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We consider items that are incepted into operation having already a random initial age and define the corresponding remaining lifetime. We show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we develop the population studies approach to the problem and generalize the setting in terms of stationary and stable populations of items. We obtain new stochastic comparisons for the corresponding population ages and remaining lifetimes that can be useful in applications. Copyright © 2014 John Wiley & Sons, Ltd.

1. The open-access scientific philosophy has been widely adopted and proven to promote considerable progress in the fields of ecology and evolution. Open-access global databases now exist on animal migration, the distribution of species, and conservation status, to mention a few. However, a gap exists for databases on population dynamics spanning the rich diversity of the animal kingdom. This information is fundamental to our understanding of the conditions that have shaped variation in animal life histories and their relationships with the environment. Furthermore, an animal population schedules of reproduction and mortality determine its invasive potential, and its risk of local extinction, which are at the core of conservation biology. 2. Matrix population models (MPMs) are among the most widely used demographic tools by animal ecologists. MPMs project population dynamics in terms of reproduction, mortality, and development over the entire life cycle. The results of MPMs have direct biological interpretations, facilitating comparisons among animal species as different as Caenorhabditis elegans, Loxodonta africana and Homo sapiens. 3. Thousand of animal demographic records exist in the form of MPMs, but they are dispersed throughout the literature, rendering comparative analyses difficult. Here, we introduce the COMADRE Animal Matrix Database version 1.0.0, an open-source online repository containing data on 402 species worldwide, from 272 studies, with a total of 1,575 population projection matrices. COMADRE also contains ancillary information (e.g. ecoregion, taxonomy, biogeography, etc.) that facilitates interpretation of the numerous demographic metrics that can be derived from its MPMs. 4. Synthesis: We introduce the COMADRE Animal Matrix Database, a resource for animal demography. The open access nature of this database, together with its ancillary information will facilitate comparative analysis, as will the growing availability of databases focusing on other traits, and tools to query and combine them. Through future frequent updates of COMADRE, and its integration with other online resources, we encourage animal ecologists to tackle global ecological and evolutionary questions with unprecedented statistical power.

Summary We analyzed MBL2 gene variants in two cohorts of centenarians, octo-nonagenarians and nonagenarians, and in the general population, one from Sardinia Island (Italy), recruited in the frame of the AKea study, and another from Campania (southern Italy), to search for haplotypes related to longevity. We also assessed in vitro the effect of mannose-binding lectin (MBL) on various human cells at different stage of senescence. The frequency of high and null activity haplotypes was significantly lower, and the frequency of intermediate activity haplotype significantly higher in centenarians and in subjects between 80 and 99 years from both the cohorts as compared each to the general population from the same geographic area. Furthermore, serum MBL concentration (also after normalization to serum albumin) was significantly lower in centenarians and in octo- and nonagenarians as compared to the general population, suggesting that intermediate MBL haplotype/activity may be protective. We also demonstrated that in vitro MBL protein bound to senescent IMR90 fibroblasts thereby causing cell lysis, but not to other types of cycle-arrested cells not in senescence. This implicates a novel role of MBL in the clearance of senescent cells.

Studies of Nordic twins suggest an increased genetic influence on mortality with age. Contrary to this, the heterogeneity hypothesis predicts that the mortality of individuals carrying a 'frail' or 'risky' genotype in a population will approach that of noncarriers with age because of selection pressure. The ApoE e4 allele is associated with an increased mortality risk, and its effect has been suggested to decrease with age. Here, we investigated the effect of ApoE e4 allele on survival in a sample of the healthiest and long-lived Danes. The study population comprised Danes born in 1905 and a replicate sample of the 1895 cohort. For the 1905 cohort, a total of 350 carriers and 1256 noncarriers of the ApoE e4 allele were followed from 1998 until death or end of follow-up. Cox regression models were used for the analysis. Of the 1606 persons with known ApoE e4 status in 1998, 1546 had died at the end of the 10-year follow-up. Carriers of the ApoE e4 allele had an increased mortality compared to noncarriers, and the influence of ApoE status on mortality increased in the age interval 92-103. For the covariates sex and independency status, the difference in relative risk of death between groups decreased with advancing age. Our findings of increasing influence of ApoE e4 allele on mortality with age do not support previous findings of decreased influence ApoE e4 allele on mortality with age, and alternative models such as the multifactorial threshold models should be considered for understanding the genetic effects on mortality at advanced age.

