The Distribution of Distance between Birthplaces of Mates

Abstract

The distribution of matrimonial distance is studied with special reference to population genetics theory. The model built is based on random diffusion of every person, who then stops his movement at the age of marriage. The time of stopping, or the age at marriage in the present model, fits satisfactorily a gamma distribution. The expected probability of matrimonial distance, based on random diffusion with a gamma stopping time of movement, is examined for three local populations from small cities of Japan. It is found that the fit is consistently with the K-distribution. For fixed age, the distribution of matrimonial distance is normal, except for very short distances. In the present materials, the correlation coefficient between the distance and the age of marriage is not significantly different from zero. Thus, the variation of individual mobility, measured by the diffusion coefficient, overrides the variance of age at marriage. If the age effect on the distribution of matrimonial distance is first order, this correlation would be expected to be strong. It is also found that immigration is very active in Ohdate and Mine as well, so that it would be very difficult to maintain a characteristically genetic specificity in these small groups from the other parts of Japan. The estimated standard deviations of migration in local groups are respectively 5.59 km, 1.54 km and 6.54 km in Ohdate, Misima and Mine