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The theory of population replacement1 treats population as a renewable resource2 in the mathematical sense of the term. A distinction is drawn between gross replacement3, where no account is taken of mortality before the end of the reproductive period (620-1), and net replacement4, in which this mortality is taken into account.
In the study of replacement a number of indices, replacement rates1 or reproduction rates1 are used. Reproduction rates are generally female reproduction rates2 or maternal reproduction rates2. The female net reproduction rate3 (see also para. 718) 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 current age-specific fertility (031-8) and mortality rates (401-2). A female gross reproduction rate4 is computed similarly on the assumption that mortality before the end of the reproductive age is zero. Male reproduction rates5 or paternal reproduction rates5 can be computed analogously using male births and a male birth cohort, and certain varieties of joint reproduction rates6 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 rates7 or generation reproduction rates7 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 index8 or J-ratio8 may be used. This ratio relates the quotient of the population of children of a given age (as a rule those under 1 year or 0-4 years) to the number of women of childbcaring age in the actual population to the corresponding quotient in the stationary population (703-6).
- 1. Some writers have used the term replacement rate for a reproduction rate which takes emigration and immigration into account. 4, In England a variant of the net reproduction rate, the so-called effective reproduction rate, has been calculated. In this rate current age-specific fertility rates (631-8} are used in combination with estimated future age-specific mortality (412-1) rates. The table which shows the product of the age-specific fertility rate and the number of years lived within this group in the life table is known as the net fertility schedule.
Other replacement indices also are computed. For instance, the net reproduction rate is sometimes split into a legitimate component1 and an illegitimate component2. Again, a nuptial net reproduction rate3 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 female rates, but it would be possible to compute analogous male rates.
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 will measure the increase of the stable population (703-2) implied by the given age-specific fertility and mortality rates (401-2), over a period equivalent to the length of a generation1 or the mean interval between successive generations1. This length of a female generation is approximately equal to the average age of mothers2 giving birth to live daughters, provided current age-specific fertility and mortality rates prevail. Replacement indices are generally current indices (cf. 153-4) which relate to hypothetical cohorts3, fictitious cohorts3 or synthetic cohorts3.
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