Volume 49 - Article 13 | Pages 309–354  

The contributions of stochastic demography and social inequality to lifespan variability

By Hal Caswell

References

Aitken, A.C. (1949). Statistical Mathematics. London: Oliver and Boyd.

Download reference:

Anderson, E.S. (1999). What is the point of equality? Ethics 109(2): 287–337.

Weblink:
Download reference:

Atkinson, A.B. (2015). Inequality: What can be done? Harvard University Press.

Weblink:
Download reference:

Bernstein, S.F., Rehkopf, D., Tuljapurkar, S., and Horvitz, C.C. (2018). Poverty dynamics, poverty thresholds and mortality: An age-stage Markovian model. PloS One 13(5): e0195734.

Weblink:
Download reference:

Borges, J.L. (1962). The Babylon lottery. In: Kerrigan, A. (ed.). Ficciones. New York: Grove Press: 65–72.

Download reference:

Braveman, P., Krieger, N., and Lynch, J. (2000). Health inequalities and social inequalities in health. Bulletin of the World Health Organization 78(2): 232–235.

Download reference:

Cam, E., Aubry, L.M., and Authier, M. (2016). The conundrum of heterogeneities in life history studies. Trends in Ecology and Evolution 31: 872–886.

Weblink:
Download reference:

Cam, E., Gimenez, O., Alpizar-Jara, R., Aubry, L.M., Authier, M., Cooch, E.G., Koons, D.N., Link, W.A., Monnat, J.Y., and Nichols, J.D. (2013). Looking for a needle in a haystack: Inference about individual fitness components in a heterogeneous population. Oikos 122(5): 739–753.

Weblink:
Download reference:

Carey, J.R. (1993). Applied demography for biologists: With special emphasis on insects. New York: Oxford University Press.

Download reference:

Carey, J.R. (2003). Longevity: The biology and demography of life span. Princeton, NJ: Princeton University Press.

Weblink:
Download reference:

Carey, J.R., Liedo, P., and Vaupel, J.W. (1995). Mortality dynamics of density in the Mediterranean fruit fly. Experimental Gerontology 30: 605–629.

Weblink:
Download reference:

Carey, J.R., Liedo, P., Xu, C., Wang, J.L., Müller, H.G., Su, Y.R., and Vaupel, J.W. (2016). Diet shapes mortality response to trauma in old tephritid fruit flies. PLoS ONE 11(7): e0158468.

Weblink:
Download reference:

Caswell, H. (2014). A matrix approach to the statistics of longevity in heterogeneous frailty models. Demographic Research 31(19): 553–592.

Weblink:
Download reference:

Caswell, H. (2011). Beyond R0: Demographic models for variability of lifetime reproductive output. PloS ONE 6(6): e20809.

Weblink:
Download reference:

Caswell, H. (2012). Matrix models and sensitivity analysis of populations classified by age and stage: A vec-permutation matrix approach. Theoretical Ecology 5(3): 403–417.

Weblink:
Download reference:

Caswell, H. (2009). Stage, age and individual stochasticity in demography. Oikos 118(12): 1763–1782.

Weblink:
Download reference:

Caswell, H. and Daalen, S.F. (2021). Healthy longevity from incidence-based models: More kinds of health than stars in the sky. Demographic Research 45(13): 397–452.

Weblink:
Download reference:

Caswell, H. and Ouellette, N. (eds.) (2016). Mortality and causes of death: Matrix formulation and sensitivity analysis. Mainz, Germany (European Population Conference 2016).

Weblink:
Download reference:

Caswell, H., Verdery, A., and Margolis, R. (2023). The formal demography of kinship V: Kin loss, bereavement, and causes of death.

Weblink:
Download reference:

Caswell, H., Vries, C., Hartemink, N., Roth, G., and Daalen, S. F. (2018). Age×stage-classified demographic analysis: A comprehensive approach. Ecological Monographs 88(4): 560–584.

Weblink:
Download reference:

Caswell, H. and Zarulli, V. (2018). Matrix methods in health demography: a new approach to the stochastic analysis of healthy longevity and DALYs. Population Health Metrics 16: 8.