This is an expanded version of comments on the future of the demography of aging at an invited session of the 2008 annual meeting of the Population Association of America. In an introduction, John Haaga offers reasons for a revival of interest in population aging, including greater realization of plasticity in aging trajectories at both individual and societal levels. Linda Martin proposes that population scientists working in aging emulate those studying fertility and family planning in previous decades, learning from interventions (in this case, aimed at increasing retirement savings and reducing disability at older ages). Changes in family structure will increasingly affect new cohorts of the elderly, and Linda Waite speculates on the ways in which changes in the economy, medicine, and the legal environment could affect the social context for aging. Research on mortality at older ages is “alive and well” asserts James Vaupel, who sets out six large questions on mortality trends and differentials over time and across species. Lastly, Wolfgang Lutz expands the scope of projections, showing the considerable uncertainty about the timing and pace of population aging in the developing world and the effects on future elderly of the increases in educational attainment in much of the world during the second half of the twentieth century.

Centenarians surpass the current human life expectancy with about 20-25 years. However, whether centenarians represent healthy aging still remains an open question. Previous studies have been hampered by a number of methodological shortcomings such as a cross-sectional design and lack of an appropriate control group. In a longitudinal population-based cohort, it was examined whether the centenarian phenotype may be a useful model for healthy aging. The study was based on a complete follow up of 39,945 individuals alive in the Danish 1905 birth cohort on January 1, 1977 identified through the Danish Civil Registration System (DCRS). Data from the Danish Demographic Database and The Danish National Patient Register (in existence since 1977) were used. The 1905 cohort was followed up from 1977 through 2004 with respect to hospitalizations and number of hospital days. Survival status was available until December 2006. Danish centenarians from the 1905 cohort were hospitalized substantially less than their shorter-lived contemporaries at the same point in time during the years 1977 through 2004. For example, at age 71-74, the proportion of nonhospitalized centenarians was 80.5% compared with 68.4% among individuals who died in their early 80s. This trend was evident in both sexes. As a result of their lower hospitalization rates and length of stay in hospital compared with their contemporaries, who died at younger ages, Danish centenarians represent healthy agers. Centenarians constitute a useful study population in the search for fixed traits associated with exceptional longevity, such as genotype.

For the species that have been most carefully studied, mortality rises with age and then plateaus or declines at advanced ages, except for yeast. Remarkably, mortality for yeast can rise, fall and rise again. In the present study we investigated (i) if this complicated shape could be modulated by environmental conditions by measuring mortality with different food media and temperature; (ii) if it is triggered by biological heterogeneity by measuring mortality in stationary phase in populations fractionated into subpopulations of young, virgin cells, and replicatively older, non-virgin cells. We also discussed the results of a staining method to measure viability instead of measuring the number of cells able to exit stationary phase and form a colony. We showed that different shapes of age-specific death rates were observed and that their appearance depended on the environmental conditions. Furthermore, biological heterogeneity explained the shapes of mortality with homogeneous populations of young, virgin cells exhibiting a simple shape of mortality in conditions under which more heterogeneous populations of older cells or unfractionated populations displayed complicated death rates. Finally, the staining method suggested that cells lost the capacity to exit stationary phase and to divide long before they died in stationary phase. These results explain a phenomenon that was puzzling because it appeared to reflect a radical departure from mortality patterns observed for other species.

Mortality data for 30 mostly developed countries available in the Kannisto–Thatcher Database on Old-Age Mortality (KTDB) are drawn on to assess the pace of decline in death rates at ages 80 years and above. As of 2004 this database recorded 37 million persons at these ages, including 130,000 centenarians (more than double the number in 1990). For men, the probability of surviving from age 80 to age 90 has risen from 12 percent in 1950 to 26 percent in 2002; for women, the increase has been from 16 percent to 38 percent. In the lowest-mortality country, Japan, life expectancy at age 80 in 2006 is estimated to be 6.5 years for men and 11.3 years for women. For selected countries, average annual percent declines in age-specific death rates over the preceding ten years are calculated for single-year age groups 80 to 99 and the years 1970 to 2004. The results are presented in Lexis maps showing the patterns of change in old-age mortality by cohort and period, and separately for men and women. The trends are not favorable in all countries: for example, old-age mortality in the United States has stagnated since 1980. But countries with exceptionally low mortality, like Japan and France, do not show a deceleration in death rate declines. It is argued that life expectancy at advanced ages may continue to increase at the same pace as in the past.

