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# Intrinsic rate of natural increase

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Intrinsic rate of natural increase  (INTRINSIC rate of natural increase)

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 a semi-stable population 8★ which is a 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.