Keyfitz N., Caswell H. Applied Mathematical Demography
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Bibliography 545
Stone, R. 1975. Towards a System of Social and Demographic Statistics.
United Nations Statistical Office, Studies in Methods, Series F, No. 18.
Sales No. E. 74, XVII. 8. United Nations, New York, New York, USA.
Stouffer, S.A. 1940. Intervening opportunities: A theory relating mobility
and distance. American Sociological Review 5:845–867.
S¨ussmilch, J.P. 1788 (1941). Die g¨ottliche Ordnung in den Ver¨anderungen
des menschilichen Geschlechts, aus der Geburt, dem Tode und der
Fortpflanzung desselben erwiesen. 3 volumes. Verlag der Buchhandlung
der Realschule, Berlin, Germany.
Sverdrup, E. 1965. Estimates and test procedures in connection with
stochastic models for deaths, recoveries and transfers between different
states of health. Skandinavisk Aktuarietidskrift 40:184–21.
Svirezhev, Y.M. and D.O. Logofet. 1983. Stability of Biological Communi-
tites. Mir Publishers, Moscow, Russia.
Sykes, Z.M. 1969. Some stochastic versions of the matrix model for pop-
ulation dynamics. Journal of the American Statistical Association
64:111–130.
Tabah, L. 1968. Representations matricielles de perspectives de popula-
tion active [Matrix representations of projections of active population].
Population 23:437–476.
Taylor, F. 1979. Convergence to the stable age distribution in populations
of insects. American Naturalist 113:511–530.
Thieme, H.R. 2003. Mathematics in Population Biology. Princeton Univer-
sity Press, Princeton, New Jersey, USA.
Thompson, J.N. and M.E. Moody. 1985. Assessing probability of interac-
tion in size-structured populations:Depressaria attack on Lomatium.
Ecology 66:1597–1607.
Thompson, W.R. 1931. On the reproduction of organisms with overlapping
generations. Bulletin of Entomological Research 22:147–172.
Thonstad, T. 1967. A mathematical model of the Norwegian educational
system. pp. 125–158 in Mathematical Models in Educational Plan-
ning. Technical Report. Organization for Economic Co-operation and
Development, Paris, France.
Tibshirani, R. 1992. Bootstrap hypothesis testing. Biometrics 48:969–970.
Tietze, C. 1962. Pregnancy rates and birth rates. Population Studies 16:31–
37.
Todaro, M.P. 1969. A model of labor migration and urban unemployment
in less developed countries. American Economic Review 59:138–148.
Trussell, J.T. 1977. Determinants of roots of Lotka’s equation. Mathemat-
ical Biosciences 36:213-227.
Tuljapurkar, S.. 1982. Why use population entropy? It determines the rate
on convergence. Journal of Mathematical Biology 13:325–337.
546 Bibliography
Tuljapurkar, S.. 1985. Population dynamics in variable environments. VI.
Cyclical environments. Theoretical Population Biology 28:1–17.
Tuljapurkar, S. 1990. Population Dynamics in Variable Environments.
Springer-Verlag, New York, New York.
Tuljapurkar, S. 1993. Entropy and convergence in dynamics and demogra-
phy. Journal of Mathematical Biology 31:253–271.
Tuljapurkar, S. and H. Caswell. 1997. Structured Population Models in
Marine, Terrestrial, and Freshwater Systems. Chapman and Hall, New
York, New York, USA.
Tuljapurkar, S. and R. Lee. 1997. Demographic uncertainty and the stable
equivalent population. Mathematical and Computer Modelling 26:39–
56.
Tuljapurkar, S.D. and S.H. Orzack. 1980. Population dynamics in vari-
able environments I. Long-run growth rates and extinction. Theoretical
Population Biology 18:314–342.
Tuljapurkar, S., N. Li, and M.W. Feldman. 1995. High sex ratios in China’s
future. Science 267: 874-876.
Trussell, J. and G. Rodr´ıguez. 1990. Heterogeneity in demographic re-
search. Pages 111–132 in J. Adams, D.A. Lam, A.I. Hermalin, and
P.E. Smouse. Convergent Issues in Genetics and Demography. Oxford
University Press, Oxford, UK.
United Nations. 1955. Age and Sex Patterns of Mortality: Model Life Tables
for Underdeveloped Countries. United Nations, New York, New York,
USA.
United Nations. 1963. Determinants and Consequences of Population
Trends. United Nations, New York, New York, USA.