Studies in fertility in the industrialized world primarily focus on the decline in average fertility and the determinants of this trend (Bongaarts 2002; UN Population Division 2003; Morgan 2003; Caldwell and Schindlmayr 2003). Variation in fertility within a population is used in an instrumental manner to link birth rates to explanatory variables by means of regressions and de compositions. The recent comprehensive work by Frejka and Sard?n (2004) reviewed changes in completed cohort fertility in industrialized countries and related them to changing age and parity patterns. The present study is interested primarily in the inter-individual diversity in fertility according to the parity distributions of women. This way of think ing about the inter-individual diversity is related to the concentration (or Lorenz) curve, showing what proportion of women have what proportion of children. Such a curve would demonstrate, for example, that 30 percent of American women born in 1931-32 have half of the children born to this cohort, while half of these women have 75 percent of the children. At the same time, 62 percent of children born to this cohort were born to mothers with four or more children, while only 3 percent were born to mothers with one child. These quantities describe something that might be called a division of labor in the matter of fertility (Vaupel and Goodwin 1987). The division of labor concept can be expressed also by an average inter-individual difference in childbearing "productivity" among women. It can be shown, for example, that the average difference between any pair of women (including women who remained childless) from the 1931-32 American cohort in the number

16. Reverse mortgage insurance would protect the lender just as conventional mortgage insurance does. However, the nature of the risk is quite different. In the latter case a borrower's death may make the loan a nonperforming one, while in the former the borrower's long life may put the lender at risk. 17. See Jacobs and Weissert, op. cit.; Garnett, Robert, and Guttentag, Jack, "The Reverse-Shared-Appreciation Mortgage," Housing Finance Review, 3(1) (Jan. 1984): 63-84. 18. Another advantage of being married is that a spouse is available to provide informal care in the home if the need arises. 19. Firman, James, "Reforming Community Care for the Elderly and the Disabled," Health Affairs, 11(1) (Spring 1983): 66-82. Frail elderly homeowners in California have taken out reverse mortgage loans for this purpose. See Kenny, Kathleen, and Belling, Bronwyn, "Home Equity Conversion: A Counseling Model," The Gerontologist, to appear.

The author notes that the new use that the U.S. Congress has established for the census namely the allocation of revenue sharing and other grants requires exactitude and does not fit with the probability models that have been so effective in other fields. He concludes that as long as the census count is reasonably close to actuality as revealed by the checks now in use its acceptance for this purpose is reasonable. The need for external quality control is indicated but it should be on the institution itself and not on individual census results. (ANNOTATION)

OBJECTIVES: To evaluate the extent to which relationships between apolipoprotein E, cognitive functioning, and survival in people aged 60 to 80 persist into advanced old age. DESIGN: Examine the effect of apolipoprotein E genotypes on baseline cognitive functioning, cognitive decline over 5 years, and survival in a cohort of 1,551 nonagenarians. SETTING: The Danish 1905 birth cohort. PARTICIPANTS: One thousand five hundred fifty-one nonagenarians from the Danish 1905 birth cohort. MEASUREMENTS: Cognitive functioning was assessed using the Mini-Mental State Examination (MMSE) and five brief cognitive tests (cognitive composite). RESULTS: The subjects were stratified into four groups by occurrence of a protective (epsilon2) or a risk (epsilon4) apo E allele (epsilon22 and epsilon23, epsilon33, epsilon24 and epsilon34, epsilon44). At intake, the mean scores for the three genotype groups were 22.1, 21.8, 21.4, and 21.0 for MMSE and 0.10, 0.07, -0.02, and 0.30 for the cognitive composite, respectively. Growth-curve analyses showed that, although individuals carrying at least one epsilon4 allele had slightly lower MMSE scores and declined slightly more rapidly over time, this effect was not statistically significant and was not apparent in scores on the cognitive composite. In subjects whose functioning was relatively well preserved (those still living and able to participate in the assessment, and whose cognitive functioning had declined less than 4 points on the MMSE), epsilon4 frequencies tended to decline at subsequent waves (P=.03, chi-square test for trend), but epsilon4 had no significant survival disadvantage (hazard ratio=1.11 (95% confidence interval=0.99-1.25; P=.07). CONCLUSION: Apo E genotype has a small effect on the probability of remaining a well-functioning nonagenarian but no separately detectable effect on cognitive functioning, cognitive decline, or survival.

