Stochastic formation of marriages is considered in continuous time. The models are parametrized in terms of the overall level of nuptiality, the relative propensity to marry by age, and the mutual attraction of potential spouses in different ages. Such measures can be used to describe time trends in the nuptiality of human populations. It is shown that if the overall intensity of nuptiality is taken to be a possibly weighted average of the intensities of the two sexes, but in a transformed scale, then different choices of scale lead to alternative concepts of population of risk, and as such to different two-sex models. Statistical estimation of the model parameters is considered, and its use in stochastic microsimulation is demonstrated.
Senescence, the physiological decline that results in decreasing survival and/or reproduction with age, remains one of the most perplexing topics in biology. Most theories attempting to explain the evolution of senescence (i.e. antagonistic pleiotropy, mutation accumulation, disposable soma) were developed over half a century ago. Confronted with empirical patterns of survival and reproduction, predictions of the theories do not hold. New theory is needed to shed light on the determinants of patterns of birth and death.
My objective is to describe the theoretical foundation, analytical framework and empirical requirements for the use of the death distribution of live-captured insects of unknown age to estimate age structure in their population. I will start with a brief overview of several high tech methods currently used to estimate insect age (and thus population age structure), most of which are costly and all of which are limited. I will then introduce the demographic concept my colleagues and I developed as an alternative to the high-tech approach. Referred to as the captive cohort methods, we show that the death distribution of live-captured individuals of unknown age can be used to: (1) determine the exact age structure of hypothetical stationary populations (i.e. life table identity); ii) estimate the age structure of wild populations using a simple model and reference life tables; and iii) estimate quantitative changes in population mean age and qualitative changes in the age extremes (young and old). I will illustrate the utility of this approach from the results of field studies on the Mediterranean fruit flies populations in Greece, and end with a discussion of the broader implications of this method in both basic and applied ecology.
L. R. Taylor (1961) and colleagues observed that, in many species, the logarithm of the variance of the density (individuals per area or volume) of a set of comparable populations was an approximately linear function of the logarithm of the mean density: for some a > 0, log(variance of population density) = log(a) + b × log(mean population density). This relationship came to be known as Taylor's law (TL) of fluctuation scaling. TL has been verified in hundreds of species from bacteria to humans and beyond: in populations of stem cells, stock market trading, precipitation, packet switching on the Internet, measles cases, and the occurrence of single nucleotide polymorphisms. We will give some empirical examples of TL and some recent theoretical developments regarding the origins, interpretations, and consequences of TL.
The first part of the talk highlights several of my early papers inspired by Nathan Keyfitz that examine the implications of mortality for a broad range of phenomena: dating a population's time of settlement; examining the impact of mortality change on life expectancy; and identifying the cause of high mortality among never-married individuals. The remainder of the talk examines one aspect of my ongoing work in biosocial surveys: the extent to which clinical and other biological markers enhance mortality prediction in older populations.
Perennial tropical and subtropical plants inhabit inherently variable environments, where both abiotic and biotic features vary from place to place and during the life times of individuals. To address ecological, evolutionary and applied demographic questions, we employ structured models (matrix projection and integral projection) using a framework that includes stage (sometimes age) structure and environmental variability. Projection models are used in two ways, to track population dynamics and to generate sample paths of individuals across the life cycle. The former concerns ecological dynamics and evolutionary demography where fitness is measured as the (stochastic) population growth rate. The latter concerns life histories, life expectancies and the timing of other key events (such as age of first reproduction). In some systems we also address rate of spread across the landscape. Issues we address quantitatively by these methods include: the effect of hurricanes on the impact of native seed predators ; integrating selection on quantitative traits across the life cycle when selection gradients vary over time; trade-offs due to the cost of reproduction; how harvest regime of non-timber forest products affects longevity of trees; life expectancy of pioneer vs shade-tolerant tropical trees; the impact of rarely occurring long distance dispersal vectors to invasion speed; effectiveness of bio-control agents on invasive trees and shrubs; and others. As models are applied to different problems, new issues and new models arise through collaborations.
Presentation Slides | Video
The 7 traditional classes of Vertebrates (3 classes of Fish, Birds, Mammals, Reptiles and Amphibians) encompass around 64 000 species and are by far the best known animal group from a demographic point of view. After having briefly recalled the reasons for the abundance and quality of the demographic information available on Vertebrates, I will review this information, covering the following salient features:
I discuss implications of these demographic characteristics of Vertebrate in a changing world, in particular in relation with climate change and the fragmentation of habitats.