Weblink:
Download reference:

Chetty, R., Stepner, M., Abraham, S., Lin, S., Scuderi, B., Turner, N., Bergeron, A., and Cutler, D. (2016). The association between income and life expectancy in the United States, 2001‒2014. Journal of the American Medical Association 315(16): 1750–1766.

Weblink:
Download reference:

Chiang, C.L. (1979). Life table and mortality analysis. World Health Organization.

Download reference:

Clutton-Brock, T.H. (1988). Reproductive success: Studies of individual variation in contrasting breeding systems. Chicago, IL: University of Chicago Press.

Download reference:

Colchero, F., Rau, R., Jones, O.R., Barthold, J.A., Conde, D.A., Lenart, A., Nemeth, L., Scheuerlein, A., Schoeley, J., and Torres, C. (2016). The emergence of longevous populations. Proceedings of the National Academy of Sciences 113(48): 7681–7690.

Weblink:
Download reference:

Edwards, R.D. (2011). Changes in world inequality in length of life: 1970–2000. Population and Development Review 37(3): 499–528.

Weblink:
Download reference:

Edwards, R.D. and Tuljapurkar, S. (2005). Inequality in life spans and a new perspective on mortality convergence across industrialized countries. Population and Development Review 31(4): 645–674.

Weblink:
Download reference:

Ekeland, I. (1993). The broken dice, and other mathematical tales of chance. Chicago, IL: University of Chicago Press.

Download reference:

Falconer, D.S. (1981). Introduction to quantitative genetics. New York: Longman.

Download reference:

Fisher, R.A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh 52(2): 399–433.

Weblink:
Download reference:

Fries, J.F. (1980). Aging, natural death, and the compression of morbidity. New England Journal of Medicine 303(3): 130–135.

Weblink:
Download reference:

Frühwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. New York: Springer.

Download reference:

Gakidou, E. and King, G. (2002). Measuring total health inequality: Adding individual variation to group-level differences. International Journal for Equity in Health 1(1): 3.

Weblink:
Download reference:

Gakidou, E.E., Murray, C.J.L., and Frenk, J. (2000). Defining and measuring health inequality: An approach based on the distribution of health expectancy. Bulletin of the World Health Organization 78: 42–54.

Download reference:

Galton, F. (1877). Typical laws of heredity. Nature 15: 492–495.

Weblink:
Download reference:

Goodman, L.A. (1969). The analysis of population growth when the birth and death rates depend upon several factors. Biometrics 25: 659–681.

Weblink:
Download reference:

Hacking, I. (1990). The taming of chance. Cambridge, UK: Cambridge University Press.

Weblink:
Download reference:

Hartemink, N. and Caswell, H. (2018). Variance in animal longevity: contributions of heterogeneity and stochasticity. Population Ecology 60: 89–99.

Weblink:
Download reference:

Hartemink, N., Missov, T.I., and Caswell, H. (2017). Stochasticity, heterogeneity, and variance in longevity in human populations. Theoretical Population Biology 114: 107–117.

Weblink:
Download reference:

Heyde, C.C., Seneta, E., and Bienayme, J. (1977). I. J. Bienayme: Statistical theory anticipated. New York: Springer.

Weblink:
Download reference:

Howard, R.A. (1960). Dynamic programming and Markov processes. New York: Wiley.

Download reference:

Jenouvrier, S., Aubry, L.M., Barbraud, C., Weimerskirch, H., and Caswell, H. (2018). Interacting effects of unobserved heterogeneity and individual stochasticity in the life cycle of the Southern fulmar. Journal of Animal Ecology 87: 212–222.

Weblink:
Download reference:

Kendall, B.E. and Fox, G.A. (2003). Unstructured individual variation and demographic stochasticity. Conservation Biology 17(4): 1170–1172.

Weblink:
Download reference:

Kendall, B.E., Fox, G.A., Fujiwara, M., and Nogeire, T.M. (2011). Demographic heterogeneity, cohort selection, and population growth. Ecology 92(10): 1985–1993.

