Explaining fruit fly longevity

Diet has independent effects on the pace and shape of aging in Drosophila melanogaster

Studies examining how diet affects mortality risk over age typically characterise mortality using parameters such as aging rates, which condense how much and how quickly the risk of dying changes over time into a single measure. Demographers have suggested that decoupling the tempo and the magnitude of changing mortality risk may facilitate comparative analyses of mortality trajectories, but it is unclear what biologically meaningful information this approach offers. Here, we determine how the amount and ratio of protein and carbohydrate ingested by female Drosophila melanogaster affects how much mortality risk increases over a time-standardised life-course (the shape of aging) and the tempo at which animals live and die (the pace of aging). We find that pace values increased as flies consumed more carbohydrate but declined with increasing protein consumption. Shape values were independent of protein intake but were lowest in flies consuming ~90 μg of carbohydrate daily. As protein intake only affected the pace of aging, varying protein intake rescaled mortality trajectories (i.e. stretched or compressed survival curves), while varying carbohydrate consumption caused deviation from temporal rescaling (i.e. changed the topography of time-standardised survival curves), by affecting pace and shape. Clearly, the pace and shape of aging may vary independently in response to dietary manipulation. This suggests that there is the potential for pace and shape to evolve independently of one another and respond to different physiological processes. Understanding the mechanisms responsible for independent variation in pace and shape, may offer insight into the factors underlying diverse mortality trajectories.

Deciphering death: a commentary on Gompertz (1825) 'On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies'

In 1825, the actuary Benjamin Gompertz read a paper, 'On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies', to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz's work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental 'law of mortality' has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz's way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Heterogeneity in the Strehler-Mildvan general theory of mortality and aging

This study examines and further develops the classic Strehler-Mildvan (SM) general theory of mortality and aging. Three predictions from the SM theory are tested by examining the age dependence of mortality patterns for 42 countries (including developed and developing countries) over the period 1955-2003. By applying finite mixture regression models, principal component analysis, and random-effects panel regression models, we find that (1) the negative correlation between the initial adulthood mortality rate and the rate of increase in mortality with age derived in the SM theory exists but is not constant; (2) within the SM framework, the implied age of expected zero vitality (expected maximum survival age) also is variable over time; (3) longevity trajectories are not homogeneous among the countries; (4) Central American and Southeast Asian countries have higher expected age of zero vitality than other countries in spite of relatively disadvantageous national ecological systems; (5) within the group of Central American and Southeast Asian countries, a more disadvantageous national ecological system is associated with a higher expected age of zero vitality; and (6) larger agricultural and food productivities, higher labor participation rates, higher percentages of population living in urban areas, and larger GDP per capita and GDP per unit of energy use are important beneficial national ecological system factors that can promote survival. These findings indicate that the SM theory needs to be generalized to incorporate heterogeneity among human populations.

Individual heterogeneity in mortality mediates long-term persistence of a seasonal microparasite

One of the primary objectives in population ecology is to understand mechanisms that allow a species to persist or to be driven to extinction. In most population models, individuals are assumed to be equivalent within any particular category such as age, sex, or morphological grouping. Individuals within such groupings, however, may exhibit considerable variation in traits that can significantly affect population trajectories. Although ecologists have long been aware of such variation, they are frequently ignored to maintain computational tractability. The few statistical models that do incorporate such heterogeneity require prohibitively large amounts of data on many individuals, making them impractical. In California's coastal prairie, a parasitic nematode, Heterorhabditis marelatus, is an important natural enemy, whose presence determines the strength and extent of a trophic cascade. Mortality of H. marelatus is strongly influenced by habitat and seasonality, which determines long-term persistence. Prior efforts to estimate mortality have suffered from difficulty in distinguishing between measurement and process error due to limitations in experimental protocol. In this study, we eliminate measurement error in the initial population size and focus on the true nature of the heterogeneity in mortality. By including individual heterogeneity in our statistical model, we are able to understand how this species is able to persist over seasonally harsh environmental conditions. Further, we extrapolate these findings to larger population sizes and illustrate that heterogeneous survival can have a significant effect on the emergent number of survivors.

