Abstract

Introduction
It was Crow and Mange in 1965 ' who first indicated how the degree of inbreeding could be calculated from the frequency of marriage between persons of the same name (isonymy), although others, e.g. Darwin (1875) 2 and Kamizaki (1954) 3 had earlier recognized the parallelism between pater¬ nally inherited genetic characters and names, and many have applied the method since 4,5.6,7,8 . An advantage in the use of surnames is that, by a rather simple method, one can distinguish random and nonrandom components of inbreeding in the population. This paper is concerned with the estimate of random isonymy in Japan. Preliminary results have been communicated elsewhere 9 .
Materials
Attempts to develop computer software for processing Chinese char¬ acters (kanji) in Japan required a survey of name lists. Tanaka 10.11.12 published statistical summaries of two insurance files, file A with 715,815 persons and file B with 2,647,911 individuals, sampled from all over Japan and compiled from names coded in Japanese characters (katakana). From the most frequent sixty names, random isonyms in Japan were calculated as 0.00184 for file A and 0.00212 for file B 9 . Not only is the complete name list of file A now avail¬ able, but also an additional file C has been provided to us by Mr. Y. Tanaka 13 . File C consists of 1,077,322 customers of department stores in Kanto district, in which Tokyo is located, and is compiled from names written in Chinese characters, the ordinary expression of Japanese surnames. A difficulty in counting the total number of Japanese surnames is that Chinese symbols may be read phonetically several ways, and Japanese letters can be translated into several Chinese characters. Ordinary Japanese names contain two or three Chinese letters 9 . Comparison of two different systems of compilation for
idom Isonymy (I) and Surname Distribution in Japa
76
names allowed the examination of possible biases in the calculation of random isonymy in Japan. In addition four name lists, taken from Takiguchi 14 , were examined, as also in the later part of the analysis were three previously pub¬ lished name lists 7,8.
Results
Random isonymy. Calculated random isonyms (i.e. the probability that two names chosen at random are the same) are 0.00238 for file A and 0.00222 for file C. An estimate (0.00184) from the most frequent sixty names from file A, which accounted for only 28 per cent of all persons, was 77 per cent of the total random isonymy calculated from the total list. This led us to study the relation between the proportion of random isonymy and that of the total population. Names were ranked in decreasing frequency, i.e. by the number of persons who have each name. From the known random isonymy of the total population (I) which could be examined, the number of surnames (K) that accounted for a given proportion (p) of the random isonymy of the total population and the sum of the persons (N) they represent were calculated. This was done for the populations represented in file A and file C as well as for four surname rankings of Takiguchi 14 (Taki A, Taki B, Taki C and Taki D). The results are given in Table 1. Because of the small sample sizes in Taki C and Taki D, tabulated numbers, N and K, do not always exactly correspond to the p-values of random isonymy, but are given the nearest numbers. The large files A and C show that ten per cent of persons with the most frequent names (approximately) account for 50 per cent of random isonymy (I); 26 per cent of persons with ca 50 names account for 80 per cent; and 50 per cent with ca 140 names for about 95 per cent. In this they are supported by the Taki A and Taki B lists though less closely at the higher percentages, while the two small Taki lists vary quite markedly. Figures 1 and 2 depict for files A and C, respectively, the cumulative proportion of total random isonymy and the cumulative frequency of persons against the number of surnames ranked in decreasing order. The agreement between the two files is remarkable. Surname distribution. Looking at the ranked name lists in the reverse direction, the least frequent surnames ranking up to m。 = 499, yielded the relation: for l < m < m。 log 10 k = a — b(log 10 m) (1) where k is the number of different names and m indicates the number of persons for a particular surname. For the remaining surnames, which are most frequent names and each occurs in many individuals, obviously k = 1 or log10k = 0. for m。＜ m (2) Figures 3 and 4 show the number of surnames by the number of persons carrying them, plotted on log-log scales for file A and file C respectively. There appear to be similar patterns shown by plots of the surname distri­ butions in Takiguchi's four lists, as well as those from two small cities, Ohdate, and Mine 7 , and from a farm village, Uto 8 , with two straight lines meeting each other at an obtuse angle. The last three sets of data include surname distri- butions of three antecedent generations, parental (P), grandparental (GP) and great-grandparental (GGP) generations. All materials are consistent with the relations (1) and (2) although populations are different from each other in the threshold 'm 。'. Regression analysis showed the slope parameters 'b' to be between 1.5-1.7 in all files except in two of Takiguchi's lists (Taki C and D) and those from Mine city, which yielded a slightly steeper slope (b = 2.0-2.4). Obvi¬ ously, the threshold 'm, ' is chosen somewhat arbitrarily by inspection of the graph, but nonetheless the consistency of the slope is remarkable (Table 2). Examination of three antecedent generations in the local surname lists indicated clearly that the name distributions have been very stable indeed during the last three generations, or probably since 1875.