Weblink:
Download reference:

Kirk, R.E. (1968). Experimental design: Procedures for the behavioral sciences. Belmont, CA: Wadsworth.

Download reference:

Krainacker, D.A. (1986). Demography of the Mediterranean fruit fly: Larval host effects. Davis, California, USA: University of California Davis.

Download reference:

Krainacker, D.A., Carey, J.R., and Vargas, R.I. (1987). Effect of larval host on life history traits of the Mediterranean fruit fly, Ceratitis capitata. Oecologia 73(4): 583–590.

Weblink:
Download reference:

Lewontin, R.C. (1972). The apportionment of human diversity. Evolutionary Biology 6: 381–398.

Weblink:
Download reference:

Li, L., Fa, W., Rui, J., Jian-Ming, H., and Yan, J. (2010). A new car-following model yielding log-normal type headways distributions. Chinese Physics B 19(2): 020513.

Weblink:
Download reference:

Lorenz, E.N. (1993). The essence of chaos. Seattle: University of Washington Press.

Weblink:
Download reference:

Luy, M., Wegner-Siegmundt, C., Wiedemann, A., and Spijker, J. (2015). Life expectancy by education, income and occupation in Germany: Estimations using the longitudinal survival method. Comparative Population Studies 40(4): 339–436.

Weblink:
Download reference:

Marescot, L., Benhaiem, S., Gimenez, O., Hofer, H., Lebreton, J.D., Olarte-Castillo, X.A., Kramer-Schadt, S., and East, M.L. (2018). Social status mediates the fitness costs of infection with canine distemper virus in Serengeti spotted hyenas. Functional Ecology 32(5): 1237–1250.

Weblink:
Download reference:

McLachlan, G. and Peel, D. (2004). Finite mixture models. New York: Wiley.

Download reference:

Murray, C.J.L., Gakidou, E.E., and Frenk, J. (2000). Response to P. Braveman et al. Bulletin of the World Health Organization 78(2): 236–237.

Download reference:

National Academies of Sciences, Engineering, and Medicine, (2023). Using population descriptors in genetics and genomics research: A new framework for an evolving field. Washington, DC: The National Academies Press.

Download reference:

Németh, L. (2017). Life expectancy versus lifespan inequality: A smudge or a clear relationship? PLoS One 12(9): e0185702.

Weblink:
Download reference:

Permanyer, I., Sasson, I., and Villavicencio, F. (2023). Group- and individual-based approaches to health inequality: towards an integration. Journal of the Royal Statistical Society Series A: Statistics in Society 0: 1–24.

Download reference:

Permanyer, I. and Scholl, N. (2019). Global trends in lifespan inequality: 1950–2015. PLoS ONE 14(5): e0215742.

Weblink:
Download reference:

Peters, T.M. and Barbosa, P. (1977). Influence of population density on size, fecundity, and developmental rate of insects in culture. Annual Review of Entomology 22(1): 431–450.

Weblink:
Download reference:

Piketty, T. and Saez, E. (2014). Inequality in the long run. Science 344(6186): 838–843.

Weblink:
Download reference:

Pinder, J.E., Wiener, J.G., and Smith, M.H. (1978). The Weibull distribution: A new method of summarizing survivorship data. Ecology 59(1): 175–179.

Weblink:
Download reference:

Popper, K.R. (1982). The Open Universe: An argument for indeterminism. From the postscript to the Logic of Scientific Discovery (1956). Totowa, NJ: Rowman and Littlefield.

Download reference:

Rényi, A. (1970). Probability theory. Amsterdam: North-Holland.

Download reference:

Robert, A., Sarrazin, F., and Couvet, D. (2003). Variation among individuals, demographic stochasticity, and extinction: Response to Kendall and Fox. Conservation Biology 17(4): 1166–1169.

Weblink:
Download reference:

Rosenbluth, G. (1951). Note on Mr. Schutz’s measure of income inequality. The American Economic Review 41(5): 935–937.