Usher, M.B. 1966. A matrix approach to the management of renewable
resources, with special reference to selection forests. Journal of Applied
Ecology 3:355–367.
Usher, M.B. 1976. Extensions to models, used in renewable resource
management, which incorporate an arbitrary structure. Journal of
Environmental Management 4:123–140.
van Sickle, J. 1977a. Analysis of a distributed-parameter population model
based on physiological age. Journal of Theoretical Biology 64:571–586.
van Sickle, J. 1977b. Mortality rates from size distributions. Oecologia
27:311–318.
van Straalen, N.M. and J.E. Kammenga. 1998. Assessment of ecotoxicity
at the population level using demographic parameters. Pages 621–644
in G. Sch¨u¨urmann and B. Markert, editors. Ecotoxicology. Wiley, New
York, New York, USA.
Vaupel, J.W. 1990. Kindred lifetimes: Frailty models in population ge-
netics. Pages 155–170 in J. Adams, D.A. Lam, A.I. Hermalin, and
Bibliography 547
P.E. Smouse. Convergent Issues in Genetics and Demography. Oxford
University Press, Oxford, UK.
Vaupel, J.W., and A.I. Yashin. 1983. The Deviant Dynamics of Death
in Heterogeneous Populations. Research Report RR-83-1. Laxenburg,
Austria: International Institute for Applied Systems Analysis.
Vaupel J.W. and A.I. Yashin. 1985. Heterogeneity’s ruses: Some surpris-
ing effects of selection on population dynamics. American Statistician.
39:176-85.
Vaupel, J.W. and A.I. Yashin. 1999. Unobserved population heterogeneity.
pp. 345–358 in D´emographie: Analyse et synth`ese. Volume 1. Dipar-
timento di Science Demografiche, Universit`a degli Studi di Roma “La
Sapienza”; Institut national d’´etudes d´emographiques, Rome, Italy.
Vaupel, J.W., K. Manton, and E. Stallard. 1979. The impact of hetero-
geneity in individual frailty on the dynamics of mortality. Demography
16:439–454.
Vaupel, J.W. et al. 1998. Biodemographic trajectories of longevity. Science
280:855–860.
Veltman, C.J., S. Nee, and M.J. Crawley. 1996. Correlates of introduction
success in exotic New Zealand birds. American Naturalist 147:542–557.
Verhulst, P.F. 1838. Notice sur la loi que la population suit dans son ac-
croissement. Correspondence Math´ematique et Physique Publi´ee par
A. Qu´etelet (Brussels) 10:113–121.
Vincent, P. 1945. Potential d’accroissement d’une population stable.
Journal de la Soci´et´e de Statistique de Paris 86:16–29.
von Foerster, H. 1959. Some remarks on changing populations. Pages 382–
407 in F. Stohlman, Jr., editor. The Kinetics of Cellular Proliferation.
Grune and Stratton, New York, New York, USA.
von Foerster, H., P.M. Mora, and L.W. Amiot. 1960. Doomsday: Friday,
13 November, A.D. 2026. Science 132:1291–1295.
Wachter, K.W. 1991. Elusive cycles: Are there dynamically possible Lee-
Easterlin models for U.S. births? Population Studies 45:109–135.
Wachter, K.W. 1997. Kinship resources for the elderly. Philosophical
Transactions of the Royal Society of London B 352:1811–1817.
Wachter, K.W. and R.A. Bulatao. 2003. Offspring: Human Fertility Be-
havior in Biodemographic Perspective. National Academies Press,
Washington, DC, USA.
Wachter, K.W. and C.E. Finch. 1997. Between Zeus and the Salmon: The
Biodemography of Longevity. National Academy Press, Washington,
D.C., USA.
Wachter, K.W. and R.D. Lee. 1989. U.S. births and limit cycle models.
Demography 26:99–115.
548 Bibliography
Wachter, K.W., D. Blackwell, and E.A. Hammel. 1997. Testing the validity
of kinship microsimulation. Journal of Mathematical and Computer
Modeling 26:89–104.
Wagner, C.H. 1982. Simpson’s paradox in real life. The American
Statistician 36:46–48.
Walls, M., H. Caswell, and M. Ketola. 1991. Demographic costs of
Chaoborus-induced defenses in Daphnia pulex: A sensitivity analysis.
Oecologia 87:43–50.
Warner, R.R. and T.P. Hughes. 1988. The population biology of reef fishes.
Proceedings of the Sixth International Coral Reef Symposium 1:149–
155.