A revolution for aging research

In the year 1992, two publications on age-specific mortality rates revealed a cessation of demographic aging at later ages in very large cohorts of two dipteran species reared under a variety of conditions. Despite some initial concerns about possible artifacts, these findings have now been amply corroborated in the experimental literature. The eventual cessation of aging undermines the credibility of simple Gompertzian aging models based on a protracted acceleration in age-specific mortality during adulthood. The first attempt to explain the apparent cessation of aging was extreme lifelong heterogeneity among groups with respect to frailty. This lifelong heterogeneity theory assumes an underlying Gompertzian aging affecting every member of an adult cohort, with a merely apparent cessation of aging explained in terms of the increasing domination of a slowly aging group among the survivors to late ages. This theory has received several experimental refutations. The second attempt to explain the cessation of aging applied force of natural selection theory. This explanation of the cessation of aging has been corroborated in several Drosophila experiments. In particular, this theory requires that both age-specific survival and age-specific fecundity cease declining in late life, which has now been experimentally established. This theory also predicts that the timing of the cessation of aging should depend on the last age of reproduction in a population's evolutionary history, a prediction that has been corroborated. While lifelong heterogeneity should reduce average age-specific mortality in late life whenever it is pronounced, the cessation of aging in late life can be explained by plateaus in the forces of natural selection whether lifelong heterogeneity is present or not. The discovery that aging ceases is one of the most significant discoveries in recent aging research, with potentially revolutionary scientific implications.

Lifelong heterogeneity in fecundity is insufficient to explain late-life fecundity plateaus in Drosophila melanogaster

Previous studies have demonstrated that fecundity, like mortality, plateaus at late ages in cohorts of Drosophila melanogaster. Although evolutionary theory can explain the decline and plateau in cohort fecundity at late ages, it is conceivable that lifelong heterogeneity in individual female fecundity is producing these plateaus. For example, consistently more fecund females may die at earlier ages, leaving only females that always laid a low number of eggs preponderant at later ages. We simulated fecundity within a cohort, assuming the two phenotypes described above, and tested these predictions by measuring age of death and age-specific fecundity for individual females from three large cohorts. We statistically tested whether there was enough lifelong heterogeneity in fecundity to produce a late-life plateau by testing whether early female fecundity could predict whether that female would live to lay eggs after the onset of the population fecundity plateau. Our results indicate that heterogeneity in fecundity is not lifelong and thus not likely to cause late-life fecundity plateaus. Because lifelong heterogeneity models for fecundity are based on the same underlying assumptions as heterogeneity models for late-life mortality rates, our test of this hypothesis is also an experimental test of lifelong heterogeneity models of late life generally.

Late life: a new frontier for physiology

Late life is a distinct phase of life that occurs after the aging period and is now known to be general among aging organisms. While aging is characterized by a deterioration in survivorship and fertility, late life is characterized by the cessation of such age-related deterioration. Thus, late life presents a new and interesting area of research not only for evolutionary biology but also for physiology. In this article, we present the theoretical and experimental background to late life, as developed by evolutionary biologists and demographers. We discuss the discovery of late life and the two main theories developed to explain this phase of life: lifelong demographic heterogeneity theory and evolutionary theory based on the force of natural selection. Finally, we suggest topics for future physiological research on late life.

Evolution of late-life mortality in Drosophila melanogaster

Aging appears to cease at late ages, when mortality rates roughly plateau in large-scale demographic studies. This anomalous plateau in late-life mortality has been explained theoretically in two ways: (1) as a strictly demographic result of heterogeneity in life-long robustness between individuals within cohorts, and (2) as an evolutionary result of the plateau in the force of natural selection after the end of reproduction. Here we test the latter theory using cohorts of Drosophila melanogaster cultured with different ages of reproduction for many generations. We show in two independent comparisons that populations that evolve with early truncation of reproduction exhibit earlier onset of mortality-rate plateaus, in conformity with evolutionary theory. In addition, we test two population genetic mechanisms that may be involved in the evolution of late-life mortality: mutation accumulation and antagonistic pleiotropy. We test mutation accumulation by crossing genetically divergent, yet demographically identical, populations, testing for hybrid vigor between the hybrid and nonhybrid parental populations. We found no difference between the hybrid and nonhybrid populations in late-life mortality rates, a result that does not support mutation accumulation as a genetic mechanism for late-life mortality, assuming mutations act recessively. Finally, we test antagonistic pleiotropy by returning replicate populations to a much earlier age of last reproduction for a short evolutionary time, testing for a rapid indirect response of late-life mortality rates. The positive results from this test support antagonistic pleiotropy as a genetic mechanism for the evolution of late-life mortality. Together these experiments comprise the first corroborations of the evolutionary theory of late-life mortality.