Download reference:

Salguero-Gómez, R., Jones, O.R., Archer, C.R., Bein, C., Buhr, H., Farack, C., Gottschalk, F., Hartmann, A., Henning, A., Hoppe, G., Romer, G., Ruoff, T., Sommer, V., Wille, J., Voigt, J., Zeh, S., Vieregg, D., Buckley, Y.M., Che-Castaldo, J., Hodgson, D., Scheuerlein, A., Caswell, H., and Vaupel, J.W. (2016). Comadre: A global data base of animal demography. Journal of Animal Ecology 85(2): 371–384.

Weblink:
Download reference:

Salguero-Gómez, R., Jones, O.R., Archer, C.R., Buckley, Y.M., Che-Castaldo, J., Caswell, H., Hodgson, D., Scheuerlein, A., Conde, D.A., and Brinks, E. (2015). The COMPADRE Plant Matrix Database: An open online repository for plant demography. Journal of Ecology 103(1): 202–218.

Weblink:
Download reference:

Schneider, D.C., Myrskylä, M., and van Raalte, A. (2023). Flexible transition timing in discrete-time multistate life tables using Markov chains with rewards. Population Studies (Population Studies (in press).).

Weblink:
Download reference:

Seaman, R., Riffe, T., and Caswell, H. (2019). The changing contribution of area-level deprivation to total variance in age at death: A population based decomposition analysis. BMJ Open 9(3): e024952.

Weblink:
Download reference:

Seligman, B., Greenberg, G., and Tuljapurkar, S. (2016). Equity and length of lifespan are not the same. Proceedings of the National Academy of Sciences 113(30): 8420–8423.

Weblink:
Download reference:

Sen, A. (1992). Inequality reexamined. Oxford, U.K: Clarendon Press.

Download reference:

Sheskin, T.J. (2010). Markov chains and decision processes for engineers and managers. CRC Press.

Download reference:

Smits, J. and Monden, C. (2009). Length of life inequality around the globe. Social Science and Medicine 68(6): 1114–1123.

Weblink:
Download reference:

Snyder, R.E. and Ellner, S.P. (2018). Pluck or luck: Does trait variation or chance drive variation in lifetime reproductive success? The American Naturalist 191(4): 90–107.

Weblink:
Download reference:

Snyder, R.E. and Ellner, S.P. (2016). We happy few: using structured population models to identify the decisive events in the lives of exceptional individuals. The American Naturalist 188(2): 28–45.

Weblink:
Download reference:

Steiner, U.K. and Tuljapurkar, S. (2012). Neutral theory for life histories and individual variability in fitness components. Proceedings of the National Academy of Sciences 109(12): 4684–4689.

Weblink:
Download reference:

Steiner, U.K., Tuljapurkar, S., and Coulson, T. (2014). Generation time, net reproductive rate, and growth in stage-age-structured populations. The American Naturalist 183(6): 771–783.

Weblink:
Download reference:

Steiner, U.K., Tuljapurkar, S., and Orzack, S.H. (2010). Dynamic heterogeneity and life history variability in the kittiwake. Journal of Animal Ecology 79(2): 436–444.

Weblink:
Download reference:

Therborn, G. (2014). The killing fields of inequality. New York: John Wiley and Sons.

Download reference:

Tuljapurkar, S. and Edwards, R.D. (2011). Variance in death and its implications for modeling and forecasting mortality. Demographic Research 24: 497–526.

Weblink:
Download reference:

Tuljapurkar, S., Steiner, U.K., and Orzack, S.H. (2009). Dynamic heterogeneity in life histories. Ecology Letters 12(1): 93–106.

Weblink:
Download reference:

Tuljapurkar, S., Zuo, W., Coulson, T., Horvitz, C., and Gaillard, J.M. (2020). Skewed distributions of lifetime reproductive success: Beyond mean and variance. Ecology Letters 23(4): 748–756.

Weblink:
Download reference:

van Daalen, S. and Caswell, H. (2015). Lifetime reproduction and the second demographic transition: Stochasticity and individual variation. Demographic Research 33(20): 561–588.

