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Part of the book series: Population and Community Biology Series ((PCBS,volume 18))

Abstract

Two-sex marriages in socially structured populations can be characterized as multiplicative perturbations of heterosexually random, or proportionate, mixing (Castillo-Chavez & Busenberg 1991). Such perturbations are expressed in terms of preferences, or affinities, of males for females, and vice versa. Male and female preferences are obviously not independent, since they depend on the availability of male and female behavioral classes. Knowledge of the preferences of one gender can characterize the preferences of both genders in socially structured populations; in other words, “it takes two to tango.” This is the basic content of the T3 Theorem. Different sets of preferences, that is, distinct behavioral classes, may give rise to identical mating probabilities, the determinants of the behavioral “ phenotypes” (Hsu Schmitz 1994; Hsu Schmitz et al. 1993). Hence, different sets of individual decisions can lead to identical social dynamics, a fact well established in genetics. The importance of the incorporation of mating systems at the population level is a neglected but central area in evolutionary biology.

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Literature Cited

  • Altman, M., and M. Morris. 1994. A clarification of the φ mixing model. Mathematical Biosciences 124: 1–8.

    Article  Google Scholar 

  • Blythe, S. P., C. Castillo-Chavez, J. Palmer, and M. Cheng. 1991. Towards a unified theory of mixinging and pair formation. Mathematical Biosciences 107: 379–405.

    Article  PubMed  CAS  Google Scholar 

  • Blythe, S. P., S. Busenberg, and C. Castillo-Chavez. 1995. Affinity in paired event probability. Mathematical Biosciences 128: 265–284.

    Article  PubMed  CAS  Google Scholar 

  • Burley, N. 1983. The meaning of assortative mating. Ethology & Sociobiology 4: 191–203.

    Article  Google Scholar 

  • Busenberg, S., and C. Castillo-Chavez. 1989. Interaction, pair formation and force of infection terms in sexually-transmitted diseases. Pp. 289–300 in C. Castillo-Chavez, ed., Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics 83. Springer-Verlag, Berlin.

    Chapter  Google Scholar 

  • Busenberg, S., and C. Castillo-Chavez 1991. A general solution of the problem of mixing sub-populations, and its application to risk-and age-structured epidemic models for the spread of AIDS. IMA Journal of Mathematics Applied in Medicine & Biology 8: 1–29.

    Google Scholar 

  • Castillo-Chavez, C., and S. Busenberg. 1991. On the solution of the two-sex mixing problem. Pp. 80–98 in S. Busenberg and M. Martelli, eds., Proceedings of the International Conference on Differential Equations and Applications to Biology and Population Dynamics. Lecture Notes in Biomathematics 92. Springer-Verlag, Berlin.

    Google Scholar 

  • Castillo-Chavez, C., S. Busenberg, and K. Gerow. 1991. Pair formation in structured populations. Pp. 47–65 in J. Goldstein, F. Kappel, and W. Schappacher, eds., Differential Equations with Applications in Biology, Physics and Engineering. Marcel Dekker, New York.

    Google Scholar 

  • Castillo-Chavez, C., S.-F. Shyu, G. Rubin, and D. Umbach. 1992. On the estimation problem of mixing/pair formation matrices with applications to models for sexually-transmit ted diseases. Pp. 384–402 in K. Dietz et al., eds., AIDS Epidemiology: Methodology Issues. Birkhauser, Boston.

    Google Scholar 

  • Castillo-Chavez, C., J. X. Velasco-Hernandez, and S. Fridman. 1995. Modeling Contact Structures in Biology. Lecture Notes in Biomathematics 100. Springer-Verlag, Berlin.

    Google Scholar 

  • Castillo-Chavez, C., S. Fridman, and X. Luo. In press. Stochastic and deterministic models in epidemiology. In Proceedings of the First World Congress of Non-Linear Analysts (Tampa, Florida, August 19-26, 1992). Walter de Gruyter, Berlin.

    Google Scholar 

  • Castillo-Chavez, C., W. Huang, and J. Li. In press. On the existence of stable pairing distributions. Journal of Mathematical Biology.

    Google Scholar 

  • Caswell, H., and D. E. Weeks. 1986. Two-sex models: Chaos, extinction and other dynamic consequences of sex. American Naturalist 128: 707–735.

    Article  Google Scholar 

  • Crow, J. F., and M. Kimura. 1970. An Introduction to Population Genetics Theory. Harper & Row, New York.

    Google Scholar 

  • Predrickson, A. G. 1971. A mathematical theory of age structure in sexual populations: Random mating and monogamous marriage models. Mathematical Biosciences 10: 117–143.

    Article  Google Scholar 

  • Gimelfarb, A. 1988a. Processes of pair formation leading to assortative mating in biological populations: Encounter-mating model. American Naturalist 131: 865–884.

