Applied Mathematical Demography

by Keyfitz, Nathan; Caswell, Hal

• ISBN13: 9780387225371
• ISBN10: 0387225374
• eBook ISBN(s): 9780387274096
• Edition: 3rd
• Format: Hardcover
• Copyright: 2005-01-30
• Publisher: Springer Nature
• More Book Details
• Purchase Benefits

Summary

The third edition of this classic text maintains its focus on applications of demographic models, while extending its scope to matrix models for stage-classified populations. The authors first introduce the life table to describe age-specific mortality, and then use it to develop theory for stable populations and the rate of population increase. This theory is then revisited in the context of matrix models, for stage-classified as well as age-classified populations. Reproductive value and the stable equivalent population are introduced in both contexts, and Markov chain methods are presented to describe the movement of individuals through the life cycle. Applications of mathematical demography to population projection and forecasting, kinship, microdemography, heterogeneity, and multi-state models are considered. The new edition maintains and extends the book's focus on the consequences of changes in the vital rates. Methods are presented for calculating the sensitivity and elasticity of population growth rate, life expectancy, stable stage distribution, and reproductive value, and for applying those results in comparative studies. Stage-classified models are important in both human demography and population ecology, and this edition features examples from both human and non-human populations. In short, this third edition enlarges considerably the scope and power of demography. It will be an essential resource for students and researchers in demography and in animal and plant population ecology. From the reviews: "If you found the original editions...to be excellent (and who amoung us has not?) then you will find the new edition to be equally so...This book is highly and unreservedly recommended for any beginning mathematical demographer." Mathematical Population Studies, 12:223-228, 2005 "The material in the second edition is retained, although the chapters are reorganized and references are updated. New chapters focusing on matrix population models are seamlessly interwoven with the second edition chapters, resulting in a thorough and comprehensive treatment of human, animal, and nonhuman demography." Journal of the American Statistical Association, December 2005

Author Biography

Hal Caswell is a Senior Scientist in the Biology Department of the Woods Hole Oceanographic Institution, where he holds the Robert W. Morse Chair for Excellence in Oceanography.

