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Biomedical subjects

S Tuljapurkar

Publications and source records attributed to S Tuljapurkar.

17 recordsLinked to original sources
PubMed2000

A universal pattern of mortality decline in the G7 countries.

Human lifespan has increased enormously this century. But we remain uncertain about the forces that reduce mortality, and about the cost implications of ageing populations and their associated social burden. The poor understanding of the factors driving mortality decline, and the difficulty of forecasting mortality are due in part to the pronounced irregularity of annual to decadal mortality change. Here we examine mortality over five decades in the G7 countries (Canada, France, Germany, Italy, Japan, UK, US). In every country over this period, mortality at each age has declined exponentially at a roughly constant rate. This trend places a constraint on any theory of society-driven mortality decline, and provides a basis for stochastic mortality forecasting. We find that median forecasts of life expectancy are substantially larger than in existing official forecasts. In terms of the costs of ageing, we forecast values of the dependency ratio (that is, the ratio of people over 65 to working people) in 2050 that are between 6% (UK) and 40% (Japan) higher than official forecasts.

Aging↗
PubMed1997

Death and taxes: longer life, consumption, and social security.

We analyze in three steps the influence of the projected mortality decline on the long run finances of the Social Security System. First, on a theoretical level, mortality decline adds person years of life which are distributed across the life cycle. The interaction of this distribution with the age distribution of labor earnings minus consumption, or of taxes minus benefits, partially determines the corresponding steady state financial consequences of mortality decline. The effect of mortality decline on population growth rates also matters, but is negligible in low mortality populations. Second, examination of past mortality trends in the United States and of international trends in low mortality populations, suggests that mortality will decline faster than foreseen by the Social Security Administration's forecasts. Third, we combine the work of the first two parts in dynamic simulations to examine the implications of mortality decline and of alternative forecasts of mortality for the finances of the social security system. Also, we use stochastic population forecasts to assess the influence of uncertainty about mortality decline on uncertainty about finances; we find that uncertainty about fertility still has more important implications than uncertainty about mortality, contrary to sensitivity tests in the official forecasts.

Actuarial Analysis↗
PubMed1995

High sex ratios in China's future.

In China in recent years, male live births have exceeded those of females by amounts far greater than those that occur naturally in human populations, a trend with significant demographic consequences. The resulting imbalance in the first-marriage market is estimated to be about 1 million males per year after 2010. These "excess" males were not easily accommodated in models with substantial changes in first-marriage patterns. The current sex ratio at birth has little effect on a couple's probability of having at least one son, so future increases in the sex ratio may well occur, especially given increasing access to sex-selective abortion.

China↗
PubMed1994

Migration in variable environments: exploring life-history evolution using structured population models.

In this paper, we explore the hypothesis that environmental variability favors the evolution of migration. Using the single-locus invasion condition for a novel allele in a variable environment, we derive conditions where increased migration rates between two sites are favored. We find that while there is a strong advantage to migrants entering a resident population with no migration, there is little advantage to migrants entering a population where the residents migrate at a different rate. Instead of an optimal rate of migration, there is a range of favored migration rates. Negative spatial correlation and a population structure including more than two sites accentuate the advantage of migration. Extending this model to include the effects of developmental delay (e.g. seed dormancy or diapause) on the evolution of migration, we find that higher levels of such delay reduce the advantage to migrants.

Animals↗
PubMed1994

Stochastic population forecasts for the United States: beyond high, medium, and low.

"This article presents and implements a new method for making stochastic population forecasts that provide consistent probability intervals. We blend mathematical demography and statistical time series methods to estimate stochastic models of fertility and mortality based on U.S. data back to 1900 and then use the theory of random-matrix products to forecast various demographic measures and their associated probability intervals to the year 2065. Our expected total population sizes agree quite closely with the Census medium projections, and our 95 percent probability intervals are close to the Census high and low scenarios. But Census intervals in 2065 for ages 65+ are nearly three times as broad as ours, and for 85+ are nearly twice as broad. In contrast, our intervals for the total dependency and youth dependency ratios are more than twice as broad as theirs, and our ratio for the elderly dependency ratio is 12 times as great as theirs. These items have major implications for policy, and these contrasting indications of uncertainty clearly show the limitations of the conventional scenario-based methods."

Age Factors↗
PubMed1993

Environmental uncertainty and variable diapause.

We analyze a stage-structured model of a population that displays variable diapause in a randomly varying environment. The ruggedness of the environment is measured by the extent of random variation in per-capita reproductive success. We show how variable diapause and environmental characteristics affect the population's stochastic growth rate. In rugged unpredictable environments, phenotypes that show some tendency to diapause are found to have a higher growth rate than nondiapausing phenotypes. In harsh rugged environments, some tendency to diapause may be all that permits population persistence. Positive serial autocorrelation causes the optimal diapause fraction to decrease, while negative autocorrelation causes that fraction to increase. The structured model behaves very differently from a scalar model for large diapause fractions even in uncorrelated environments, and in many cases predicts a broad optimum. The difference between models is due to the extreme variability of stage structure in populations subject to even small variability when diapause tendency is high.

Animals↗
PubMed1993

Entropy and convergence in dynamics and demography.

