Vaccinating the oldest against COVID-19 saves both the most lives and most years of life.

Many competing criteria are under consideration for prioritizing COVID-19 vaccination. Two criteria based on age are demographic: lives saved and years of future life saved. Vaccinating the very old against COVID-19 saves the most lives, but, since older age is accompanied by falling life expectancy, it is widely supposed that these two goals are in conflict. We show this to be mistaken. The age patterns of COVID-19 mortality are such that vaccinating the oldest first saves the most lives and, surprisingly, also maximizes years of remaining life expectancy. We demonstrate this relationship empirically in the United States, Germany, and South Korea and with mathematical analysis of life tables. Our age-risk results, under usual conditions, also apply to health risks.

On Negative Heritability and Negative Estimates of Heritability.

We consider the problem of interpreting negative maximum likelihood estimates of heritability that sometimes arise from popular statistical models of additive genetic variation. These may result from random noise acting on estimates of genuinely positive heritability, but we argue that they may also arise from misspecification of the standard additive mechanism that is supposed to justify the statistical procedure. Researchers should be open to the possibility that negative heritability estimates could reflect a real physical feature of the biological process from which the data were sampled.

Hypothetical errors and plateaus: A response to Newman.

Newman questions recent claims about a plateau in mortality rates for Italians beyond age 105 on the basis of a hypothetical model. His model implies implausibly high error rates for extreme ages. For individuals over 110, for whom birth certificates have been collected, the form in which Italian births were registered precludes the kinds of clerical errors in year of birth that Newman assumes.

Response to Comment on "The plateau of human mortality: Demography of longevity pioneers".

Beltrán-Sánchez et al based their comment on misleading calculations of the maximum survival age. With realistic numbers of people attaining age 105 and the estimated plateau, the Jeanne Calment record is indeed plausible.

Statistical properties of simple random-effects models for genetic heritability.

Random-effects models are a popular tool for analysing total narrow-sense heritability for quantitative phenotypes, on the basis of large-scale SNP data. Recently, there have been disputes over the validity of conclusions that may be drawn from such analysis. We derive some of the fundamental statistical properties of heritability estimates arising from these models, showing that the bias will generally be small. We show that that the score function may be manipulated into a form that facilitates intelligible interpretations of the results. We go on to use this score function to explore the behavior of the model when certain key assumptions of the model are not satisfied - shared environment, measurement error, and genetic effects that are confined to a small subset of sites. The variance and bias depend crucially on the variance of certain functionals of the singular values of the genotype matrix. A useful baseline is the singular value distribution associated with genotypes that are completely independent - that is, with no linkage and no relatedness - for a given number of individuals and sites. We calculate the corresponding variance and bias for this setting.

The plateau of human mortality: Demography of longevity pioneers.

Theories about biological limits to life span and evolutionary shaping of human longevity depend on facts about mortality at extreme ages, but these facts have remained a matter of debate. Do hazard curves typically level out into high plateaus eventually, as seen in other species, or do exponential increases persist? In this study, we estimated hazard rates from data on all inhabitants of Italy aged 105 and older between 2009 and 2015 (born 1896-1910), a total of 3836 documented cases. We observed level hazard curves, which were essentially constant beyond age 105. Our estimates are free from artifacts of aggregation that limited earlier studies and provide the best evidence to date for the existence of extreme-age mortality plateaus in humans.

Evolutionary shaping of demographic schedules.

Evolutionary processes of natural selection may be expected to leave their mark on age patterns of survival and reproduction. Demographic theory includes three main strands--mutation accumulation, stochastic vitality, and optimal life histories. This paper reviews the three strands and, concentrating on mutation accumulation, extends a mathematical result with broad implications concerning the effect of interactions between small age-specific effects of deleterious mutant alleles. Empirical data from genomic sequencing along with prospects for combining strands of theory hold hope for future progress.

The age-specific force of natural selection and biodemographic walls of death.

W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full nonlinear demographic model for mutation accumulation recently developed by Evans, Steinsaltz, and Wachter, we find surprising differences. Nonlinear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine predictions in other cases, and allow walls of death at ages before the end of reproduction. Haldane's principle for genetic load has an exact but unfamiliar generalization.

Vital Rates from the Action of Mutation Accumulation.

New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard functions. We apply these models to questions in the biodemography of longevity, including proposed explanations of Gompertz hazards and mortality plateaus.

Biodemography Comes of Age.

Biodemography has emerged and grown over the last fifteen years, with loyal and farsighted support from its patrons. As it enters what might be called its adolescence as a field, it faces challenges along with abounding opportunities. One challenge is to continue to generate knowledge that contributes to human health and well-being. A second is to insist on high standards of quality control within its crossdisciplinary environment. Opportunities appear in a variety of directions, including mathematical modeling, genomic analyses, and field studies of aging in the wild.

Relationships between period and cohort life expectancy: gaps and lags.

This paper offers an empirical and analytic foundation for regarding period life expectancy as a lagged indicator of the experience of real cohorts in populations experiencing steady improvement in mortality. We find that current period life expectancy in the industrialized world applies to cohorts born some 40-50 years ago. Lags track an average age at which future years of life are being gained, in a sense that we make precise. Our findings augment Ryder's classic results on period-cohort translation.

AIDS and the elderly of Thailand: projecting familial impacts.

We apply aggregate demographic analysis and computer microsimulation to project the number of older Thais who will lose children to AIDS during their own lifetimes and to assess their involvement with ill children through caregiving and coresidence. Parental bereavements from AIDS are predicted to peak at around 80,000 per year between 2003 and 2007. Despite an HIV prevalence of only 2%, 13% of Thais who were over age 50 as of 1995 are likely to experience the loss of at least one adult child to AIDS, and 12% of them will lose multiple children. The chance of losing an adult child during one's lifetime will be 70% higher than if there were no AIDS epidemic.