Complex adaptive systems, aging and longevity

Mortality and reproduction are intimately entwined in the study of aging and longevity. I apply the modern theory of complex adaptive systems (nonlinear, stochastic, dynamic methods) to questions of aging and longevity. I begin by highlighting major questions that must be answered in order to obtain a deeper understanding of aging. These are: (i) What should (in an evolutionary sense) mortality trajectories look like? (ii) Why does caloric restriction slow aging? (iii) Why does reproduction cause delayed mortality? (iv) Why does compensatory growth cause delayed mortality? I show how dynamic state variable models based on stochastic dynamic programming (Clark & Mangel, 2000) can be used to embed genetic theories of senescence (either mutation accumulation or antagonistic pleiotropy) in the somatic environment, as George Williams called for in 1957, and how they make the disposable soma theory of aging operational. Such models will allow unification of genetic and phenotypic theories of aging.

Phenomenological theory of mortality evolution: its singularities, universality, and superuniversality

The probability to survive to the age x universally increases with the mean lifespan x(bar). For species as remote as humans and flies, for a given x the rate of its evolution with x is constant, except for the narrow vicinity of a certain x(bar) = x* (which equals 75 years for humans and 32 days for flies and which is independent of age, population, and living conditions). At x(bar) approximately x* the evolution rate jumps to a different value. Its next jump is predicted at x(bar) approximately 87 years for humans and approximately 59 days for flies. Such singularities are well known in physics and mathematics as phase transitions. In the considered case different population "phases" have significantly different survival evolution rates. The evolution is rapid-life expectancy may double within a lifespan of a single generation. Survival probability depends on age x and mean longevity x(bar) only (for instance, survival curves of 1896 Swedes and 1947 Japanese with approximately equal x(bar) are very close, although they are related to different races in different countries at different periods in their different history.) With no adjustable parameters, its presented universal law quantitatively agrees with all lifetable data. According to this law, the impact of all factors but age reduces to the mean lifespan only. In advanced and old age, this law is superuniversal--it is approximately the same for species as remote as humans and flies. It yields survival probability that linearly depends on the mean lifespan x(bar). As a result, when human x(bar) almost doubles (from 35.5 to 69.3 years), life expectancy at 70 years increases from 8 to 9.5 years only. Other implications of the universal law are also considered.

Mortality invariants and their genetic implications

Old noninbred fly mortality decreases according to the inverse linear law and reduces to a single suborder-specific age. Relative child mortality (the mortality at a given age related to the mortality at 10 years) from 1 mo to 11 years is the same with 8% mean accuracy for all humans, independent of race, country, sex, and birth year (from 1780 to 1995), in contrast to birth mortality, which in developed countries changed fiftyfold during the last century. The concept of invariants, which is very powerful in physics, is applied to mortality of species as remote as humans and flies. It provides quantitative estimates for the selection of hereditary Methuselahs, who live, e.g., over six-mean lifespans and who may be relatively young biologically. It also demonstrates that old fly and relative child mortality are determined genetically and that the former is related to genetic heterogeneity.

A model for antagonistic pleiotropic gene action for mortality and advanced age

Association or linkage studies involving control and long-lived populations provide information on genes that influence longevity. However, the relationship between allele-specific differences in survival and the genetic structure of aging cohorts remains unclear. We model a heterogeneous cohort comprising several genotypes differing in age-specific mortality. In its most general form, without any specific assumption regarding the shape of mortality curves, the model permits derivation of a fundamental property underlying abrupt age-related changes in the composition of a cohort. The model is applied to sex-specific survival curves taken from period life tables, and Gompertz-Makeham mortality coefficients are calculated for the French population. Then, adjustments are performed under Gompertz-Makeham mortality functions for three genotypes composing a heterogeneous cohort, under the constraint of fitting the resultant mortality to the real French population mortality obtained from life tables. Multimodal curves and divergence after the 8th decade appear as recurrent features of the frequency trajectories. Finally, a fit to data previously obtained at the angiotensin-converting-enzyme locus is realized, explaining what had seemed to be paradoxical results-namely, that the frequency of a genotype known as a cardiovascular risk factor was increased in centenarians. Our results help explain the well-documented departure from Gompertz-Makeham mortality kinetics at older ages. The implications of our model are discussed in the context of known genetic effects on human longevity and age-related pathologies. Since antagonistic pleiotropy between early and late survival emerges as a general rule, extrapolating the effects measured for a gene in a particular age class to other ages could be misleading.

