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By N. Keyfitz, Hal Caswell

ISBN-10: 0387225374

ISBN-13: 9780387225371

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Extra info for Applied Mathematical Demography, Third Edition (Statistics for Biology and Health)

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But this simplicity of the backward process is more than offset by intermarriage. Demography must transcend the detail of family trees, just as macroeconomics must aggregate the detail of individual transactions. The various sections of this book can be thought of as different ways of summarizing genealogies for the purpose of drawing conclusions on populations. A useful summarizing device is to consider only one sex at a time. A large part of our work will treat only the female side of the population, or only the male side.

5 A Mixture of Populations Having Different Rates of Increase A population of initial size Q growing at rate r numbers Qert at time t, r being taken as fixed and the population as homogeneous. Now suppose heterogeneity—a number of subpopulations, of which the ith is initially Qi growing at rate ri , so that at time t the total number is N (t) = i Qi eri t . We will show that the total never stabilizes, that its rate of increase forever increases, and that the composition constantly changes. The definition of rate of increase over a finite time δ may be written as 1 N (t + δ) − N (t) , N (t) δ and in the limit as δ tends to zero this becomes 1 dN (t) .

If it is decreasing at constant rate µ, as will be the case if it is closed and subject to a constant death rate µ, and it numbers lx at the start, then at the end of 5 years it will be lx+5 = lx e−5µ , as in the preceding section. 1) as a first approximation to the desired ratio lx+5 /lx . 81274. l65 This would be exact if either (a) the death rate were constant through the 5-year age interval, or (b) the population exposed to risk were constant through the 5-year age interval. Neither of these, however, applies in practice; in general, beyond age 10 the death rate is increasing through the interval and the population is diminishing.

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Applied Mathematical Demography, Third Edition (Statistics for Biology and Health) by N. Keyfitz, Hal Caswell

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