The Eventual Frequencies of Kin in a Stable Population

Abstract

Associated with every real birth cohort of women is a set of probabilities {f k} of eventually having k daughters. With a variant of stable population theory, these probabilities are used to generate the entire probability distributions, as well as all moments, for all categories of kin who are female and female-related. With additional assumptions, a full two-sex model for all kin also is given. The two-sex model is applied to a cohort of U.S. women born in the mid-twentieth century, suggesting plausible frequencies of kin in a stationary population.

This is a preview of subscription content, access via your institution.

References

  1. Atkins, John R. 1974. On the Fundamental Consanguineal Numbers and their Structural Basis. American Ethnologist 1:1–31.

    Article  Google Scholar 

  2. Barrai, I., L. L. Cavalli-Sforza, and A. Moroni. 1962. Frequencies of Pedigrees of Consanguineous Marriages and Mating Structure of the Population. Annals of Human Genetics 25:347–377.

    Article  Google Scholar 

  3. Bongaarts, John. 1975. A Method for the Estimation of Fecundability. Demography 12:645–660.

    Article  Google Scholar 

  4. Farber, Bernard. 1971. Kinship and Class. New York: Basic Books.

    Google Scholar 

  5. Firth, Raymond, Jane Hubert, and Anthony Forge. 1969. Families and their Relatives. London: Routledge and Kegan Paul.

    Book  Google Scholar 

  6. Goodman, Leo A., Nathan Keyfitz, and Thomas W. Pullum. 1974. Family Formation and the Frequency of Various Kinship Relationships. Theoretical Population Biology 5:1–27.

    Article  Google Scholar 

  7. —. 1975. Addendum. Theoretical Population Biology 8:376–381.

    Article  Google Scholar 

  8. Hajnal, John. 1963. Random Mating and the Frequency of Consanguineous Marriage and its Genetic Implications. Proceedings of the Royal Society (London B) 159:125–177.

    Article  Google Scholar 

  9. Harris, Theodore E. 1963. The Theory of Branching Processes. Englewood Cliffs, N.J.: PrenticeHall.

    Google Scholar 

  10. Keyfitz, Nathan. 1968. Introduction to the Mathematics of Population. Reading, Mass.: Addison-Wesley.

    Google Scholar 

  11. Krishnamoorthy, S. 1979. Family Formation and the Life Cycle. Demography 16:121–129.

    Article  Google Scholar 

  12. Le Bras, Herve. 1973. Parents, Grands-parents, Bisaieux. Population 28(1):9–388.

    Article  Google Scholar 

  13. MacCluer, Jean W., and William J. Schull. 1970. Frequencies of Consanguineous Marriage and Accumulation of Inbreeding in an Artifical Population. American Journal of Human Genetics 22:160–175.

    Google Scholar 

  14. Preston, Samuel H. 1976. Family Sizes of Children and Family Sizes of Women. Demography 13:105–114.

    Article  Google Scholar 

  15. Pullum, Thomas W. 1975. On the Analysis of Family Continuation Probabilities which are Composition-Specific. Journal of Mathematical Biosciences 24:93–105.

    Article  Google Scholar 

  16. Schneider, David M., and Raymond T. Smith. 1973. Class Differences and Sex Roles in American Kinship and Family Structure. Englewood Cliffs, N.J.: Prentice-Hall.

    Google Scholar 

  17. Sheps, Mindel, and Jane Menken. 1972. Models of Conception and Birth. Chicago: University of Chicago Press.

    Google Scholar 

  18. U.S. Bureau of the Census. 1979. Current Population Reports, Series P-20, No. 341. Fertility of American Women: June, 1978. Washington, D.C.: U.S. Government Printing Office.

    Google Scholar 

  19. Wachter, Kenneth W., Eugene A. Hammal, and Peter Laslett. 1978. Statistical Studies of Historical Studies of Historical Social Structures. New York: Academic Press.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pullum, T.W. The Eventual Frequencies of Kin in a Stable Population. Demography 19, 549–565 (1982). https://doi.org/10.2307/2061018

Download citation

Keywords

  • Current Population Survey
  • Stable Population
  • Probability Generate Function
  • Direct Descendant
  • Sibship Size