Table of Contents

Preface to the Third Edition	vii
Preface to the Second Edition	xi
Preface to the First Edition	xiii
Acknowledgments	xvii
A Word About Notation	xxv
1 Introduction: Population Without Age	1	(28)
1.1 Definitions of Rate of Increase	2	(1)
1.2 Doubling Time and Half-Life	3	(6)
1.3 One-Sex Versus Two-Sex Models: Descendants of the Pilgrim Fathers	9	(2)
1.4 How Many People Have Lived on the Earth?	11	(2)
1.5 A Mixture of Populations Having Different Rates of Increase	13	(5)
1.6 Rate of Increase Changing over Time	18	(2)
1.7 Logistic Increase and Explosion	20	(3)
1.8 The Stalled Demographic Transition	23	(2)
1.9 Differential Fertility Due to the Demographic Transition	25	(1)
1.10 Matrices in Demography	26	(3)
2 The Life Table	29	(19)
2.1 Definition of Life Table Functions	29	(2)
2.2 Life Tables Based on Data	31	(8)
2.3 Further Small Corrections	39	(1)
2.4 Period and Cohort Tables	40	(1)
2.5 Financial Calculations	41	(1)
2.6 Cause-Deleted Tables and Multiple Decrement	42	(4)
2.7 The Life Table as a Unifying Technique in Demography	46	(2)
3 The Matrix Model Framework	48	(23)
3.1 The Leslie Matrix	49	(2)
3.2 Projection: The Simplest Form of Analysis	51	(4)
3.3 The Leslie Matrix and the Life Table	55	(7)
3.4 Assumptions: Projection Versus Forecasting	62	(2)
3.5 State Variables and Alternatives to Age-Classification	64	(1)
3.6 Age as a State Variable: When Does it Fail?	65	(2)
3.7 The Life Cycle Graph	67	(2)
3.8 The Matrix Model	69	(2)
4 Mortality Comparisons; The Male-Female Ratio	71	(22)
4.1 The Multiplicity of Index Numbers	73	(3)
4.2 Should We Index Death Rates or Survivorships?	76	(2)
4.3 Effect on e0 of Change in μ(χ)	78	(10)
4.4 Everybody Dies Prematurely	88	(5)
5 Fixed Regime of Mortality and Fertility	93	(34)
5.1 Stable Theory	94	(3)
5.2 Population Growth Estimated from One Census	97	(6)
5.3 Mean Age in the Stable Population	103	(4)
5.4 Rate of Increase from the Fraction Under 25	107	(2)
5.5 Birth Rate and Rate of Increase Estimated for a Stable Population	109	(2)
5.6 Several Ways of Using the Age Distribution	111	(7)
5.7 Sensitivity Analysis	118	(3)
5.8 Promotion Within Organizations	121	(6)
6 Birth and Population Increase from the Life Table	127	(21)
6.1 The Characteristic Equation	128	(5)
6.2 A Variant Form of the Characteristic Equation	133	(2)
6.3 Perturbation Analysis of the Intrinsic Rate	135	(3)
6.4 Arbitrary Pattern of Birth Rate Decline	138	(3)
6.5 Drop in Births Required to Offset a Drop in Deaths	141	(3)
6.6 Moments of Dying and Living Populations	144	(4)
7 Birth and Population Increase from Matrix Population Models	148	(35)
7.1 Solution of the Projection Equation	148	(7)
7.2 The Strong Ergodic Theorem	155	(10)
7.3 Transient Dynamics and Convergence	165	(10)
7.4 Computation of Eigenvalues and Eigenvectors	175	(1)
7.5 Mathematical Formulations	176	(7)
8 Reproductive Value from the Life Table	183	(25)
8.1 Concept of Reproductive Value	184	(6)
8.2 Ultimate Effect of Small Out-Migration Occurring in a Given Year	190	(1)
8.3 Effect of Continuing Birth Control and Sterilization	191	(2)
8.4 Large Change in Regime	193	(1)
8.5 Emigration as a Policy Applied Year After Year	194	(2)
8.6 The Momentum of Population Growth	196	(3)
8.7 Eliminating Heart Disease	199	(1)
8.8 The Stable Equivalent	200	(6)
8.9 Reproductive Value as a Contribution to Future Births	206	(2)
9 Reproductive Value from Matrix Models	208	(8)
9.1 Reproductive Value as an Eigenvector	208	(5)
9.2 The Stable Equivalent Population	213	(3)
10 Understanding Population Characteristics	216	(29)
10.1 Accounting for Age Distribution	217	(6)
10.2 More Women Than Men	223	(2)
10.3 Age at Marriage	225	(11)
10.4 The Foreign-Born and Internal Migrants	236	(2)
10.5 Human Stocks and Flows	238	(3)
10.6 The Demography of Organizations	241	(4)
11 Markov Chains for Individual Life Histories	245	(23)
11.1 A = T + F	245	(6)
11.2 Lifetime Event Probabilities	251	(2)
11.3 Age-Specific Traits From Stage-Specific Models	253	(15)
12 Projection and Forecasting	268	(35)
12.1 Unavoidable and Impossible	268	(4)
12.2 The Technique of Projection	272	(6)
12.3 Applications of Projection	278	(4)
12.4 The Search for Constancies	282	(5)
12.5 Features of Forecasting and Forecasting Error	287	(5)
12.6 The Components of Forecasting Error Ex Ante	292	(4)
12.7 Ex Post Evaluation of Point Estimates	296	(3)
12.8 A Division of Labor	299	(2)
12.9 Interval Estimates as Currently Provided	301	(2)
13 Perturbation Analysis of Matrix Models	303	(32)
13.1 Eigenvalue Sensitivity	305	(12)
13.2 Elasticity Analysis	317	(4)
13.3 Sensitivities of Eigenvectors	321	(4)
13.4 Life Table Response Experiments	325	(2)
13.5 Fixed Designs	327	(2)
13.6 Random Designs and Variance Decomposition	329	(3)
13.7 Regression Designs	332	(1)
13.8 Prospective and Retrospective Analyses	333	(2)
14 Some Types of Instability	335	(35)
14.1 Absolute Change in Mortality the Same at All Ages	335	(3)
14.2 Proportional Change in Mortality	338	(3)
14.3 Changing Birth Rates	341	(2)
14.4 Announced Period Birth Rate Too High	343	(5)
14.5 Backward Population Projection	348	(4)
14.6 The Time to Stability	352	(6)
14.7 Retirement Pensions	358	(3)
14.8 The Demography of Educational Organization	361	(2)
14.9 Two Levels of Students and Teachers	363	(2)
14.10 Mobility in an Unstable Population	365	(1)
14.11 The Easterlin Effect	366	(4)
15 The Demographic Theory of Kinship	370	(29)
15.1 Probability of Living Ancestors	372	(7)
15.2 Descendants	379	(2)
15.3 Sisters and Aunts	381	(5)
15.4 Mean and Variance of Ages	386	(1)
15.5 Changing Rates of Birth and Death	387	(1)
15.6 Sensitivity Analysis	388	(6)
15.7 Deriving Rates from Genealogies	394	(2)
15.8 Incest Taboo and Rate of Increase	396	(1)
15.9 Bias Imposed by Age Difference	397	(2)
16 Microdemography	399	(45)
16.1 Births Averted by Contraception	399	(11)
16.2 Measurement of Fecundity	410	(15)
16.3 Three-Child Families Constitute a Population Explosion	425	(2)
16.4 A Family-Building to Avoid Extinction	427	(3)
16.5 Sex Preference and the Birth Rate	430	(3)
16.6 Parental Control over Sex of Children	433	(6)
16.7 Mean Family Size from Order-of-Birth Distribution	439	(1)
16.8 Parity Progression	440	(1)
16.9 Lower Mortality and Increase	441	(3)
17 The Multi-State Model	444	(17)
17.1 Single Decrement and Increment-Decrement	446	(3)
17.2 The Kolmogorov Equation	449	(3)
17.3 Expected Time in the Several States	452	(3)
17.4 Projection	455	(1)
17.5 Transition Versus Instantaneous Probability of Moving	456	(3)
17.6 Stable Population	459	(2)
18 Family Demography	461	(16)
18.1 Definitions	462	(2)
18.2 Kinship	464	(5)
18.3 The Life Cycle	469	(2)
18.4 Household Size Distribution	471	(3)
18.5 Economic, Political, and Biological Theory	474	(1)
18.6 Family Policy	475	(2)
19 Heterogeneity and Selection in Population Analysis	477	(17)
19.1 Conditioning and the Interpretation of Statistical Data	479	(2)
19.2 Heterogeneity and Selection	481	(1)
19.3 Application to Mortality	482	(4)
19.4 Modelling Heterogeneity	486	(6)
19.5 Experimentation	492	(2)
20 Epilogue: How Do We Know the Facts of Demography?	494	(19)
20.1 Proportions of Old People	496	(5)
20.2 Promotion in Organizations	501	(2)
20.3 No Model, No Understanding	503	(1)
20.4 Too Many Models	504	(1)
20.5 Development and Population Increase	504	(4)
20.6 How Nature Covers Her Tracks	508	(2)
20.7 The Psychology of Research	510	(3)
Bibliography	513	(38)
Index	551