The effects of reproduction on longevity and fertility in male Drosophila melanogaster

We examined the effect of reproduction on subsequent survival and fecundity of male Drosophila melanogaster by reversing the reproductive status of individuals part-way through life. Reproduction had a much more marked effect on fertility than survival: males with a history of reproduction showed complete sterility at a time when upwards of 80% of their cohort were still alive. Analyses of survival rates alone gave a misleading measure of the impact of ageing. Sterility appeared to be attributable mainly to a reduction in sperm count. Early reproduction caused permanent, irreversible damage to both survival and fecundity, with risk playing an apparently minor role. Individual differences in frailty appeared to be of little consequence for the interpretation of these reversal experiments, although its possible occurrence made definite detection of risk difficult.

What demographers can learn from fruit fly actuarial models and biology

Historically demographers have viewed the results of actuarial studies of nonhuman species, particularly those on invertebrates such as fruit flies, as largely irrelevant to investigations on human populations. In this paper I present life table data from large scale studies on the Mediterranean fruit fly, and show that they provide important insights into fundamental aspects of mortality relevant to human populations: the trajectory of mortality at older ages, sex mortality differentials, the concept of maximal life span, and demographic heterogeneity and selection. An overriding theme of the paper is the need for demographers to acquire a heightened awareness of new developments in biology including areas such as evolutionary ecology, experimental demography, and molecular medicine.

Effect of density on age-specific mortality in Drosophila: a density supplementation experiment

Age-specific mortality rates were studied at two adult density levels in four inbred lines of Drosophila melanogaster. In experimental populations, adult densities were maintained at constant levels throughout the experiment by replacing dead flies with live, marked mutants. In control populations, densities declined naturally as the cohorts aged. For all experimental populations the best mortality model is the two-stage Gompertz model, with slower mortality acceleration at older ages. Flies in the experimental populations generally lived longer than flies in control populations, regardless of sex, genotype, or initial density level. The data demonstrate that deceleration of age-specific mortality rates at older ages is not caused by declining cohort densities. Mortality deceleration is a real phenomenon that raises serious questions about the evolution of senescence.

Mortality dynamics of density in the Mediterranean fruit fly

The effects on medfly age-specific mortality of three types of densities--initial, current, and cumulative--were examined using sex-specific data from two sets of studies: (1) previous research on mortality patterns in 1.2 million individuals maintained in 167 different cages (1992 Science 258, 457) and ii) density experiments using a total of 210,000 individuals contained in 49 cages and maintained at one of three initial densities--2500, 5000 and 10,000 flies/cage. A central death rate was computed for each of the 216 cages at specified numerical levels (e.g., 5000, 4000, 1000, 500, 100, and so forth), which was distributed over a range of ages. This yielded a series of mortality schedules at "equivalent current densities." Two main results are reported. First, the leveling off and decline in mortality at the most advanced ages as observed in the original study of 1.2 million medflies cannot be explained as an artifact of declining current densities at older ages. Second, increased initial density heightened the mortality level at each age but had essentially no effect on mortality pattern. The overall methodology and many of the results are believed to be general and thus both logistical and conceptual implications for gerontology and population biology are discussed.

The tails of survival curves

This article focuses on the occasional individuals of many species that live longer than is usual for their populations--here called longevity outliers. They appear to be exceptions to the usual patterns of mortality rates that increase with age. There is no model of survivorship that accommodates all of these individuals. They are less vulnerable to the usual causes of death than most in their populations. There are hints of genetically based mechanisms in the form of life-prolonging genes in invertebrates and genetic resistance to fatal diseases in higher organisms. The reasons why longevity outliers ultimately die are not known. Based on well-established trends, I predict that there will be many more humans reaching very old ages in the next century.

Mortality rates in a genetically heterogeneous population of Caenorhabditis elegans

Age-specific mortality rates in isogenic populations of the nematode Caenorhabditis elegans increase exponentially throughout life. In genetically heterogeneous populations, age-specific mortality increases exponentially until about 17 days and then remains constant until the last death occurs at about 60 days. This period of constant age-specific mortality results from genetic heterogeneity. Subpopulations differ in mean life-span, but they all exhibit near exponential, albeit different, rates of increase in age-specific mortality. Thus, much of the observed heterogeneity in mortality rates later in life could result from genetic heterogeneity and not from an inherent effect of aging.

Shigella dysenteriae type 1 infections in US travellers to Mexico, 1988

In 1825, the actuary Benjamin Gompertz read a paper, ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’, to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz's work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental ‘law of mortality’ has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz's way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.