The concept of population reproduction
Topic 11. Reproduction of the population
The main feature of the population is that, despite constant changes in its size and structure, it remains as a population, i.e. as a self-reproducing set of people . One could even say that the population preserves itself, remains itself precisely and exclusively thanks to these continuous changes.
This process of self-preservation of the population in the course of its continuous changes is called population reproduction, and it is this process that forms the subject of demography as a science.
Reproduction of the population- this is a constant renewal of the size and structure of the population in the process of changing generations of people, through birth and death. The set of parameters that determine this process is called the regime of population reproduction.
The parameters that determine the reproduction of the population are fertility and mortality, presented in the form of their indicators, as well as the number of arrivals and the number of departures1.
Usually, the reproduction of the population is not considered as a whole, but in relation to any one sex, most often female. The choice of the female population is due to the following factors:
· The reproductive period in women is shorter than in men;
· The main parameters of female reproductive performance (the number of children born to a woman, her age at birth, etc.) are much more accessible than the analogous characteristics for men, especially with regard to extramarital birth.
The role of age as a universal independent variable of demographic analysis and its constant change (each person inevitably either dies or becomes older, i.e., more strictly speaking, moves to a different age group) determine the fact that in the analysis of population reproduction much attention is paid to age , study of this process in the context of age groups.
Reproduction indicators refer to a real or hypothetical cohort (generation), i.e. are essentially cohort.
If certain sex and age differentiated fertility and mortality are set, as well as the secondary sex ratio, which is a universal biological constant and is equal to approximately 105-106 live births of boys per 100 live births of girls, then this completely determines the reproduction of the population and its age-sex structure. The totality of these parameters is what they mean when they talk about the mode of population reproduction.
Since the reproduction of the female population is usually investigated, the whole question boils down to considering the age-specific mortality rate of women and the frequency of birth of girls in women of different ages.
Mortality is usually measured using the survival-to-age function X years, i.e. using the function . In practice, they use the values of the numbers surviving to age X years from the complete mortality tables of the female population. A generalizing characteristic of female mortality is the average life expectancy of a newborn, i.e. .
Gross reproduction rate is the number of girls that each woman will give birth on average over the entire reproductive period. When calculating the gross coefficient, it is assumed that there is no mortality among women until the end of reproductive age.
The gross reproduction rate of the population is equal to the total fertility rate multiplied by this proportion of girls among newborns:
where R - gross reproduction rate; TVR - total fertility rate; ASBR x - age-specific fertility rates; - the proportion of girls among newborns.
In Russia, the average value of the proportion of girls among newborns over the past 40 years was approximately 0.487.
As can be seen from the calculation formula, the gross reproduction rate of the population is the total fertility rate adjusted for the secondary sex ratio.
The gross reproduction rate of the population can be interpreted in different ways:
· As an age-standardized fertility rate;
· As the average number of daughters that a group of women who started life at the same time could give birth if they all lived to the end of their childbearing period;
· As the ratio between the number of women of one generation, for example, at the age of 15, to the number of their daughters at the same age, provided that there is no mortality during the childbearing period;
· As the relationship between female births in two successive generations, assuming that no one dies between the beginning and the end of the reproductive period.
The last three definitions are usually used when talking about real cohorts.
2. Indicators of population reproduction: total fertility rate, gross reproduction rate, net reproduction rate
To get a real idea of the nature of population reproduction, indicators are needed that do not depend on the sex and age structure. In the early 1930s. German demographer, economist, statistician R. Kuchinsky (1876-1947) and domestic scientist, demographer, health care organizer G.A. Batkis (1895-1960) used indicators that give a clear picture of the state of the number of the new and old generation in the years adjacent to the years of the population censuses, helping to determine the extent to which the living population has prepared a replacement for itself:
Total fertility rate;
Gross reproduction rate;
Net reproduction rate.
The total fertility rate shows the number of children born on average by one woman for the entire fertile period of her life (i.e. from 15 to 49 years inclusive). It is calculated like this:
where nx is the age-specific fertility rate for women aged x years.
The calculation can also be performed for five-year intervals:
and for 10 year olds:
An example of calculating the total fertility rate is given in table. one.
Table 1. Calculation of the total fertility rate for the rural population of the Novosibirsk region, 1999
| Mother's age, years | Average age fertility rate per year,% | "Expected" number of children for the entire age interval |
As follows from the table. 1, for their entire fertile period, every 1000 rural women in the Novosibirsk region will give birth to 1404 (1403.5) children, i.e. 1.414 on average per woman, or roughly 140 children per 100 women.
