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Population dynamics and momentum in a growing population

The illustrations below demonstrate the population dynamics when replacement fertility rates are adopted by a growing population. As an example we have taken the 2010 population of the 'Least developed countries' as defined by the UN1. These illustrations are generated by projecting the 2010 population by age and sex forward with the prevailing mortality regime and the new replacement-level fertility rates.

Following the change to replacement level fertility rates, the NRR immediately assumes the value of 1 and the intrinsic growth rate (Lotka's r) immediately becomes 0, indicating that the population will eventually stop growing. However, the population will undergo considerable changes in size and in its age distribution in the years before becoming stationary. These dynamics are described by the change in the population pyramids (left panel), the crude rates (right panel) and the total population size (right panel). The two horizontal red lines on the population pyramid delineate women's reproductive age range between menarche and menopauze (15-49).

All changes in the crude rates and, ultimately, in population size occur only because of the age-compositional changes, since the age-specific fertility and mortality rates themselves are fixed.

Figure 2: Population dynamics in the Least Developed Countries following an immediate adoption of replacement fertility rates (2010 - 2135)

 

Changes in the size of birth cohorts

The instantaneous adjustment to the new replacement level fertility regime implies a large reduction in the number of annual births in the first projection step (here 5 years). That decline is, however, short-lived because the number of births will start increasing again in the second projection step. The reason for the renewed increase is that the population had been growing just before the replacement level fertility regime took effect, and the relatively large pre-transition cohorts are slowly moving through their reproductive ages. In fact, the number of births will continue to grow for 20 years or so. After that, the first birth cohorts born under the new fertility regime are moving through their prime childbearing years. The initial dent in the age structure thus echoes a generation later when the smaller cohorts of children reach adulthood and start bearing children themselves.

Eventually the irregularities age out of the population pyramid and are barely visible after 75 years. Note that these dents in the age structure would persist for longer if all childbearing is concentrated in a smaller age range. In the hypothetical case where all childbearing would be concentrated in a 5-year age interval, the dents in the age structure are still clearly visible after 100 years (click here for a pop up with an illustration link ). The fact that human reproduction is spread over 35 years between menarche and menopause thus helps to even out the initial distortions in the age structure produced by the drastic decline in fertility.

Momentum and ageing

In a growing population, momentum coincides with population ageing: compared to the starting population, the relative share of the population below age 15 declines (the base of the population pyramid shrinks) and that of adults and the elderly increases considerably (the top of the pyramid becomes broader). This can be seen by comparing the population pyramid of the starting population (light blue) with the population pyramid representing the age structure after 100 years.

Trends in the CBR

The fertility reduction and the changes in the population age structure described earlier will also have implications for other demographic measures characterizing population dynamics. After an initial and drastic decline in the number of births and the birth rate in the first projection step, the CBR increases because the relative share of women in reproductive ages increases. The CBR peaks about 20 years after the fertility transition, and declines thereafter because the large pre-transition cohorts age out of the reproductive age range and are replaced by the first cohorts of women born after the new fertility regime took effect.

Trends in the CDR

The trend in the CDR is also characterized by an initial decline following the fertility transition and that is due to a reduction in the number of infants and young children who typically have high mortality rates (particularly in low income countries). After a decade or so, the CDR will start increasing again because of the combined effects of growing birth cohorts and population ageing.

Trends in the CRNI

With replacement level fertility rates, unchanging mortality and no migration, the population will eventually become stationary and that implies that: CDR=CBR and that CRNI=0 (and since we are assuming zero migration, CRNI=CGR=0). In the case of the Least Developed Countries this happens after about 100 years (at that point the CGR is not exactly 0, but |CGR|<0.01%). Interestingly, the CGR increases shortly after the fertility transition before setting in a sustained decline. In that sense, the CGR reproduces the trend in the CBR, reinforced by the initial decline in the CDR. Populations can also experience short periods of negative growth during the course of becoming stationary. This most likely occurs in populations with a very large fertility decline, and in populations with highly concentrated fertility schedules.

Change in the total population size

Population momentum is the growth that occurs between the start of the fertility decline and the moment that the population becomes stationary and stops growing. In our example, the total population of the least developed countries would grow from 832,329,000 to 1,276,043,000 even if all these countries had immediately adopted a replacement level fertility regime. Expressed in terms of a ratio, momentum for the least developed countries is 1,276,043,000/832,329,000=1.5331, implying that it would still grow by about 53% after the fertility transition.

1Source (data and country classifications): United Nations, Department of Economic and Social Affairs, Population Division (2011). World Population Prospects: The 2010 Revision, Volume I: Comprehensive Tables. ST/ESA/SER.A/313