Demographic dynamics is formally equivalent to the dynamics of a Markov chain, as is true of some nonlinear dynamical systems. Convergence to demographic equilibrium can be studied in terms of convergence in the Markov chain. Tuljapurkar (1982) showed that population entropy (Kolmogorov-Sinai entropy) provides information on the rate of this convergence. This paper begins by considering finite state Markov chains, providing elementary proofs of the relationship between convergence rate and entropy, and discusses in detail the uses and limitations of entropy as a convergence measure; these results also apply to Markovian dynamical systems. Next, new qualitative and quantitative arguments are used to discuss the demographic meaning of entropy. An exact relationship is established giving population entropy in terms of the eigenvalues of the Leslie matrix characteristic equation. Finally, the significance of imprimitive and periodic limits is discussed in relation to population entropy.

Demography↗
PubMed1992

Stochastic population forecasts and their uses.

"The properties and uses of stochastic forecasts are discussed here. For linear stochastic projections, we show how the computation of forecast moments and the statistical distribution of forecasts depend on the multiplicative and autoregressive structure of the dynamics. Both scalar and vector projection methods are discussed, and their similarities are explored. Next we discuss the uses of stochastic forecasts, arguing that it is important to relate forecasts to the specific decision-making criteria of particular forecast users. The example of [the U.S. system of] Social Security is used to show how a dynamic programming approach may be used to explore alternative decisions in a probabilistic context."

Americas↗
PubMed1991

Disease in changing populations: growth and disequilibrium.

This paper examines simple age-structured models of childhood disease epidemiology, focusing on nonstationary populations which characterize LDCs. An age-structured model of childhood disease epidemiology for nonstationary populations is formulated which incorporates explicit scaling assumptions with respect both to time and to population density. The static equilibrium properties and the dynamic local stability of the model are analyzed, as are the effects of random variability due to fluctuations in demographic structure. We determine the consequences of population growth rate for: the critical level of immunization needed to eradicate an endemic disease, the transient epidemic period, the return time which measures the stability of departures from epidemiological equilibrium, and the power spectrum of epidemiological fluctuations and combined demographic-epidemiological fluctuations. Growing populations are found to be significantly different from stationary ones in each of these characteristics. The policy implications of these findings are discussed.

Age Factors↗
PubMed1990

Age structure, environmental fluctuations, and hermaphroditic sex allocation.

This paper studies sex allocation in an age-structured population of hermaphrodites living in a temporally fluctuating environment. The general condition for the evolutionary stable state (ESS) of allocation is derived for density-independent dynamics. This condition is used to determine the effect on the deterministic ESS of a dependence of survival rates on allocation. It is also used to identify the special conditions under which a stochastic ESS is given by a product rule and show how demographic structure and the correlation structure of vital rates determines the stochastic ESS.

Biological Evolution↗
PubMed1990

Delayed reproduction and fitness in variable environments.

Many organisms delay the initiation of reproduction even though such delay is not adaptive in a constant environment. Theoretical arguments in this paper show that delaying reproduction can increase fitness in a sufficiently variable environment. This paper uses stochastic demography to analyze the fluctuating population structure produced by environmental uncertainty. The results explain previously puzzling features of life cycle delays observed in nature, predicting that populations of the same species living in environments of differing harshness can display different life history phenotypes, a number of distinct life history phenotypes can coexist neutrally within a single population, and genetic polymorphisms are easily maintained if heterozygotes have intermediate life history phenotypes.

Adaptation, Physiological↗
PubMed1989

An uncertain life: demography in random environments.

This paper concisely reviews the demography of populations with random vital rates, highlights examples and techniques which yield insight into population dynamics, summarizes the state of significant applications of the theory, and points to open problems. The central picture in this theory is of a time-varying but statistically stationary equilibrium for population, sharply distinct from the notions of classical demography. The deepest biological insights from the theory reveal the temporal structure of life histories to be a rich arena for natural selection.

Animals↗
PubMed1987

Cycles in nonlinear age-structured models. I. Renewal equations.

A variety of density-dependent population models can be described by nonlinear renewal equations. This paper develops analytical tools for such models to study the sustained population cycles which arise by bifurcation. The results obtained describe explicitly the direction of bifurcation, and the period, form, and dynamic stability of sustained cycles. The results are illustrated by application to a cohort-controlled model of human populations which has been proposed as a formalization of the Easterlin effect.

Age Factors↗
PubMed1985

Population dynamics in variable environments. VI. Cyclical environments.

This paper studies the dynamics of an age-structured population which experiences cyclical variation in vital rates. The principal features of population behavior are found to be contained in an explicitly calculable response function. Three distinct regimes of qualitative behavior are described when cycle period is respectively much less than, of the order of, and much greater than the average generation length. These results make explicit the way in which transient properties corresponding to average vital rates determine population response to cycles.

Animals↗
PubMed1984

Demography in stochastic environments. I. Exact distributions of age structure.

The steady state distribution of age structure is studied for populations with two age classes and stochastic vital rates. For a serially uncorrelated dichotomic vital rate the distribution of age structure is found analytically to be a singular steplike function; outside a specific region of vital rate values the singular function crosses a threshold to a smooth function. For a vital rate following a correlated two state Markov process the joint distributions of age structure and environment are found analytically to be singular steplike functions; again a threshold marks a transition to a smooth function. For fecundities which are serially uncorrelated but continuously distributed the age structure distribution is obtained as a smooth analytic function for all parameter values. These explicit results have applications to studies of age structure and average growth rate.

Age Factors↗