    Google Scholar 

  • Gimelfarb, A. 1988b. Processes of pair formation leading to assortative mating in biological populations: Dynamic interaction model. Theoretical Population Biology 34: 1–23.

    Google Scholar 

  • Hsu Schmitz, S.-F. 1994. Some theories, estimation methods and applications of marriage functions in demography and epidemiology. Ph.D. diss. Cornell University, Ithaca, N.Y.

    Google Scholar 

  • Hsu Schmitz, S.-F., and C. Castillo-Chavez. 1994. Parameter estimation in non-closed social networks related to dynamics of sexually transmitted diseases. Pp. 533–559 in E. Kaplan and M. Brandeau, eds., Modeling the AIDS Epidemic: Planning, Policy and Prediction. Raven Press, New York.

    Google Scholar 

  • Hsu Schmitz, S.-F., and C. Castillo-Chavez In press. Completion of mixing matrices for non-closed social networks. In Proceedings of the First World Congress of Non-Linear Analysts (Tampa, Florida, August 19-26, 1992). Walter de Gruyter, Berlin.

    Google Scholar 

  • Hsu Schmitz, S.-F., S. Busenberg, and C. Castillo-Chavez. 1993. On the evolution of marriage functions: It takes two to tango. Biometrics Unit Technical Report BU-1210-M. Cornell University, Ithaca, N.Y.

    Google Scholar 

  • Karlin, S. 1979a. Models of multifactorial inheritance: I, Multivariate formulations and basic convergence results. Theoretical Population Biology 15: 308–355.

    Google Scholar 

  • Karlin, S. 1979b. Models of multifactorial inheritance: II, The covariance structure for a scalar phenotype under selective assortative mating and sex-dependent symmetric parental-transmission. Theoretical Population Biology 15: 356–393.

    Google Scholar 

  • Karlin, S. 1979c. Models of multifactorial inheritance: III, Calculation of covariance of relatives under selective assortative mating. Theoretical Population Biology 15: 394–423.

    Google Scholar 

  • Karlin, S. 1979d. Models of multifactorial inheritance: IV, Asymmetric transmission for a scalar phenotype. Theoretical Population Biology 15: 424–438.

    Google Scholar 

  • Karlin, S. 1980. Models of multifactorial inheritance: V, Linear assortative mating as against selective (non-linear) assortative mating. Theoretical Population Biology 17: 255–275.

    Google Scholar 

  • Kendall, D. G. 1949. Stochastic processes and population growth. Journal of the Royal Statistical Society B 11: 230–264.

    Google Scholar 

  • Keyfitz, N. 1949. The mathematics of sex and marriage. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics & Probabilty 4: 89–108.

    Google Scholar 

  • Lubkin, S., and C. Castillo-Chavez. In press. A pair formation approach to modeling inheritance of social traits. In Proceedings of the First World Congress of Non-Linear Analysts (Tampa, Florida, August 19-26, 1992). Walter de Gruyter, Berlin.

    Google Scholar 

  • McFarland, D. D. 1972. Comparison of alternative marriage models. Pp. 89–106 in T. N. E. Greville, ed., Population Dynamics. Academic Press, New York.

    Google Scholar 

  • Parlett, B. 1972. Can there be a marriage function? Pp. 107–135 in T. N. E. Greville, ed., Population Dynamics. Academic Press, New York.

    Google Scholar 

  • Pollard, J. H. 1973. Mathematical Models for the Growth of Human Populations. Cambridge University Press.

    Google Scholar 

  • Rubin, G., D. Umbach, S.-F. Shyu, and C. Castillo-Chavez. 1992. Application of capture-recapture methodology to estimation of size of population at risk of AIDS and/or other sexually-transmitted diseases. Statistics in Medicine 11: 1533–1549.

    Article  PubMed  CAS  Google Scholar 

  • Sattenspiel, L., and C. Castillo-Chavez. 1990. Environmental context, social interactions, and the spread of HIV. American Journal of Human Biology 2: 397–417.

    Article  Google Scholar 

  • Wagener, D. K. 1976. Preferential mating: Nonrandom mating of a continuous phenotype. Theoretical Population Biology 10: 185–204.

    Article  PubMed  CAS  Google Scholar 

  • Wilson, S. R. 1973. The correlation between relatives under the multifactorial models with assortative mating: I, The multifactorial model with assortative mating. Annals of Human Genetics 37: 289–304.

    Google Scholar 

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Castillo-Chavez, C., Schmitz, SF.H. (1997). The Evolution of Age-Structured Marriage Functions: It Takes Two to Tango. In: Tuljapurkar, S., Caswell, H. (eds) Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. Population and Community Biology Series, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5973-3_18

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  • DOI: https://doi.org/10.1007/978-1-4615-5973-3_18

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