Waugh, W.A.O. 1971. Career prospects in stochastic social models
with time-varying rates. Fourth Conference on the Mathematics of
Population. East-West Population Institute, Honolulu, Hawaii.
Weck, F.A. 1947. The mortality rate and its derivation from actual
experience. Record of the American Institute of Actuaries 36:23–54.
Weinberg, C.R. and D.B. Dunson. 2000. Some issues in assessing human
fertility. Journal of the American Statistical Association 95:300–303.
Werner, P.A. and H. Caswell. 1977. Population growth rates and age ver-
sus stage-distribution models for teasel (Dipsacus sylvestris Huds.).
Ecology 58:1103–1111.
Westoff, C.F. and R.R. Rindfuss. 1974. Sex preselection in the United
States: Some implications. Science 184:633–636.
Westoff, C.F., R.G. Potter, Jr., and P.C. Sagi. 1963. The Third Child:
A Study in the Prediction of Fertility. Princeton University, Office of
Population Research, Princeton, New Jersey, USA.
Whelpton, P.K. 1936. An empirical method of calculating future popula-
tion. Journal of the American Statistical Association 31:457–473.
Whelpton, P.K. 1946. Reproduction rates adjusted for age, parity, fecun-
dity, and marriage. Journal of the American Statistical Association
41:501–516.
Wicksell, S.D. 1931. Nuptiality, fertility, and reproductivity. Skandinavisk
Aktuarietidskrift (Stockholm), pp. 125–157.
Widjojo N. 1970. Population Trends in Indonesia. Ithaca, N.Y.: Cornell
University Press.
Wilkinson, J.H. 1965. The Algebraic Eigenvalue Problem. Clarendon Press,
Oxford, UK.
Wilkinson, J.H. and C. Renisch. 1971. Linear Algebra. Springer-Verlag,
New York, New York, USA.
Willekens, F. 1978. The Demography of Labor Force Participation. Re-
search memorandum RM-78-17. Laxenburg, Austria: International
Institute for Applied Systems Analysis.
Bibliography 549
Willekens, F. and A. Rogers. 1977. More Computer Programs for
Spatial Demographic Analysis. Research memorandum RM-77-30.
International Institute for Applied Systems Analysis, Laxenburg,
Austria.
Williams, G.C. 1957. Pleiotropy, natural selection, and the evolution of
senescence. Evolution 11:398–411.
Williams, G.C. 1966. Natural selection, the costs of reproduction, and a
refinement of Lack’s principle. American Naturalist 100:687–690.
Wilson, C. 2004. Fertility below replacement level. Science 304:207–209.
Wilson, E.B. and R.R. Puffer. 1933. Least squares and population growth.
Proceedings of the American Academy of Arts and Sciences 68:285–382.
Wilson, E. O. 1975. Sociobiology: The New Synthesis. Cambridge, Mass.:
Harvard University Press.
Winkler, W. 1959. Wieviele Menschen haben bisher auf der Erde gelebt?
International Population Conference, Vienna, 1959, pp. 73–76. Inter-
national Union for the Scientific Study of Population.
Winsor, C.P. 1932. A comparison of certain symmetrical growth curves.
Journal of the Washington Academy of Sciences 22:73–84.
Wolf, D.A. 2001. The role of microsimulation in longitudinal data analysis.
Canadian Studies in Population 28:313–339.
Wolf, S.L., H.X. Barnhart, et al. 1996. Reducing frailty and falls in older
persons: An investigation of tai chi and computerized balance training.
Journal of the American Geriatric Society 44:489.
Wolfenden, H. H. 1925 (rev. ed. 1954). Population Statistics and Their
Compilation. University of Chicago Press, Chicago, Illinois, USA.
Wood, J.W. 1994. Dynamics of Human Reproduction: Biology, Biometry,
Demography.deGruyter,NewYork,NewYork,USA.
Wood, J.W. and M. Weinstein. 1990. Heterogeneity in fecundability: The
effect of fetal loss. Pages 171–188 in J. Adams, D.A. Lam, A.I. Her-
malin, and P.E. Smouse (editors) Convergent Issues in Genetics and
Demography. Oxford University Press, New York, New York, USA.
Wood, J.W., D.J. Holman, K.M. Weiss, A.V. Buchanan, and B. Lefor. 1992.
Hazards models for human population biology. Yearbook of Physical
Anthropology 35:43–87.
Wood, J.W., D.J. Holman, A.I. Yashin, R.S. Peterson, M. Weinstein, and
M.-C. Chang. 1994. A multistate model of fecundability and sterility.
