzing the behavior of cross-sectional physical growth curves
with a fixed time axis of the 1960s, we clarify physical growth phenomena with a focus on ethnic
and regional environmental differences.
METHODS
Subjects
Data for males and females aged 1 to 18 years old in countries around the world, cited from
figures and tables in the Appendices shown in the book “Worldwide variation in human growth”
by Eveleth and Tanner [14], were used. The growth data shown in that book were measured in
the 1960s, and it should be noted that they were collected from numerous articles related to
growth research. The growth data used in this study are handled in four broad global regions
showing the features of racial differences. The breakdown of those countries is 14 countries in
the European region (Kingdom of Belgium, Republic of Bulgaria, Czechoslovakia, Republic of
Estonia, Republic of Finland, French Republic, Federal Republic of Germany, Kingdom of
Hungary, Italian Republic, Kingdom of the Netherlands, Kingdom of Norway, Swiss
Confederation, United Kingdom, Russian Federation), 7 countries in the African region
(Republic of Ghana, Republic of Liberia, United Republic of Tanzania, Republic of Senegal,
Republic of South Africa, Republic of Rwanda), 8 countries in the American region (Bermuda
Islands, Republic of Cuba, Republic of Guatemala, Republic of Haiti, Jamaica, Republic of Peru,
Republic of Suriname, United States of America), and 4 countries in the Asian region (Japan,
Taiwan, South Korea, Hong Kong).
Subjects
Cross-sectional growth data for height and weight from age 1 to 18 in the countries classified
in the four global regions were screened, and cross-sectional growth data for countries in the
four categorized regions were arranged and the distance values for height and weight at the
points of 6 and 18 years old were calculated. Then, racial and ethnic differences in each of the
four global regions were investigated. Next, the wavelet interpolation model (WIM) was applied
to the growth data for height and weight from 6 to 18 years old in the four global regions, and
the growth distance values and velocity curves were described. The age at maximum peak
velocity (MPV) and the MPV were identified from the described velocity curves. The derived
ages at MPV of height and weight were investigated between the four categorized regions, and
racial and ethnic differences were investigated from the perspective of a biological parameter
(age at MPV of height).
Wavelet interpolation model
The wavelet interpolation method (WIM) is a method in which data points are interpolated
with a wavelet function to approximately describe a growth curve from given growth data.
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European Journal of Applied Sciences (EJAS) Vol. 10, Issue 4, August-2022
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Growth distance value curves are then drawn, the drawn growth distance value curves are
differentiated, growth velocity value curves are derived. Growth distance values at times such
as the pubertal peak or the age at menarche and the age at menarche can then be investigated.
The effectiveness of the wavelet interpolation method is shown in the sensitive reading of local
events and a very high approximation accuracy. Details on the theoretical background and
evidence for its validity are omitted here as they have been described in previous reports by
Fujii [13, 15, 16, 17]. The wavelet interpolation model is applied to the growth distance values
of height and weight of boy s and girls aged 6 to 18 years in countries around the world. Then,
age at MPV (Maximum Peak Velocity) is identified from the velocity curve derived from
differentiating the growth distance values of height and weight. This age at MPV is the age at
maximum peak velocity during puberty (peak age of puberty) and has a meaning as a biological
parameter. Biological parameters are described in detail by Fujii [13].
Example of application of the wavelet interpolation model
Figure 1 shows graphs of the wavelet interpolation model applied to height growth in the
United Kingdom in the European region and Japan in the Asian region. The black squares are
the growth distance curve and the black circles are the velocity curve. The peak shown in the
velocity curve is the age at MPV, and judging from the age at MPV of height in the graphs for the
United Kingdom and Japan, it is seen that the age at MPV of height is later in the United Kingdom.
From this analysis, it is understood with regard to racial differences that Mongoloids, which are
Asian races, have lower heights and earlier maturation than Caucasoid races. The wavelet
interpolation model is applied to height and weight growth in countries of the four categorized
global regions for this type of analysis.
Figure 1-1. Height growth distance and velocity curve in United Kingdom described by the
wavelet interpolation model
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Fujii, K. (2022). Examination of Universal Racial Differences in Biological Parameters: Analysis Based on Wavelet Interpolation Model. European
Journal of Applied Sciences, 10(4). 363-378.
URL: http://dx.doi.org/10.14738/aivp.104.12722
Figure 1-2. Height growth distance and velocity curve in Japan described by the wavelet
interpolation model
RESULTS
Height and weight values at the age of 6 and 18, and the amount of increase in growth
between those ages
Tables 1–4 show the height and weight values at age 6 and age 18 in world countries, and the
amount of increase in height and weight from age 6 to age 18. First, the height value at age 6
and the height value at age 18 are both shown to be the tallest in the European region among
the four world regions. The amount of increase in growth was shown to be greater in countries
that have taller heights at age 18. The greatest increase in the European region was 62.1 cm in
Moscow, Russia (USSR). The countries showing the largest growth increases were the same for
boys and girls. There were many countries in the European region, and when mean height at
age 18 was calculated it was 175 cm for boys and 163 cm for girls. Based on the standard
deviation, the tallest places for boys were judged to be the Netherlands, Finland, Norway, and
Moscow, Russia (USSR). The tallest countries for girls were the Netherlands, Finland, Norway,
and Switzerland. In the African region, the height value and weight value were both lower than
in the European region, and a large difference was seen. In the African region, however, there
was large variation between countries and comparison was difficult.
In the Asian region, South Korea had the largest increase and Japan had the largest amount of
growth after Hong Kong. Adult values for height were the highest in Japan and low in South
Korea, but the difference was not large. In the American region, height was 175 cm for boys and
163 cm for girls in the USA in North America, which was the average in the European region,
but there was much variation in the Central and South American region. Height was short in
countries such as Peru, Guatemala, and Suriname, and tall in countries such as Bermuda, Haiti,
and Kingston, Jamaica. The height difference between these two extremes may be said to be the
difference between people of Asian descent and indigenous people (Peru, Guatemala,
Suriname) and African Negroids (Bermuda, Haiti, Jamaica).