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710
The theory of population replacement^{1} treats population as a renewable resource^{2} in the mathematical sense of the term. A distinction is drawn between gross replacement^{3}, where no account is taken of mortality before the end of the reproductive period (6201), and net replacement^{4}, in which this mortality is taken into account.
711
In the 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} (see also para. 718) is defined as the average number of live daughters that would be born to a hypothetical female birth cohort (1162) which would be subjected to current agespecific fertility (0318) and mortality rates (4012). 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 varieties 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 socalled replacement index^{8} or Jratio^{8} 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 04 years) to the number of women of childbcaring age in the actual population to the corresponding quotient in the stationary population (7036).
 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 socalled effective reproduction rate, has been calculated. In this rate current agespecific fertility rates (6318} are used in combination with estimated future agespecific mortality (4121) rates. The table which shows the product of the agespecific fertility rate and the number of years lived within this group in the life table is known as the net fertility schedule.
712
Other replacement indices also are computed. For instance, the net reproduction rate is sometimes split into a legitimate component^{1} and an illegitimate component^{2}. Again, a nuptial net reproduction rate^{3} has been computed, showing the number of legitimate daughters that will be born to a newlyborn 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.
713
The net reproduction rate (7113) and the intrinsic rate of natural increase (7031) are closely related to one another. The net reproduction rate will measure the increase of the stable population (7032) implied by the given agespecific fertility and mortality rates (4012), over a period equivalent to the length of a generation^{1} or the mean interval between successive generations^{1}. This length of a female generation is approximately equal to the average age of mothers^{2} giving birth to live daughters, provided current agespecific fertility and mortality rates prevail. Replacement indices are generally current indices (cf. 1534) which relate to hypothetical cohorts^{3}, fictitious cohorts^{3} or synthetic cohorts^{3}.
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