We explain how upward transfers from adult children to their elderly parents might evolve as an interrelated feature of a deepening intergenerational division of labor. Humans have a particularly long period of juvenile dependence requiring both food and care time provided mainly by younger and older adults. We suggest that the division of labor evolves to exploit comparative advantage between young and old adults in fertility, childcare and foraging. Eventually the evolving division of labor reaches a limit when the grandmother's fertility reaches zero (menopause). Continuing, it may hit another limit when the grandmother's foraging time has been reduced to her subsistence needs. Further specialization can occur only with food transfers to the grandmother, enabling her to reduce her foraging time to concentrate on additional childcare. We prove that this outcome can arise only after menopause has evolved. We describe the conditions necessary for both group selection (comparative steady state reproductive fitness) and individual selection (successful invasion by a mutation), and interpret these conditions in terms of comparative advantages.
Fertility levels decline to below replacement is a common trend; and it will lead to declining populations that press less on environment and resources but suffer increase in the pension burdens of pay-you-go systems. Funded pension systems transfer cohorts saving to consumption, and hence their pension burdens are invariant to fertility change. Comparing the difference between the pension burdens of the two systems in certain periods could provide relevant information to the decision on whether or not to establish funded pension systems to cope with low fertility. A time-referred cohort old-dependence ratio is proposed in this paper, which is comparable to the period old-dependence ratio at a certain time, purely demographic, and could be computed for all the countries and areas of the world. Examples are given for China, Japan and Republic of Korea, which indicate that low-fertility populations are sustainable, but require more sophisticated means to sustain.
A socioeconomically differentiated population evolves through differential fertility, mortality, marriage, and migration of socioeconomic groups, as well as through intergenerational social mobility. If mobility processes are non-Markovian -- that is, include net associations of socioeconomic status across more than two generations -- then the demography of mobility is more complex. Many types of multigenerational effects are possible, including those that work through mobility itself and those that work through demographic processes. In some circumstances, multigenerational effects may also arise from remote ancestral conditions, as well as from intergenerational connections between the characteristics of specific more proximate kin. The short and longer run implications of these effects also depend on whether mobility processes depend on the characteristics of one sex or both sexes. This paper describes this array of possible multigenerational effects, shows the conditions under which the socioeconomic characteristics of an individual in one generation may affect future generations, and illustrates these results with data from the Qing Dynasty era of China and the contemporary United States.
Demography is often a key driver of the burden of infectious diseases, via both its impact on dynamics and the existence of age-patterns of affliction. Rubella, a directly transmitted, immunising childhood infection is an extreme example of this. Although rubella is generally a mild and even asymptomatic infection of children, infection in the early weeks of pregnancy can lead to birth of a child with Congenital Rubella Syndrome. The syndrome is associated with a range of symptoms, including deafness, blindness, and mental retardation. I will introduce models combining human and epidemiological dynamics for rubella; highlighting their application to the key public health question of when demographic and epidemiological conditions are such that the introduction of the rubella vaccine will not lead to an increase in the burden of Congenital Rubella Sydnrome; and placing this in the current global demographic context.
Presentation Slides | Video
Nathan Keyfitz's contributions to formal and to applied demography began and ended with an outstanding ability to distill and focus analyses so to generate fundamental insights from even the most unpromising models and data. I will attempt to channel a small amount of his ability. I will present analyses of the demographic and genetic trajectory of the human sex ratio from conception to birth and analyses of the dynamics and statics of morbidity and mortality across the course of human life and across cohorts. Both analyses generate fundamental new insights into human development.
The Intrinsic Linkage approach assumes a linear relationship between a population's age/ state composition, the dominant (intrinsic) component of the projection matrix that moves that population forward, and the resultant population composition. Here, that approach is extended to multistate models, and new relationships are developed to determine population growth and state composition. Under Intrinsic Linkage, a population can be analytically projected to any future point from knowledge of the linkage parameter(s) and the dominant component of the population projection matrices. Illustrative examples show how population values vary with the linkage parameter, how cyclical models can be specified, and how the approach can synthesize cohort analyses.
The dependency ratio is the number of young and non-working old supported by an average worker. That ratio is a principal determinant of realized per-capita consumption, which in turn depends on productivity, and desired per-capita consumption. Human wellbeing in turn depends in large part on realized consumption. Before the rise of the modern industrial state, population growth rate determined the dependency ratio and hence affected wellbeing. In the reverse direction, fertility and mortality varied with wellbeing, and hence so did growth rate. The result was a feedback system that produced population equilibrium at which dependency was binding, an essentially Malthusian equilibrium. In industrial states, the link between fertility and wellbeing has weakened. However, the growth of wellbeing depends on growth in productivity, consumption, and dependency. Now the growth rate of dependency can and does become binding.