Weblink:
Download reference:

van Daalen, S.F. and Caswell, H. (2020). Demographic sources of variation in fitness. In: Sear, R., Lee, R., and Burger, O.F. (eds.). Human evolutionary demography. Open Book Publishers.

Download reference:

van Daalen, S.F. and Caswell, H. (2017). Lifetime reproductive output: Individual stochasticity, variance, and sensitivity analysis. Theoretical Ecology 10: 355–374.

Weblink:
Download reference:

van Daalen, S.F. and Caswell, H. (2020). Variance as a life history outcome: Sensitivity analysis of the contributions of stochasticity and heterogeneity. Ecological Modelling 147: 198856.

Weblink:
Download reference:

van Daalen, S.F., Hernández, C.M., Caswell, H., Neubert, M.G., and Gribble, K.E. (2022). The contributions of maternal age heterogeneity to variance in lifetime reproductive output. The American Naturalist 199(5): 000-000.

Weblink:
Download reference:

van Raalte, A.A. and Caswell, H. (2013). Perturbation analysis of indices of lifespan variability. Demography 50(5): 1615–1640.

Weblink:
Download reference:

van Raalte, A.A., Kunst, A.E., Lundberg, O., Leinsalu, M., Martikainen, P., Artnik, B., Deboosere, P., Stirbu, I., Wojtyniak, B., and Mackenbach, J.P. (2012). The contribution of educational inequalities to lifespan variation. Population Health Metrics 10(1): 1–10.

Weblink:
Download reference:

van Raalte, A.A., Sasson, I., and Martikainen, P. (2018). The case for monitoring life-span inequality. Science 362(6418): 1002–1004.

Weblink:
Download reference:

Varas Enríquez, P.J., Van Daalen, S., and Caswell, H. (2022). Individual stochasticity in the life history strategies of animals and plants. PLoS ONE 17(9): e0273407.

Weblink:
Download reference:

Vaupel, J.W. (2010). Biodemography of human ageing. Nature 464(7288): 536–542.

Weblink:
Download reference:

Vaupel, J.W. (1988). Inherited frailty and longevity. Demography 25(2): 277–287.

Weblink:
Download reference:

Vaupel, J.W. and Carey, J.R. (1993). Compositional interpretations of medfly mortality. Science 260: 1666.

Weblink:
Download reference:

Vaupel, J.W., Carey, J.R., Christensen, K., Johnson, T.E., Yashin, A.I., Holm, N.V., Iachine, I.A., Kannisto, V., Khazaeli, A.A., and Liedo, P. (1998). Biodemographic trajectories of longevity. Science 280(5365): 855–860.

Weblink:
Download reference:

Vaupel, J.W., Manton, K.G., and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3): 439–454.

Weblink:
Download reference:

Vaupel, J.W. and Missov, T.I. (2014). Unobserved population heterogeneity: A review of formal relationships. Demographic Research 31(22): 659–688.

Weblink:
Download reference:

Vaupel, J.W. and Yashin, A.I. (1985). Heterogeneity’s ruses: Some surprising effects of selection on population dynamics. American Statistician 39(3): 176–185.

Weblink:
Download reference:

Vaupel, J.W., Zhang, Z., and Raalte, A.A. (2011). Life expectancy and disparity: An international comparison of life table data. BMJ Open 1(1): e000128.

Weblink:
Download reference:

Vindenes, Y., Engen, S., and Saether, B.E. (2008). Individual heterogeneity in vital parameters and demographic stochasticity. The American Naturalist 171(4): 455–467.

Weblink:
Download reference:

Wilmoth, J.R. and Horiuchi, S. (1999). Rectangularization revisited: Variability of age at death within human populations. Demography 36(4): 475–495.

Weblink:
Download reference:

Yashin, A.I., Vaupel, J.W., and Iachine, I.A. (1994). A duality in aging: the equivalence of mortality models based on radically different concepts. Mechanisms of Ageing and Development 74(1): 1–14.

Weblink:
Download reference:

Zhang, Z. and Vaupel, J.W. (2009). The age separating early deaths from late deaths. Demographic Research 20: 721–730.

Weblink:
Download reference:

Back to the article