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Multilingual Demographic Dictionary, second unified edition, English volume
71
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710
The theory of population replacement ^{1} or population reproduction ^{1} (see § 116) treats population as a renewable resource ^{2} in the mathematical sense of the term. A distinction is drawn between gross reproduction ^{3} or gross replacement ^{3}, where no account is taken of mortality before the end of the reproductive period (620-1), and net reproduction ^{4} or net replacement ^{4}, in which this mortality is taken into account.
- 1. Also reproductivity. For another sense of reproduction see 601-2.
711
In this study of replacement a number of indices, replacement rates ^{1} or reproduction rates ^{1} are used. Reproduction rates are generally female reproduction rates ^{2} or maternal reproduction rates ^{2}. The female net reproduction rate ^{3} is defined as the average number of live daughters that would be born to a hypothetical female birth cohort (116-2) which would be subjected to a set of current age-specific fertility (631-8) and mortality rates (401-2). A female gross reproduction rate ^{4} is computed similarly on the assumption that mortality before the end of the reproductive age is zero. Male reproduction rates ^{5} or paternal reproduction rates ^{5} can be computed analogously using male births and a male birth cohort, and certain types of joint reproduction rates ^{6} which take both sexes into account have been proposed. Where the experience of an actual cohort is used in the construction of reproduction rates, cohort reproduction rates ^{7} or generation reproduction rates ^{7} are obtained. The mortality and the fertility rates used in the construction of these rates will refer to different periods of time. Where statistics of fertility by age are not available, the so-called replacement index ^{8} may be used. This ratio relates the quotient of the population of children of a given age (as a rule those 0-4 years) to the number of women of childbearing age in the actual population, to the corresponding quotient in the stationary population (703-6).
712
Other replacement indices are also computed. For instance, the net reproduction rate is sometimes split into a legitimate component ^{1} and an illegitimate component ^{2}. Again, a nuptial reproduction rate ^{3} has been computed, showing the number of legitimate daughters that will be born to a newly-born female if current rates of mortality, fertility, nuptiality and dissolution of marriage remain unchanged. Generally such rates are for females, but it would be possible to compute analogous rates for males.
713
The net reproduction rate (711-3) and the intrinsic rate of natural increase (703-1) are closely related to one another. The net reproduction rate measures the increase in the stable population (703-2) implied by the given age-specific fertility and mortality rates over a period equivalent to the mean length of a generation ^{1} or the mean interval between successive generations ^{1}. This length of a female generation is equal to the mean age of mothers ^{2} giving birth to live daughters, with current age-specific fertility and mortality rates. Period reproduction rates are current indices (cf. 152) which relate to hypothetical cohorts ^{3} or synthetic cohorts ^{3}.
- 2. The mean age of fertility, i.e., the mean age of the fertility schedule is only approximately equal to the mean length of a generation. The mean length of a male generation similarly is equal to the mean age of fathers at the birth of their children.
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