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Multilingual Demographic Dictionary, second unified edition, English volume
70
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701
The interaction of fertility, mortality and migration leads to a consideration of population growth ^{1}. A zero population growth ^{10★} refers to a population of invariable size. It is convenient to regard population decline ^{2} as negative growth ^{3}. A distinction may be drawn between a closed population ^{4} in which there is no migration either inwards or outwards and whose growth depends entirely on the difference between births and deaths, and an open population ^{5} in which there may be migration. The growth of an open population consists of the balance of migration ^{6} or net migration ^{6} and natural increase ^{7}, which is the excess of births over deaths ^{8} or deficit of births over deaths ^{9★} sometimes called the balance of births and deaths ^{8}. Any change in one variable affects the overall growth and structure of a population; in this context growth effects ^{11★} and structural effects ^{12★} are determined.
702
The ratio of total growth in a given period to the mean population of that period is called the growth rate ^{1}. Occasionally this rate is computed with the population at the beginning of the period rather than with the mean population as a denominator. When population increase over a period of more than one calendar year is studied, the mean annual rate of growth ^{2} may be computed. In computing this rate it is sometimes assumed that the population is subjected to exponential growth ^{3} during the period, and time is treated as a continuous variable. The size of an exponential population ^{4} would grow as an exponential function of time. The exponential growth rate ^{5} is equal to the instantaneous rate of growth ^{5}. The ratio of natural increase (701-7) to the average population during a period is called the crude rate of natural increase ^{6} and is equal to the difference between the crude birth rate and the crude death rate. The vital index ^{7} is the ratio of the number of births to the number of deaths during a period; this measure is no longer much used.
- 3. When time is treated as a discrete variable, reference is made to geometric growth.
- 4. This is occasionally called a Malthusian population, but the term is ambiguous in view of its sociological connotations (see 906-1).
703
It can be shown that when a closed population (701-4) is subjected to constant age-specific fertility and mortality rates (631-8; 412-1) for a sufficiently long period of time, its annual rate of increase will tend to become constant. This constant rate of increase is called the intrinsic rate of natural increase ^{1}, and a population which has reached this stage is called a stable population ^{2}. The proportion of persons in different age groups in such a population will be constant, i.e., the population will have a stable age distribution ^{3}. This stable age distribution is independent of the initial age distribution ^{4} and depends only on the fertility and mortality rates that are kept constant. Human populations never reach exact stability in practice, as fertility and mortality rates constantly change, but the computation of a stable population as a model and of its intrinsic rates may provide an index of the growth potential ^{5} of a set of age-specific fertility rates applied to a non stabilized age structure. Related to the growth potential, the moment of inertia of a population or demographic momentum ^{11★} should be mentioned: it refers to the dynamics hidden in the age structure due to a delayed growth response caused by the biological fact that from the time of birth of a cohort (116-2) to the beginning of their period of fertility (620-1) a certain amount of time passes. A population may for this reason still grow, even though the birth rate drops long ago. The reverse case is also possible. The momentum is particularly altered in case of discontinuity in the evolution of births and abrupt reversals of trends. A stable population in which the intrinsic rate of natural increase is zero is called a stationary population ^{6}. In such a population the numbers in a given age group are equal to the integral of the survivorship function (431-3) of the life table taken between the upper and lower age limits of the group, multiplied by a factor of proportionality common to all age groups. A quasi-stable population ^{7} is a formerly stable population with constant fertility and gradually changing mortality; characteristics of this type of population are similar to those of semi-stable populations ^{8★} which are closed population with a constant age structure. A logistic population ^{9} is a population growing in accordance with the logistic law ^{10} of growth, i.e., a population in which the growth rate decreases as a linear function of the population already alive and which will tend asymptotically to an upper limit.
- 1. The intrinsic rate, also called by its inventor Lotka, the true rate of natural increase, is equal to the difference between the intrinsic birth rate (or stable birth rate) and the intrinsic death rate (or stable death rate).
- 2. Stable, adj. - stability, n. - stabilize, v.
Stable population analysis uses the properties of stable population models to estimate various characteristics of real populations. - 6. Stationary, adj. - stationarity, n.
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