Demography 31:403–426.
Wu, L.S.Y. and D.B. Botkin. 1980. Of elephants and men—a discrete,
stochastic model for long-lived species with complex life histories.
American Naturalist 116:831–849.
Wunsch, G. 1966. Courbes de Gompertz et perspectives de f´econdit´e.
Recherches Economiques (Louvain) 32:457–468.
550 Bibliography
Yashin, A.I. and I.A. Iachine. 1997. How frailty models can be used for
evaluating longevity limits: Taking advantage of an interdisciplinary
approach. Demography 34:31–48.
Yashin, A.I., J.W. Vaupel, and I.A. Iachine. 1994. A duality in aging: The
equivalence of mortality models based on radically different concepts.
Mechanisms of Ageing and Development 74:1–14.
Yashin, A.I., I.A. Iachine, K.F. Andreev, and U. Larsen. 1998. Multistate
models of postpartum infecundity, fecundability and sterility by age
and parity: Methodological issues. Mathematical Population Studies
7:51–78.
Yule, G. U. 1906. Changes in the marriage and birth rates in England and
Wales during the past half century. Journal of the Royal Statistical
Society 68:18–132.
Zelinsky, W. 1971. The hypothesis of the mobility transition. Geographical
Review 46:219–249.
Index
abortion
births prevented by, 408
absorbing Markov chain, 240, 248
age at first reproduction, 258
age at marriage, 225
age-classified model
characteristic equation, 149
elasticity of eigenvalues, 317
fertility
birth-flow, 56
birth-pulse, 60
from stage-classified model, 256
from life table, 55
generation time, 264
reproductive value, 210
right eigenvector, 161
sensitivity of eigenvalues, 306
stable age distribution, 93, 161
survival
birth-flow, 55
birth-pulse, 58
from stage-classified model, 255
age-within-stage distribution, 266
annuity, 41
arc, 67
assumptions, 62
asymptotic analysis, 54
backward projection, 348
Bayesian estimation, 488
birth interval, 400
birth-flow, 55
fertilities, 56
survival probabilities, 55
birth-pulse, 55
fertilities, 60
survival probabilities, 58
black-legged kittiwake
heterogeneity, 489
bone fractures, 252
branching process, 210, 293, 427
Calathea ovandensis
population momentum, 173
changing birth rates, 341
characteristic equation, 128
age-classified model, 149
and convergence, 353
implicit differentiation of, 305
Cohen’s cumulative distance, 170
competing causes of death, 42
complex roots, 179
constraints, 312
contraception
births averted by, 399
552 Index
effect on rate of increase, 191
cross-sectional relations
versus longitudinal, 285
cumulant
generating function, 120, 218
cumulants, 104, 133
damping ratio, 165
age-classified, 352
human populations, 167, 352
insects, 167
multiregional models, 167
stage-classified models, 167
data
interpretation of, ix
demographic stochasticity
and branching processes, 293
demographic transition, 23
dependency ratio, 223, 500
desert tortoise
elasticity of eigenvalues, 320, 321
matrix for, 304
sensitivity of eigenvalues, 308, 312
development
effect on population growth, 505
diagonalizability, 264
difference equation, 179
Dipsacus sylvestris, see teasel
disease
effect of eliminating, 199
effect on rate of increase, 143
doubling time, 3
Easterlin effect, 288, 366
as a nonlinear model, 368
economic hierarchies, 243
educational organizations, 361
eigenvalue
and rate of increase r, 179
dominant, 159
as population growth rate, 160
elastcity of, 317
in solution of projection equation,
148
sensitivity of, 305
subdominant, 165, 166
eigenvector, see left eigenvector, see
right eigenvector
elasticity
matrix, 317
of eigenvalues
as contributions to growth rate,
319
in age-classified models, 317
in desert tortoise, 320, 321
in teasel, 320
to lower-level parameters, 320
to matrix entries, 317
emigration
as a policy, 194
one-time departure, 190
entropy, 80, 166
environmental stochasticity, 512
ergodic theorem
strong, 155
ergodicity, 54
Euler’s theorem, 319
expectation of life, 30, 71, 339, 447
effect of mortality change, 78
from Markov chain, 256
multi-state, 452
family
defined, 462
family life cycle, 469
family size, 228
fecundity, 50
measurement of, 410
Gini index, 418, 478
Pearl index, 414
female dominance, 129
fertility, 50
and fecundity, 410
age-specific, 256
life table methods, 423
replacement level, 426
forecast
interval estimates, 301
quality of, 297
