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  • Title: Alternative least square solutions for a two-sex stable population model.
    Author: Mitra S.
    Journal: Genus; 1982; 38(3-4):39-50. PubMed ID: 12312902.
    Abstract:
    The effect of minimizing the sum of squares of deviations between births generated by the sex-age specific brithrates of a given period of time and that obtained by adjusting these same rates proportionately so as to maintain a constant sex-ratio at birth at all times is examined. An alternative function is presented, defined in terms of a uniform relative rate of change in the specific rates for all ages for females and another such rate for male counterparts. This model provides unique solutions for the age specific birthrates that also approach stability over time. These changes have been shown to take place in a manner so that the total number of births remain the same with what the reproductive population of both sexes would have given birth to had they experienced an average of the net maternity and net paternity rates. The method outlined in this paper is based on a definition of the problem that is different from those used by the earlier researchers. In the attempt to hold the variations of the net maternity and paternity rates to a minimum, subject to a constant sex-ratio at birth, the authors found the importance of the average of the 2 functions, the net parenthood rates. A few years from the beginning of the process, determined normally by the highest age of the reproductive males, the trajectory of births becomes equivalent to that generated by a situation in which birth cohorts of both sexes are subjected to experience a simple average of the initial net maternity and net paternity rates at all times. While in reality each sex experiences its own set of rates consistent with that of the other sex at any given time, the result in terms of the actual number of births remains the same if each sex has to experience a set of rates obtained by averaging the 2 rates not only at the initial time period but also that at the time in question.
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