Beom Jun Kim et al.: "Blood-type distribution", Physica, A 373, 533–540, 2007.遺伝子形AとBの比率により民族間距離を算出し、2次元にプロットしたのがこれ:
Abstract
We statistically verify the Hardy–Weinberg principle in genetics by investigating the independence of ABO-blood types of married couples. The allelic frequencies derived from the phenotypic frequencies in ethnic groups via the Hardy–Weinberg principle are used to define a genetic distance (called the blood distance in this work) between two groups. The blood distances are compared with the geographic distances, and then used to construct a network of ethnic groups. We also investigate the relationship between the ABO blood types and the human personalities, gauged by the Myers-Briggs-type indicator (MBTI) psychological test. The statistical χ2-test reveals the independence between the blood types and MBTI results with an exception of type B males. A psychological implication is discussed.
The blood distance is defined as dbloodij=(血液型の比率だけで定められた距離だが、かなり、それらしく見えている。
(pi-pj)2+(qi-qj)2 )1/2, where pi and qi are the frequencies of the allele IA and IB in the i-th group.[Enlarge]
[4] The phenotypic frequencies of blood types are from http://www.bloodbook.com/world-abo.html
アノマリーとしては、図右側の欧州な領域のネットワークに、Eskimos(Alaska)とJapaneseが入り込んでいること。逆にアジアンな左側の領域のネットワークにHindus(Bombay)が入り込んでいる。また、SardiniansがUSA(Black)の彼方につながっている。Hindus(Bombay)はAryanとDravidianごちゃまぜかもしれないが、ソースには記載がない。
ゲノムの比較が可能な時代にあって、この研究が民族間距離の推定に活躍するとは思えない。しかし、それらしい民族間距離が推定されたことが、配偶者選択に血液型が中立的であることを示唆していることは、ひとつの成果かもしれない。
なお、BJ Kim[2007]は、配偶者選択に血液型が影響しないことの確認を次のように行っている:
2. Blood types of couples
In order to check the validity of the assumption of the random mating that the choice of partner has nothing to do with the blood type the partner has, we conducted a survey to which 292 married couples answered (see Table 1). For example, the number 26 in the cell for the "female B" and "male A" is the number of couples with the female of the phenotype B and the male A. The numbers in parentheses are obtained from the Hardy–Weinberg principle of the random mating. For instance, the expected number for (male A, female B) is given by (79/292) × (81/292) ×292 〜21.9. The use of the so-called χ2-test in statistics is a standard way to check the validity of the null hypothesis of the independence of two categories, male and female blood types in this work. The test is based on the χ2 distribution of the square of random variables following the normal distribution of mean zero and unit variance [2]. From Table 1, we get
X2 = Σi=116 (Oi - Ei)2/Ei = 10.7
where i = 1, 2, ..., 16 is the index for each cell in Table 1, Oi is the observed frequency and Ei is the expected frequency from the Hardy–Weinberg hypothesis. Since the sum of frequencies for male A, male B, male AB, and male O is the total number of males (the same holds for female frequencies), only three among four frequencies are independent, which leads to the number of degrees of freedom ν= 3 × 3 = 9. For the χ2 distribution with nine degrees of freedom, the probability that X2 has a larger value than 16.92 is 0.05.1 In other words, one can reject the null hypothesis of the random mating with the error threshold p = 0.05 (called the p-value in χ2-test) when X2=16.92. Consequently, much smaller value 10.7 than 16.92 makes us conclude that there is no statistically significant evidence to reject the null hypothesis. Roughly speaking, the observed frequencies in Table 1 are compatible with the Hardy–Weinberg hypothesis of random mating.
It is known that marriages are often assortative. For example, tall women feel comfortable with tall men, rich family tends to marry rich family, and so on. The above analysis not only provides an empirical justification of the Hardy–Weinberg hypothesis in terms of blood types, but also indicates indirectly that human characteristics which are playing some roles in choosing partners are not strongly related with bloodtypes. Let us imagine that a person with the blood-type A is taller than average. If this is true, then we expect more couples in the cell for (male A, female A) than the numbers expected from blood-type blind marriages. However, the above analysis indicates that there is no evidence that male A prefers female A.
Table 1 Blood phenotypes of 292 married couples
Female A Female B Female AB Female O Total
Male A 27 (25.7) 26 (21.9) 9 ( 7.3) 17 (24.1) 79
Male B 28 (28.6) 23 (24.4) 6 ( 8.1) 31 (26.8) 88
Male AB 9 (11.7) 10 (10.0) 1 ( 3.3) 16 (10.9) 36
Male O 31 (29.0) 22 (24.7) 11 ( 8.2) 25 (27.1) 89
Total 95 81 27 89 292
The numbers within the parentheses are the frequencies expected from the random mating hypothesis of Hardy–Weinberg. The X2 = 10.7 is obtained (see text) and thus we conclude that the observed frequencies do not have statistically significant deviations from the expected ones to reject the null hypothesis of the random mating. [p-value is 0.05 and the number of degrees of freedom ν = 9 (3 × 3) ].
タグ:Blood type
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