~) denote the probability that the surnames of two males, drawn without replacement from generation t, are identical by descent from generation T. The conditional expectations of /(1) and Q (I), given male surname frequencies of some ancestral generation T, are (A.I) because the probability that two distinct males have the same name is the sum of the probabilities that (1) their names are identical by descent from generation T and (2) they are descended from distinct males in generation T with the same surname. Equation (A. 1) can be rewritten as (A. 2) Here we encounter a problem. Without knowledge of Q(7), we cannot relate Q (I) to the probability of identity by descent. In the absence of data from generation T, we can proceed only by making some assumption about the value of Q(T). The greatest simplicity is achieved if Q(7) is assumed to equal O. Note that, because Q(7) is the probability that two distinct random males in generation T have the same surname, it equals o if and only if each male in generation T has a unique surname. Under this rather strong assumption, (A. 3) Doubts about Isonymy / 667 This result (for surnames) can be related to ¢~), the inbreeding coefficient (for autosomal genes), through two well-known formulas (Hartl 1980). If t - 7 «: Me, then *(t) ~ t - 7 d A-,(t) ~ t - 7 (A.4) 7 ~ Me an '1'7 ~ 2Ne ' where Me, the effective number of males, is the reciprocal of the probability that two males have the same father and Ne is the effective population size. These approximations are discussed in detail by Crow (1980). If t - 7 «: Me and Me = Ne12, then (A.5) Therefore, to the extent that these assumptions are justified, QI4 (or 1/4) can be interpreted as an estimate of the inbreeding coefficient relative to generation 7. This is the formula proposed by Crow and Mange (1965). This shows that the assumptions are sufficient to justify Crow and Mange's result, but are they also necessary? Note that, if some males in generation 7 had the same surname, then Q(7) > 0, Eq. (A.2) does not reduce to Eq. (A.3), and the formula of Crow and Mange does not hold. This proves the necessity of the strong monophyletic assumption. The formula of Crow and Mange is valid only if in some ancestral founding stock all males had different surnames. Acknowledgments I thank Jim Crow and Lynn Jorde for comments. The work was supported in part by the National Institutes of Health under grant MGN 1 R29 GM39593-01. Received 5 July 1990; revision received 8 January 1991. Literature Cited Crow, J.F. 1980. The estimation of inbreeding from isonymy. Hum. Bioi. 52:1-14. Crow, J.F. 1983. Discussion of \"Surnames as markers of inbreeding and migration.\" Hum. Bioi. 55:383-397. Crow, J.F., and A.P. Mange. 1965. Measurement of inbreeding from the frequency of marriages between persons of the same surname. Eugen. Q. 12:199-203. Fix, A. 1978. The role of kin-structured migration in genetic microdifferentiation. Ann. Hum. Genet. 41 :329-339. Hartl, D. 1980. Principles of Population Genetics. Sunderland, Mass.: Sinauer Associates. Holgate, P. 1971. Drift in the random component of isonymy. Biometrics 21 :448-451. Jacquard, A. 1975. Inbreeding: One word, several meanings. Thear. Popul. Bioi. 7:338-363. Jorde, L.B. 1989. Inbreeding in the Utah Mormons: An evaluation of estimates based on pedigrees, isonymy, and migration matrices. Ann. Hum. Genet. 53:339-355. 668/ ROGERS Lasker, G.W. 1985. Surnames and Genetic Structure. New York: Cambridge University Press. Neel, J.V., and F. Salzano. 1967. Further studies on the Xavante Indians. X. Some hypotheses-generalizations resulting from these studies. Am. J. Hum. Genet. 19:554- 574. Rogers, L.A. 1987. Concordance in isonymy and pedigree measures of inbreeding: The effects of sample composition. Hum. Bio!. 59(5):753-767. Smouse, P.E., V.J. Vitzthum, and J.V. Nee!. 1981. The impact of random and lineal fission on the genetic divergence of small human groups: A case study among the Yanomama. Genetics 98:179-197."}]},"highlighting":{"704613":{"ocr_t":[]}}}
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