We develop new approach to understand stability of a population and further understanding of population momentum. These ideas can be generalized to populations in ecology and biology.
During the last decades, the age structure of populations in Europe has become older and populations have become more diverse in terms of citizenship. These trends are likely to persist in the future. Political scientists hypothesize that policy makers, in the interest of being re-elected, will increasingly turn to older voters and neglect the interests of a growing number of disenfranchised foreign citizens. Quantitative estimations of the future development of electorates to substantiate such discussions however have not yet been published. This project addresses this omission by focusing on Germany. It uses multistate population projections to analyse the demographic development of the German electorate. In particular, it estimates the extent to which the electorate will age in the future, and whether the disenfranchised foreign population in Germany is in fact likely to grow in size.
In the first decade of the twenty first century the Mexican life expectancy changed from a long trend of increase to stagnation. These changes concur with an increase in deaths by homicides that the country experienced in that decade. There are 138,461 official reported deaths by homicide in the period of 2000 to 2010. However, the time trend shows an increase in the counts of homicides in the later years from an annual number of 10,000 to 25,000 deaths in 2010. We quantify the impact of these changes in homicides and other causes of death in life expectancy. The changes in the age-patterns of the life table functions are also studied. Our preliminary results show that the male life expectancy remained around the value of 72 years from 2000 to 2010. However, the apparent stagnation in life expectancy is resultant of increase in homicides and diabetes deaths on one hand, and the positive improvements observed in other causes of death on the other. The negative impact of homicides is particularly observed at ages 15 and 50, and diabetes for ages 45 and more, and they account for almost an entire year of the male life expectancy. Mexican males would have observed a 2 years increase in life expectancy if homicides and diabetes deaths had been avoided.
We present a construction technique for nonstandard finite difference (NSFD) schemes for
systems of nonlinear differential equations. While NSFD schemes have been employed to calculate
numerical solutions to difficult nonlinear differential equations to machine precision as well as for
difference equations for discrete problems, these schemes are not used by the bulk of mathematicians
and scientists. Currently the technique needed to define an NSFD scheme for a particular differential
equation requires extensive physical insight into the behavior of the modeled entity and has not been
extended to general systems of nonlinear differential equations.
The scheme presented here is not meant to replace those schemes designed for use on very specific problems, instead it is to be used for problems that do not have an NSFD scheme already defined.
One advantage that the alternate NSFD method presented here is that this method allows transitions from linear to nonlinear schemes without the need to change schemes when the nonlinear coefficients approach zero for nontrivial amounts of time. It also handles the inclusion or exclusion of nonhomogeneous constant terms. This is an advantage over schemes designed for a specific problem.
We examine and demonstrate importance of the adult modal age at death (M) in longevity research. Unlike the life expectancy at birth (e0) and median age at death, M is determined solely by old-age mortality as far as mortality follows the regular pattern. It represents the location of "old-age death heap" in the age distribution of deaths, and captures mortality shifts more accurately than conditional life expectancies such as e65. Due to these characteristics, patterns of trends and differentials in M can be noticeably different from those in other lifespan measures, as indicated in some examples. In addition, M plays central roles in major models of adult mortality such as the Gompertz, logistic and Weibull models. Although M may not be directly determined from erratic mortality data, a recently developed method for deriving M from the P-spline-smoothed mortality curve based on penalized Poisson likelihood is highly effective in estimating M.
Unobserved heterogeneity in mortality risk is pervasive and consequential. Mortality deceleration—the slowing of mortality's rise with age—has been considered an important window into heterogeneity that otherwise might be impossible to explore. This paper argues that deceleration patterns may reveal surprisingly little about the heterogeneity that putatively produces them. I show that even in a very simple model—one composed of just two subpopulations with Gompertz (exponential) mortality—(1) aggregate mortality can decelerate even while a majority of the cohort is frail; (2) multiple decelerations are possible; and (3) mortality selection can produce acceleration as well as deceleration. Simulations show that these patterns are plausible in model cohorts that in the aggregate resemble cohorts in the Human Mortality Database. I argue that these results: challenge some conventional heuristics for understanding the relationship between selection and deceleration; undermine certain inferences from deceleration timing to patterns of social inequality; and imply that standard parametric models, assumed to plateau at most once, may sometimes badly misestimate deceleration timing—even by decades.