Recent research indicates that tooth-cementum annulations (TCA) may be used more reliably than other morphological or histological traits of the adult skeleton to estimate age. Until now, however, confidence intervals for age estimated by this method have not been available for paleodemographic and forensic applications. The present study addresses this problem. Based on a large known-age sample, age estimates by TCA were conducted in a blind study involving 363 teeth. Tooth-root cross sections were made using a refined preparation technique. Improved digital graphic procedures and enhancement strategies were used to produce digital images with a specially adapted software package. This resulted in high concordance between the TCA age estimates and chronological age. Assessment of the method's accuracy, as expressed by 95% confidence intervals, showed that error bounds for age estimates do not exceed 2.5 years. Sex differences, intraindividual correlations, and the effects of periodontal disease were studied. None of these indicators had a quantitative effect on the number of TCA bands when the proposed methodological standard was followed. We conclude that the TCA technique is a reliable method for estimating a subject's age from cementum annulations.

Mutations in RAS2, CYR1, and SCH9 extend the chronological life span in Saccharomyces cerevisiae by activating stress-resistance transcription factors and mitochondrial superoxide dismutase (Sod2). Here we show that mutations in CYR1 and SCH9 also extend the replicative life span of individual yeast mother cells. However, the triple deletion of stress-resistance genes MSN2/MSN4 and RIM15, which causes a major decrease in chronological life span, extends replicative life span. Similarly, the overexpression of superoxide dismutases, which extends chronological survival, shortens the replicative life span and prevents budding in 30–40% of virgin mother cells. These results suggest that stress-resistance transcription factors Msn2/Msn4 negatively regulate budding and the replicative life span in part by increasing SOD2 expression. The role of superoxide dismutases and of other stress-resistance proteins in extending the chronological life span of yeast, worms, and flies indicates that the negative effect of Sod2, Msn2/Msn4/Rim15 on the replicative life span of S. cerevisiae is independent of aging.

OBJECTIVES: To elucidate whether well-known predictions of mortality are reduced or even reversed, or whether mortality is a stochastic process in the oldest old. DESIGN: A multidimensional survey of the Danish 1905 cohort conducted in 1998 with follow-up of vital status after 15 months. SETTING: Denmark. PARTICIPANTS: All Danes born in 1905, irrespective of physical and mental status were approached. Two thousand two hundred sixty-two persons of 3,600 participated in this survey. MEASUREMENTS: Professional interviewers collected data concerning sociodemographic factors, smoking, alcohol consumption, body mass index, physical and cognitive performance, and health during a visit at the participant’s residency. Cox regression models were used to evaluate predictors of mortality. RESULTS: Five hundred seventy-nine (25.7%) of the 2,249 participants eligible for the analysis died during the 15 months follow-up. Multivariate analyses showed that marital status, education, smoking, obesity, consumption of alcohol, and number of self-reported diseases were not associated with mortality. Disability and cognitive impairment were significant risk factors in men and women. In addition poor self-rated health was associated with an increase in mortality in women. CONCLUSION: In the oldest old, several known predictors of mortality, such as sociodemographic factors, smoking, and obesity, have lost their importance, but a high disability level, poor physical and cognitive performance, and self-rated health (women only), predict mortality, which shows that mortality in the oldest old is not a stochastic process. J Am Geriatr Soc 51:1365–1373, 2003.