The total fertility rate as an indicator of population reproduction is not without its drawbacks. Thus, he does not take into account: first, that the reproduction of the new generation can be characterized by the number of girls that each woman leaves behind; secondly, that some children die before reaching the age of their mother at the time of their birth, leaving behind no offspring or leaving fewer children in comparison with their peers who have happily survived to the end of the childbearing period.
The first drawback can be eliminated using the gross reproduction rate R b, calculated by the formula
where d is the proportion of girls born.
For the example shown in table. 1, and for d - 0.488
R b = 1.4035 0.488 = 0.6849.
Consequently, every 1000 women leaves behind 685 girls (684.9), i.e. even simple reproduction is not carried out in the rural population of the region.
The advantage of the gross coefficient is that its value is not influenced by the composition of the population by sex and that it takes into account the age composition of women of fertile age. However, it does not take into account the mortality rate of women of fertile age.
For the most accurate characteristics of population reproduction, the net coefficient is used. In the statistical literature, it is called pure or purified. It shows the number of girls that each woman leaves behind on average, taking into account the fact that some of them will not live up to the age of their mother at the time of their birth.
However, if each of their women of reproductive age gives birth to R daughters on average, this does not mean that the number of daughters 'generation will be R times greater or less than the number of mothers' generation. After all, not all of these daughters will live to the age at which their mothers were at the time of birth. And not all daughters will survive to the end of the reproductive period. This is especially true in countries with a high mortality rate, where up to half of the newborn girls may not survive until the beginning of the reproductive period, as was the case, for example, in Russia before the First World War. In our time, of course, this is no longer the case (in 2004, more than 98% of newborn girls survived to the beginning of the reproductive period), but in any case, an indicator is needed that also takes into account mortality. Taking into account the assumption of zero mortality until the end of the reproductive period, the gross reproduction rate of the population has practically not been published or used recently. An indicator that also takes into account mortality is the net reproduction rate of the population, or otherwise the Boeck-Kuchinski coefficient, proposed by the German statistician and demographer G.F.R. Byeck. Otherwise, it is called the net reproduction rate of the population. It is equal to the average number of girls born in a woman's lifetime and surviving to the end of the reproductive period, given the birth and death rates.
The following formulas are used to calculate the net coefficient Rn:
a) for one-year age groups:
,
where n x - age coefficients for women in the age group X years; d is the proportion of girls born;
The average number of women living in the stationary population of life tables in the age range from X to X + 1;
b) for five-year age groups:
R b = 
where - age-specific fertility rates for women in the age group from X to X + 4;
Average number of living women from life tables in the age range from X to X + 4 (+ +1 + +2 + +3 + +4);
c) for ten-year age groups:
R b = 
,
where - age-specific fertility rates for women in the age group from X to X + 9;
The average number of women living in the stationary population of persons of survival in the age range from x to x + 9.
Example. The number of women in the stationary population of the Novosibirsk region (according to life tables) and age-specific fertility rates are known:
Let's calculate the net reproduction rate. Let's define the "expected" number of children.
| Age group (years) | |
| 44,3487400:1000=21592 121,5484863:1000=58911 71,7481410:1000=34517 28,8477476:1000=13751 11,1472404:1000=5244 3,2465094:1000=1488 0,1454729:1000=46 |
With the proportion of girls born d = 0.488 Rn = 135 5490.488:
100,000 = 0.66148, or rounded 0.662.
Consequently, every 1000 rural women leaves behind only 662 girls. This confirms the initial conclusion that a mode of narrowed reproduction has been established in this population.
The advantage of the net coefficient lies in the fact that it takes into account the birth rate in certain age groups of women at the time of compilation of life tables, and when calculating it, the mortality rate of the population, the probability of surviving to the next age group are taken into account. In statistical practice, the following scale for assessing the net reproduction rate is adopted: when Rn = 1.0, simple reproduction occurs; for Rn> 1.0 - extended, for Rn< 1,0 - суженное.
B.S. Yastremsky established the relationship between the total fertility rate, fertility rate (special fertility rate, fertility rate) and reproduction rates (Tables 2 and 3).
Table 2. Relationship between fertility rates
Table 3. The relationship between fertility and reproduction rates
Therefore, the border between narrowed and simple reproduction lies between the meanings:
· Special birth rate from 100 to 150 ‰;
· Gross reproduction rate from 0.86 to 1.29 ‰;
· The total fertility rate from 15 to 22 ‰.
The net reproduction rate can be calculated not only for the female population, but also for the male population using the same method. In this case, it shows how many boys each man leaves behind, taking into account the fact that some of them will not live up to the age of their father at the time of their birth.
To calculate the net reproduction rate of the male population by one-year groups, the following formula can be used:
,
where are the age coefficients of the birth of children in families for men of the age group x years,
The number of living men in the stationary population of life tables in the age range from X years to X + 1;
d M is the proportion of boys born.
