Surnames in Sardinia. II. Computation of migration matrices from surname distributions in different periods

A method is described for obtaining migration matrices from data on frequency distributions of transmissible traits in at least two different periods. In the present case, surname frequency distributions were used. In this way migration matrices describing rates of movement among nine areas of Sardinia were found for the period 1850-1970. Data were kinship matrices from surname distributions over two or three time periods. Population growth was included in the model under the assumption that expected family size in all areas was constant, or that outside estimates of the relative family sizes exist. Use of variable vs. constant growth rates did not drastically affect the estimated matrices. The matrices estimated for different time periods are similar. Estimates of net migration into the different areas were relatively insensitive to different methods of summarizing statistics. The elements of the matrices indicate strong effects on migration rates of distance between areas, and somewhat weaker effects of economic differences. The diagonal elements of the matrices show a high negative correlation with independent estimates of rates of immigration into the same areas.