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Growth and Structure of Human Populations: A Mathematical Investigation

Growth and Structure of Human Populations: A Mathematical Investigation

Copyright Date: 1972
Pages: 248
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  • Book Info
    Growth and Structure of Human Populations: A Mathematical Investigation
    Book Description:

    Although mathematical demography has traditionally studied the so-called stable population (fixed mortality and fertility schedules), Ansley Coale investigates now the dynamics of population growth and structure-the changing age composition of a population as birth and death rates fluctuate.

    Originally published in 1972.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6777-6
    Subjects: Sociology

Table of Contents

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  1. Front Matter
    (pp. i-iv)
  2. Preface
    (pp. v-vi)
  3. Table of Contents
    (pp. vii-2)
  4. CHAPTER 1 Fertility, Mortality, and Age Distributions: Introduction
    (pp. 3-15)

    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...

  5. CHAPTER 2 The Stable Population
    (pp. 16-60)

    We saw in Chapter 1 that the age distribution of any closed population is wholly determined by the recent history of its fertility and mortality. A helpful device in understanding how age compositions are deter mined is to imagine a history of fertility and mortality schedules that have not changed for many years. If fertility and mortality have been fixed, and remain so, the recent history of the population is unchanging from year to year, and since according to Lopez’ theorem two populations with the same histories have the same age composition, it follows that the age structure must be...

  6. CHAPTER 3 Convergence of a Population to the Stable Form
    (pp. 61-116)

    In discussions of the stable population from Lotka’s pioneering work to the present, and in the related literature on self-renewing aggregates, little attention has been given to analyzing theprocessof convergence from arbitrary initial circumstances to the stable form. Renewal theory, as well as Lotka’s proof that under stipulated conditions a population becomes stable, is concerned with proofs of existence—with the proof of ultimate convergence, not with intermediate states, nor with the duration of the process. The literature on the use of stable population concepts for estimation and other pragmatic purposes has not included a systematic study of...

  7. CHAPTER 4 Population with Fertility That Changes at a Constant Rate
    (pp. 117-151)

    The stable population is a device that displays the implications forage composition, birth rates, death rates, and rates of increase, of specified schedules of fertility and mortality, on the assumption that the schedules prevail long enough for other influences to be erased. In the last chapter the evolution of the population during the disappearance of these other influences was analyzed. In actual fact the stable population is never achieved, and its characteristics are closely approached in actual populations only because of a tendency for certain kinds of demographic change to have limited or self-canceling effects on age composition. A question...

  8. CHAPTER 5 Birth Sequences and Age Distributions with Changing Mortality
    (pp. 152-164)

    In this chapter the age distribution effects of mortality change will be examined by a case study of one form of change—the effects of entering a period of constantly declining mortality after a long history of unchanging mortality. It will be necessary to impose somewhat unrealistic specifications on the nature of the change in mortality, but the general circumstances (major sustained changes in mortality newly initiated) are shared by many populations in low income countries, and the effects on the age distribution are thus of some importance. Much of the argument is closely analogous to that employed in treating...

  9. CHAPTER 6 The Birth Sequence and the Age Distribution That Occur When Fertility Is Subject to Repetitive Fluctuations
    (pp. 165-193)

    In this chapter we continue the examination of the birth sequences and age distributions that result from certain time sequences of change in fertility and mortality. In Chapters 4 and 5 the sequences analyzed were monotonic trends in fertility or mortality; here our attention turns to the eifects of repetitious fluctuations in fertility. Most of the chapter will be devoted to the simplest form of repetitive variation—a pure sine wave. We shall find that a sinusoidal fluctuation in fertility produces fluctuations in births (around an exponential trend) that may be different in magnitude and phase from the fertility fluctuations,...

  10. CHAPTER 7 The Relation Between the Birth Sequence and Sequence of Fertility Schedules in Any Time Pattern Derived by Fourier Analysis
    (pp. 194-205)

    The birth sequences and age distributions resulting from periodic fluctuations in fertility at a single frequency derived in Chapter 6 are highly abstract, since (with the partial and scarcely important excep tion of seasonal variations) such fluctuations have not been recorded in any historical data of which I am aware. In this chapter a method is developed for calculating (by Fourier analysis) the birth sequence resulting from any arbitrary time sequence of fertility change, provided the fertility sequence is of sufficient duration to determine the birth sequence, that the age structure of fertility is fixed, and that mortality is constant....

  11. CHAPTER 8 Conclusion
    (pp. 206-218)

    It is evident even to its author that this book may not be an easy one to read. Its difficulty is not caused primarily by the use of advanced mathematics (it rarely goes beyond the level encountered by a college sophomore studying physics), but because the mathematics may be in fields not familiar to the mathematically inclined social scientist, and because from time to time a series of complicated ideas and interrelations are introduced within a short space. This concluding chapter is intended to restate in less technical form, and in a few instances to extend, some of the important...

    (pp. 219-224)
  13. INDEX
    (pp. 225-227)