Discussion
Random isonyms, 0.00238, 0.00222, 0.00177 and 0.00232, calculated from file A, file C, Taki A and Taki C, respectively, could be taken as repre- sentative of all Japan. The insurance file (file A) and the department store file (file C) might have contained individuals from the same family, but it is currently not possible to detect any bias this causes in calculating random isonymy. Yet, it is satisfying that the two files yielded very similar figures despite the fact that they were compiled in completely different ways. Taki A was from Who's Who in Medicine and Taki B was from Who's Who in Japan about forty years ago. Nonetheless, the four estimates from these different sources are remarkably consistent. Including an estimate from file B, pre¬ viously calculated from the first sixty highly ranked names 9, a simple average of these five estimates becomes 0.0022; this is taken as representing random isonymy in all Japan. That is, on average two random pairs per thousand throughout Japan share the same surname. Studies of file A and file C indicate that the first half of the population whose surnames are ranked in decreasing order by the number of persons with the same name is sufficient for the calculation of random isonymy for 95 per cent of the total random isonymy, and could be calculated from the first 48.28 and 48.83 per cent of persons (Table 1). This estimate comes from the first phase of what appears to be an historic distribution, with a point of rotation at a threshold. The second phase, relating to the least frequent names, may be used for the study of human migration or dynamics of surname transmission in populations. In files A and C the proportions of population from the least frequent surnames to the threshold were respectively 49.65 and 42.82 per cent. The extreme of the two phases is seen in Takiguchi's lists as well as in three local lists. The threshold m o , however, may disappear when the sample is small, as occurred in the surname distribution from the parental generation in Mine city (Tables 2 and 3). This biphasic distribution of Japanese surnames might be the reflection of naming processes at the time of the Meiji Restoration. In 1875 the govern¬ ment proclaimed that a name was mandatory for everyone. Before that time, only the governing classes could use names officially. To meet the new requirements, there were two main ways to provide a name: the creation of a unique surname, or the resurrection of the name of an ancient ancestor. The former would increase the number of different names and would act as a force of diversification, while the latter would tend in the opposite direction. Counterbalance of the two forces might have generated the relation (1) in the least frequent name distribution. The remainder, the most frequent names of persons, would be largely polyphyletic, each name having multiple origins at the time of the naming process. The differences in the slope parameter between most of the series (b = 1.5-1.7), and the three others (Taki C and Taki D and Mine city, b = 2.0-2.4) may perhaps be attributed to sample size 14 . However, this seems unlikely, for data from Ohdate and Uto showed b = 1.5-1.7 even though the sample sizes are much smaller than Taki C and Taki D. This disparity is probably due to either human movement or heterogeneity of the material. To Mine city, with its mining industry, many workers come and go and so contribute rare surnames to the name list. Taki C and Taki D are from directories of university alumni, in whose selection there may well be some bias by surname distri- bution from all Japan. The larger the value of b, the more unique names are.
a and b are regression coefficients in the equation (1). m o = threshold. N 1 = number of persons with least frequent names. K ' = number of names among N ' persons. I = Great-grandparental, II = Grandparental, III = Parental generation.
lumber of names. N = Number of persons. I = Random isonym
reat-grandparental, II = Grandparental, III = Parental generate
es are ranked in decreasing frequency.
82
A Trend in Frequency of Blood-Related Marriages in Japan15
p = proportion of blood related marriages Active immigration and emigration would increase the number of different surnames and, as a result, there would be more persons with unique surnames in the population. Therefore human movements at the local level might be one of the causes of steeper slopes. Human movement may also be assessed from the average number of names per individual, in those persons with the least frequent names; by K 1 /N 1 , where N 1 is the number of persons with the least frequent names and K 1 is the number of names among them. As shown in Table 2, this ratio seems to be a good indicator of human movements when comparisons were made between populations. The three rankings, file A, Taki A and Taki B, yielded 0.07m 0.09 and 0.08 respectively, might represent all Japan; the smaller value of 0.02 from file C is perhaps due to limitation of the area studied to the Kanto district. Mine city is known as a centre of active immigration, and Taki C and Taki D are similarly heterogenous, being direct- ories of university alumni. Three localities, Ohdate, Mine and Uto, as shown by the different generation lists, were stable, but movement seems to have increased in the latest generation, consistent with a recent trend of increasing human movement in Japan. Finally, calculated random isonymy, 0.0022, certainly does not neces¬ sarily reflect genetic inbreeding, but is to be regarded as a basic variable for studying the evolution of surnames in Japan since 1875. Secular decrease in the frequency of consanguineous marriages in Japan has occurred (Table 4), a trend already revealed by isonymy studies 7 , 8 ; however, those studies attri- buted the decreasing tendency to reduction in nonrandom inbreeding. There- fore, the comparison of isonyms at different times or localities would be of little use in attempts at genetic interpretation.
Acknowledgements
We are indebted to Mr. Yasuhito Tanaka who generously provided us with the complete listings of surnames, file A and file C. We also thank Mr. Kenjiro Fukuhisa and Mr. Sadao Shibata for assistance in running computer programmes on an ACOS-700S installed at the National Institute of Radio- logical Sciences. The expert secretarial assistance of Mrs. Hiroko Ito is also deeply appreciated.