Examining population structure through the use of surname matrices: methodology for visualizing nonrandom mating.

The analysis of nonrandom mating using the frequency of marital isonymy indirectly measures the degree of population structure. However, population structure is the result of all matings in a population. Difficulties with large surname matrices have resulted in data being summarized into a single statistic or collapsed into brief tables, with considerable loss of information. By using sophisticated computer graphing procedures and displays, it is possible to directly analyze the mating structure of a community. If P is a vector of proportions for each male surname i (i = 1, 2, 3, ..., n), Q a similar vector of female surnames j(j = 1, 2, 3, ...,m), then the expected frequency matrix E of each possible mating is P x Q. The difference D between the observed frequency matrix O and the expected matrix is O-E. The D matrix is graphed with the x axis containing the male surnames, the y axis the female surnames, and the z axis the difference values dij. Negative values represent negative nonrandom mating and positive values positive nonrandom mating. From 5417 marriages (1840-1963) in the Midlands of Tasmania, those between spouses having 1 of 194 core names were extracted. We analyze these marriages utilizing the new technique and examine the surface of the graph and statistical analysis of its finer structure. Among the results was the demonstration of frequency-dependent selection of surnames. This finding has significant implications for microevolution of human populations, as surnames have existed for possibly 700 years.