This study is based on survey data from a sample of 8,805 elders aged 80–105 in 22 provinces of China. Rural oldest old are significantly more active in daily living than urban oldest old; adaptation is perhaps the major explanation of this difference. Female oldest old are seriously disadvantaged in functional capacities and self–reported health as compared with their male counterparts. Percentages of being active in daily living, having good physical performance, normal cognitive function and well–being drop dramatically from age 80–84 to 100–105. Proportion reporting satisfaction in current life, however, remains almost constant from age 80–84 to 90–94 and declines slightly afterwards. This may suggest that being more positive in self–feeling of life is one of the secrets of longevity.

THE NUMBER OF oldest old persons in China, defined here as aged 80 and older, is calculated by the United Nations to climb from about 11.5 million in the year 2000 to 27 million in 2020, 39 million in 2030, 64 million in 2040, and 99 million in 2050. 1 Under the UN’s medium fertility assumption, 2 the percent aged 65 and older is expected to increase from 6.9 in 2000 to 15.7 in 2030 and 22.7 in 2050, while the share of the oldest old which in 2000 is 13 percent of the elderly population will be some 30 percent in 2050. The main reason the number of oldest old will climb so quickly after 2030 is that China’s “baby boomers,” who were born in the 1950s and 1960s, will fall into the category of “oldest old” at that time. During 2000‐50 the population of the oldest old will grow faster than any other age group in China. This phenomenon is not limited to China. The average annual rates of increase of oldest old persons between 2000 and 2050 are expected to be around 4.3 percent in China, India, and Mexico and 2.2‐2.8 percent in Canada, Japan, the United States, Germany, and France (UN 2001b). The rate of increase of the Chinese oldest old subpopulation is much faster (4.4 percent vs. 2.7 percent) than that of the entire elderly population aged 65 and older. The oldest old are much more likely to need help in daily living than the younger elderly. The oldest old consume medical care and other services and benefits of government and private transfers far out of proportion to their numbers. As evidenced later in this article, the proportion of individuals leading active daily lives declines and the disability rate increases dramatically with age among the Chinese oldest old. Torrey (1992: 382) estimated that in the United States, the Medicare costs of those aged 80 and older are 77, 60, and 36 percent higher than those of the younger elderly aged 65‐69, 70‐74, and

The logistic regression model is a popular model for data analysis in epidemiological research. In this paper, we use this model to analyze genetic data collected from gene-longevity association studies. This new approach models the probability of observing one genotype as a function of the age of investigated individuals. Applying the model to genotype data on the TH and 3'ApoB-VNTR loci collected from an Italian centenarian study, we show how it can be used to model the different ways that genes affect survival, including sex- and age-specific influences. We highlight the advantages of this application over other available models. The application of the model to empirical data indicates that it is an efficient and easily applicable approach for determining the influences of genes on human longevity.

Summary 1. A graphic technique is presented in which data on age-specific reproduction of individuals are portrayed using: (i) a horizontal life line, the length of which is proportional to individual longevity; (ii) colour-coded segments depicting the level of reproduction at each age; and (iii) a cohort survival schedule created by rank-ordering individual life lines from shortest- to longest-lived. 2. The resulting graphic, referred to as an event history diagram, portrays data at the individual level and thus allows visual comparisons of detailed life-history patterns such as age of first reproduction, longevity, ages of high, medium, low and zero reproduction, and post-reproductive period. 3. Example graphs are shown for reproductive and longevity data gathered on 1000 medfly females. The average female lived 35·6 days and laid 759·3 eggs and therefore the graphs display information for 35 600 fly days and the age-distribution of laying for 759 300 eggs. 4. Because the graphics provide a means for visualizing large amounts of data precisely and efficiently, they reveal details and nuances in the data that are not apparent from conventional graphic methods. 5. The advantages of longitudinal data gathered on individuals and reasons why visualizing individual-level data is important are discussed.

A comparison of the costs and benefits of 57 lifesaving programs reveals striking disparities across agencies and programs in cost/life saved and even greater disparities in cost/life-year saved. Within a broad range the monetary value assigned to the benefits of averting a death usually does not alter the policy implications of the analyses. The findings suggest that despite the substantial disagreements and uncertainties in the theory and practice of valuing lives, careful quantitative analysis can be helpful in setting health, safety, and environmental priorities.