Fertility, Mortality, and Age Distributions: Introduction

The age composition of a population that neither gains nor loses by migration is determined by the recent sequence of fertility and mortality risks at each age to which it has been subject. Its overall birth rate, death rate, and rate of increase at each moment are determined by the current age composition and the current age schedules of fertility and mortality. In principle, then, both age composition and vital rates can be determined from knowledge of the history and present value of fertility and mortality schedules. Consider a female population in which the annual death rate of persons at age a and time t is μ,(a, t), and the annual rate of bearing a female child at age a and time t is m(a, l). If these schedules are specified for a sufficient time interval — in practice no more than a century — the age composition, birth rate, death rate, and rate of increase can all be calculated. If an age distribution in the past is among the available data, the calculation of current age composition and vital rates can be made by standard methods of population projection. If no past age distribution is stipulated, it appears at first that knowledge of past fertility and mortality schedules is not sufficient to calculate the current age distribution. However, Alvaro Lopez has proven a conjecture made by the author in 1957: that two arbitrarily chosen age distributions no matter how different, subject to identical sequences — whether varying or constant — of fertility and mortality, ultimately generate populations with the same age composition (Coale [2], Lopez [8, 9], also McFarland [10]). Age distributions gradually "forget" the past. It is therefore possible to reproduce the age composition of a given population by projecting an arbitrarily selected initial population from many years in the past, employing the age schedules of fertility and mortality that the population actually experienced in the interim. If the period of projection is long enough, the effect of the arbitrary initial age composition wholly disappears, and the current age composition (c (a, t0)) is seen to be entirely a function of μ(a, t) and m(a, t) during a substantial interval before t0. Moreover, if (c(a, t)da) is the proportion of the female population between age a and a + da, b(t) is the birth rate and d(t) the death rate, and ωis the highest age attained,

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The rate of increase of the population at time t — r(t) — is the difference between h(t) and d(t), and the proportionate increase in numbers 2 r (t)dt

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from t1 to t2 is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The principal purpose of this book is to analyze the relation of levels, age patterns, and time patterns of fertility and mortality to the growth and age composition of populations. If our minds could readily visualize the outcome of the large number of multiplications and additions that constitute a population projection, the book could be terminated right here, or at most would need to include a brief description of how a population projection is made and a recapitulation of Lopez' proof. But in view of our incapacity to visualize elaborate calculations, what has been presented is enough to enable a demographer merely to calculate an age distribution, a birth rate, a death rate, and a rate of increase from a long sequence of fertility and mortality schedules without providing him the basis for understanding what features of mortality, fertility, and their changes account for particular characteristics of the age structure, for changes in the birth and death rates, etc. In trying to explain how age structures are formed, and vital rates determined, we shall consider the age distributions produced by schedules of fertility and mortality that do not change with the passage of time (Chapters 2 and 3); and then the age distributions produced by changing fertility and mortality (Chapters 4 to 7).

Fertility and Mortality Schedules in Human Populations

FERTILITY SCHEDULES

The variation of the rate of childbearing with age depends partly on biological factors. The capacity to conceive and bear children normally begins at about age 15 (following menarche), attains a broad maximum beginning at about age 20, falls slightly by age 30, and then follows an accelerated pace of decline after age 35. A typical mean age at the birth of the last child among married women not practicing birth control is about 40 years; only a small minority can bear children after age 45 and practically none after age 50.

The actual curve of childbearing as a function of age of course depends not only on the varying capacity to conceive and bear live issue, but on variations with age in exposure to intercourse with a fertile partner, and on whether or not measures are taken in different degree at different ages to prevent conception or to cause an early termination of pregnancy. The rise of fertility with age is strongly affected by laws and customs that determine when women enter fertile unions. Among societies in which marriage is ordinarily a prerequisite for fruitful intercourse, there are wide variations in mean age at marriage, from less than 15 to nearly 30 years. The decline of fertility with age is influenced by the rising incidence of widowhood, divorce, and perhaps of abstinence, as well as by declining fecundability. The practice of contraception and abortion could in principle reduce fertility at any age in the fertile span and thus produce an essentially arbitrary modification of the age structure of fertility; but, in fact, voluntary control seems always to cause a greater proportionate reduction of fertility among older women (i.e., women 30 to 45) than among younger.

Figure 1.1 shows schematically how the principal factors that determine the shape of fertility schedules operate. In panel A the variations in the shape of age-specific fertility schedules of cohabiting women that occur with and without contraception are shown. The schedules have been adjusted so that the maximum of each is 100; otherwise the schedule of women practicing contraception would ordinarily have a lower maximum. In panel B can be seen variations in the proportion of women cohabiting, again with the maximum proportions set at 100. With very...