Index

Handout for the Department Meeting 19920428

Repeating pairs of surnames and population genetic structure

¶ Relethford, J.H. (1992) Analysis of Marital Structure in Massachusetts Using Repeating Pairs of Surnames. Human Biology, 64(1): 25-33.

References

1. Lasker, G.W. and Kaplan, B.A. (1985) Surnames and Genetic Structure: Repetition of the same Pairs of Names of Married Couples, a Measure of Subdivision of the Population. Human Biology, 57(3): 431-440.
2. Relethford, J.H. (1988) Estimation of Kinship and Genetic Distance from Surnames. Human Biology, 60(3): 475-492.
3. Crow, J.F. (1980) The Estimation of Inbreeding from Isonymy. Human Biology, 52(1): 1-14.
4. Nei, M. (1987) Molecular Evolutionary Genetics. pp.130-144, Columbia University Press, New York.
5. Bhatia, K. and Wilson, S.R. (1981) The Application of Gene Diversity Analyses to Surname Diversity Data. Human Biology, 88: 121-133.

Hardy-Weinberg principle in population genetics (see 4.)

When X₁₁, X₁₂, X₂₂ are genotype frequencies, if the size of the population is sufficiently large, and if mating is completely random and endogamous,
X₁₁=x₁², X₁₂=2x₁x₂, X₂₂=x₂² (1)
where x₁ and x₂ are gene frequencies of the allele A₁ and the allele A₂, respectively.

In the small population, many factors modify genotype frequencies from this principle. With the fixation index (F),
X₁₁=(1-F)x₁²+Fx₁, X₁₂=2(1-F)x₁x₂, X₂₂=(1-F)x₂²+Fx₂ (2)

If inbreeding is only a factor which affect genotype frequencies, the fixation index is same as inbreeding coefficient. In the case that the population is composed of several subdivision,
F=ð² / E(x)(1-E(x))
where ð means standard deviation and E(x) means the average of x.

Equations used in Relethford (1992)

RP= SUM_iSUM_j S_ij(S_ij-1) / N(N-1) (1)
where S_ij is the number of marriages with groom's name i and bride's name j and N is the total number of marriages (=SUM_iSUM_j S_ij).

RP_r=(SUM_i S_i²-N)(SUM_j S_j²-N) / N²(N-1)² (2)

z=(RP-RP_r) / SE(RP_r) (3)