The calculation is carried out in a similar way for five- and ten-year age groups.
Table 4. Initial data for calculating the reproduction rates of the male and female population of the region, people
Note. Age groups: for women - 15-49 years old, for men - 18-55 years old.
Let's calculate the number of births per 1000 people of the population (n x) as (N x: S x 1000).
| Age group | Women | Men |
| 45 and older Average |
Hence the total fertility rate according to the formula:
51,000 for women:
=(78,3 + 226,7 + 193,2 + 106,2 + 36,3 + 8,9 + 1,6)5:1000 = 3,26;
for men:
+ (23,0 + 234,3 + 231,2 + 146,6 + 68,3 + 18,2 + 5,7)5:1000 = 3,64,
those. each woman leaves an average of 3.26 children for the entire fertile period of her life, a man - 3.64.
The gross reproduction rate of the population is calculated by the formula R b =:
3,260,488 = 1,591;
3,640,512 = 1,864,
those. each woman left on average 1,591 girls, men - 1,864 boys.
To go to the definition of the net coefficient, we calculate the "expected" number of children:: 1000, for example,
for women: 78.3485 117: 1000 = 37 985;
for men: 23.0487 370: 1000 = 11210, etc.
Net reproduction rate:
for women formula
R b = ): 
;
for men formula
): 
.
Consequently, every 1000 women, on average, leaves behind 1529 girls, taking into account the fact that some of them will not live up to the age of their mother at the time of their birth, and every 1000 men - 1724 boys, provided that some of them will not live up to the age of their father at the time of their birth. birth. The net coefficient of the male population is higher than the net coefficient of the female population by 0.196 points, or 12.8%.
In the second half of the XX century. in the world there was a tendency towards a decrease in all three indicators of population reproduction, and for economically developed countries it crossed the boundaries of simple reproduction (Fig. 1).
Rice. 1. Curve of the net coefficient for 1960-2006.
The first turning point in the modern demographic history of Russia was 1964, when the fall in the net reproduction rate of the Russian population crossed the line of generational replacement. In the same year, the mortality curve began to creep upward, which, in the end, led to the shameful modern level of life expectancy of Russians.
Period X is a characteristic resonant surge caused by politics and the environment of the 80s: a slow, jerky rise, a small upper plateau and an accelerating collapse well below the point of initial growth. It is noteworthy that the collapse of the population reproduction rate began long before the arrival of the "criminal liberal government" and a sharp deterioration in the socio-economic situation of the Soviet people.
Period Y- is divided into two political eras: the Yeltsin era, when uncertainty grew and the socio-economic situation of the majority of the country's population worsened; and the Putin era - when certainty grew, the vertical of power was strengthened, the socio-economic situation improved, the optimism of the voting majority multiplied.
The graph clearly shows the growth of the curve since 1999, the post-default year: the pre-active demographic policy is still 8 years old.
According to UN forecasts, by the period 2010-2014. the regions with narrowed population reproduction will include Europe Abroad, Asia Abroad, Australia and Oceania. The highest level of the net ratio will remain in Africa. And 109 women will leave behind 109 girls in America.
In Russia, the process of narrowed reproduction is deepening (see Table 5.)
Table 5. Dynamics of the net reproduction rate of the population in the Russian Federation in 1960 - 2000.
The narrowed reproduction of the urban population began by the end of the 1950s, the rural population - from 1993.
In 2000, every 1000 women of fertile age left 529 girls in cities, and 704 in rural areas.
According to the Demographic Yearbook, the total fertility rate for the period from 1991 to 2000 varied across the CIS countries from 1.10 in Ukraine to 4.09 in Turkmenistan. In Europe in 1999, the Czech Republic had the lowest level of the indicator - 1.12, and France - 1.77. In Asia for 1995-2000. the highest level was reached by Iran - 5.30 and Saudi Arabia - 5.80, the lowest - Japan - 1.39; China had 1.80, India had 3.40. In Africa, the total fertility rate reached 3.81 in Algeria, 3.74 in Egypt, and 3.25 in South Africa (1995-2000). In America for 1995-2000. Canada had the lowest level of indicator - 1.64, the highest - Mexico - 2.75; in the USA -2.02; in Australia - 1.80 (1996), in New Zealand - 1.97 (1997).
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NET REPRODUCTION RATIO
(net reproduction rate) The number of female children in the population divided by the number of adult women in the previous generation. The figure obtained in this way is a good guide to future trends in population size, which will increase if the ratio is greater than one.
Finance. Dictionary. 2nd ed. - M .: "INFRA-M", Publishing house "Ves Mir". Brian Butler, Brian Johnson, Graham Sidwell, et al. General editorial: Ph.D. Osadchaya I.M.. 2000 .
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