Comparison of observed and expected levels of genetic diversity based on surname frequencies: An example from historical Massachusetts

The inverse of random inbreeding based on surname frequencies (1/Fr ) is an estimate of genetic diversity, and its expectation is a function of the number of migrants into a population. Observed and expected values of (1/Fr ) were compared to determine if observed diversity matches theoretical expectations under conditions of rapid demographic change using data from historical Massachusetts.Data on migration and surnames were taken from 6,038 marriage records from the eighteenth and nineteenth centuries from five towns in north-central Massachusetts. Data for each town were broken down into a number of time cohorts defined by year of marriage, giving 33 samples based on town and year of marriage. The number of migrants (M) and the inverse of the random component of inbreeding (1/Fr ) were derived for each sample based on surname frequencies.There was no significant difference between observed and expected values of 1/Fr in samples where there were 100 or more migrants. However, 1/Fr was significantly higher in samples where M < 100, which is possibly due to these samples not having reached equilibrium, resulting in higher than expected values of 1/Fr . Regression of residual values of 1/Fr (observed-expected) on the number of years since settlement supports this interpretation.The number of migrants affects the level of genetic diversity inferred from surname frequencies, and the relationship between observed and expected measures depends on the number of migrants and the proximity of a given sample to an equilibrium state.