vs. projection, 63
forecasting
and projection, 269
extrapolation versus mechanism,
288
fraction of young and old, 217
frailty, 482
age-dependent, 491
continuous distribution of, 486
Index 553
fundamental matrix, 240, 249
Galton-Watson process, see branching
process
generalized inverse, 348
generation time, 264
Gini index, 418
Gopherus agassizii, see desert tortoise
H, 80, 102, 339
heterogeneity, 477
in fecundity, 414, 417
and Simpson’s paradox, 479
in frailty, 482
in mortality, 91
in rate of increase, 13, 483
Markov chain Monte Carlo
methods, 489
homogeneous function, 319
household, 462
size distribution, 471
human population
sensitivity of eigenvectors, 324
human populations
damping ratio, 167
eigenvalues of, 154
elasticity of eigenvalues, 317
i-state, 64
imprimitive matrix, 162
insurance, 41
irreducible matrix, 156
Keyfitz’s ∆, 170
killer whale
age-specific survivorship, 256
inter-pod variance in λ, 330
life cycle graph for, 68
life expectancy of, 256
LTRE, 330
Markov chain decomposition, 247
stable equivalent population, 213
left eigenvector
in solution of projection equation,
148
reproductive value, 208
Leslie matrix, 49, see age-classified
model
Lexis diagram, 39, 97
life cycle graph, 67
life table, 29, 55
cause of death eliminated, 42, 279
multi-state, 445
multiple decrement, 45
period and cohort, 40
life table response experiment, see
LTRE
lifetime event probabilities, 251
living father and mother
probability, 465
logistic population growth, 20
logit transform, 284, 489
Lomatium grayi
probability of attack, 251
longitudinal relations
versus cross-sectional, 285
loop, 156
Lotka integral equation, 176
LTRE, 325
fixed design, 327
random design, 329
regression design, 332
Markov chain
absorbing, 248
as model of life cycle, 246
fundamental matrix of, 249
marriage, 227
duration of, 234
Matlab, ix, 175
matrix
diagonalizable, 264
elasticity, 317
fundamental, 249
imprimitive
population growth, 162
irreducible, 156
Leslie, see Leslie matrix
primitive, 157
reducible, 156
population growth, 163
McKendrick–von Foerster equation,
180
mean age of childbearing, 207
microdemography, 399
migration, 237
model fertility tables, 284
554 Index
model life table, 95, 101
momentum, 172, 196, 281
mortality
male and female, 72
multi-regional model
convergence, 168
multiregional models, 237
net reproductive rate, 128, 183, 440,
447
multi-regional, 454
stage-classified, 262
node, 67
nonlinear models, 368
notation, xxv
Orcinus orca, see killer whale
organizations
demography of, 241
educational
demography of, 361
promotion in, 121, 365, 501
voting in, 242
p-state, 64
parity progression, 440
partial differential equation, 180
path, 156
Pearl index, 417
pension, 118
pensions, 358
period of oscillation, 169, 179
Perron–Frobenius theorem, 156, 159
perturbation analysis, 55
polychaete
LTRE, 328
population growth rate, see
eigenvalue, see rate of increase
dominant eigenvalue as measure of,
160
population momentum, 172
power method, 175
prediction, see forecast
primitive matrix, 157
projection, 200, 268
age-classified matrix model, 272
and forecasting, 269, 288
backward, 348
errors, 292
longitudinal and cross-sectional,
285
multi-state, 455
multi-state models, 275
relational methods, 283
simple versus complex models, 276
vs. forecasting, 63
projection interval, 49, 67
promotion, see organizations
prospective perturbation analysis, 333
quasi-stable population, 335
R
0
, see net reproductive rate
rate of increase, 2, see population
growth rate
age,parity, and nuptiality, 231
and age distribution, 494
and parity progression, 440
and promotion, 121
changing over time, 18
continuous and discrete, 179
effect of development, 505
effect of disease, 143
estimated from age distribution,
107
estimation from one census, 97
from characteristic equation, 128
instantaneous, 5
iterative calculation, 130
reducible matrix, 163
reproductive value, 206
age-specific, 185, 210
and extinction, 209
and sensitivity, 316
as an eigenvector, 208
from Lotka integral equation, 185
from the life cycle graph, 212
stage-specific, 211
retrospective perturbation analysis,
333
right eigenvector
age-classified model, 161
as stable population structure, 161
in solution of projection equation,
148
self-loop, 67, 156
senescence, 306