The fractionation experiment: reducing heterogeneity to investigate age-specific mortality in Drosophila

Using a penalized likelihood to detect mortality deceleration

We suggest a novel method for detecting mortality deceleration by adding a penalty to the log-likelihood function in a gamma-Gompertz setting. This is an alternative to traditional likelihood inference and hypothesis testing. The main advantage of the proposed method is that it does not involve using a p-value, hypothesis testing, and asymptotic distributions. We evaluate the performance of our approach by comparing it with traditional likelihood inference on both simulated and real mortality data. Results have shown that our method is more accurate in detecting mortality deceleration and provides more reliable estimates of the underlying parameters. The proposed method is a significant contribution to the literature as it offers a powerful tool for analyzing mortality patterns.

Terminal life history: late-life fecundity and survival in experimental populations of Drosophila melanogaster

There are two life history landmarks that can be used to define the terminal period in individual Drosophila melanogaster females: the cessation of daily oviposition, which defines the start of the retired stage, and final oviposition, which defines the start of post-ovipository survival. The terminal period is a substantial component of D. melanogaster life history. Analysis of published data on the daily fecundity and survival of 3971 individually maintained, mated female flies reveals that the terminal period is far more variable within populations than other life history components, including total adult life span. It has been reported that there is a negative correlation between fecundity and duration of the terminal state in recently collected wild stocks. Here I show that the negative correlation occurs in multiple inbred and outbred lab-adapted populations as well. In terms of proportion of adult life, lower fecundity flies spend on average twice as much time in the terminal stage as higher fecundity flies from the same population. Both high and low fecundity flies experience end-of-life plateaus in mortality, with the former exhibiting higher plateau levels. The negative correlation between fecundity and terminal survival is of sufficient magnitude to create heterogeneity among the oldest old: the final 10% of survivors are predominately flies with a history of high fecundity, but about one in five is a low fecundity fly with long terminal stage.

Multiple Metazoan Life-span Interventions Exhibit a Sex-specific Strehler-Mildvan Inverse Relationship Between Initial Mortality Rate and Age-dependent Mortality Rate Acceleration

The Gompertz equation describes survival in terms of initial mortality rate (parameter a), indicative of health, and age-dependent acceleration in mortality rate (parameter b), indicative of aging. Gompertz parameters were analyzed for several published studies. In Drosophila females, mating increases egg production and decreases median life span, consistent with a trade-off between reproduction and longevity. Mating increased parameter a, causing decreased median life span, whereas time parameter b was decreased. The inverse correlation between parameters indicates the Strehler-Mildvan (S-M) relationship, where loss of low-vitality individuals yields a cohort with slower age-dependent mortality acceleration. The steroid hormone antagonist mifepristone/RU486 reversed these effects. Mating and mifepristone showed robust S-M relationships across genotypes, and dietary restriction showed robust S-M relationship across diets. Because nutrient optima differed between females and males, the same manipulation caused opposite effects on mortality rates in females versus males across a range of nutrient concentrations. Similarly, p53 mutation in Drosophila and mTOR mutation in mice caused increased median life span associated with opposite direction changes in mortality rate parameters in females versus males. The data demonstrate that dietary and genetic interventions have sex-specific and sometimes sexually opposite effects on mortality rates consistent with sexual antagonistic pleiotropy.

Retired flies, hidden plateaus, and the evolution of senescence in Drosophila melanogaster

Late-life plateaus in age-specific mortality have been an evolutionary and biodemographic puzzle for decades. Although classic theory on the evolution of senescence predicts late-life walls of death, observations in experimental organisms document the opposite trend: a slowing in the rate of increase of mortality at advanced ages. Here, I analyze published life-history data on individual Drosophila melanogaster females and argue for a fundamental change in our understanding of mortality in this important model system. Mortality plateaus are not, as widely assumed, exclusive to late life, and are not explained by population heterogeneity-they are intimately connected to individual fecundity. Female flies begin adult life in the working stage, a period of active oviposition and low but accelerating mortality. Later they transition to the retired stage, a terminal period characterized by limited fecundity and relatively constant mortality. Because ages of transition differ between flies, age-synchronized cohorts contain a mix of working and retired flies. Early- and mid-life plateaus are obscured by the presence of working flies, but can be detected when cohorts are stratified by retirement status. Stage-specificity may be an important component of Drosophila life-history evolution.

On the analysis and interpretation of late-life fecundity in Drosophila melanogaster

Late-life plateaus have been described in both cohort and individual trajectories of fecundity in Drosophila melanogaster females. Here I examine life history data recently analyzed by Le Bourg and Moreau (2014) and show that non-linearity in the cohort trajectory of fecundity is largely explained by heterogeneity in the duration of reproductive life spans. A model specifying linear post-peak decline of fecundity in individual flies provides a better fit to the data than one that combines linear decline with late-life fecundity plateaus. Using repeated measures analysis of variance, I show that age-dependent trends in individual fecundity are mostly linear, while among the most longevous individuals up to 20% of the variation in trends is non-linear. Plateaus in individual trajectories might be explained by evolutionary processes or by random environmental variation. The dominant role of environmental variation is supported by several observations, including the high variability of late-life fecundity, the occurrence of occasional individual plateaus in inbred lines, and the observation of plateaus in only a fraction of the population. Plateau and non-plateau flies identified by Le Bourg and Moreau (2014) have, on average, the same total fecundity and the same fecundity trajectories. The available evidence suggests that the environmental variance for late-life fecundity is sufficiently large to produce occasional individual trajectories that resemble plateaus but are not heritable.

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.

Targeting copper induced oxidative damage to proteins by ligation: a novel approach towards chelation therapy for oxidative stress disorders

DIDE and rhodanine prevent the copper induced oxidative damage to proteins by binding copper into a redox inactive state.

Evolution of aging: individual life history trade-offs and population heterogeneity account for mortality patterns across species

A broad range of mortality patterns has been documented across species, some even including decreasing mortality over age. Whether there exist a common denominator to explain both similarities and differences in these mortality patterns remains an open question. The disposable soma theory, an evolutionary theory of aging, proposes that universal intracellular trade-offs between maintenance/lifespan and reproduction would drive aging across species. The disposable soma theory has provided numerous insights concerning aging processes in single individuals. Yet, which specific population mortality patterns it can lead to is still largely unexplored. In this article, we propose a model exploring the mortality patterns which emerge from an evolutionary process including only the disposable soma theory core principles. We adapt a well-known model of genomic evolution to show that mortality curves producing a kink or mid-life plateaus derive from a common minimal evolutionary framework. These mortality shapes qualitatively correspond to those of Drosophila melanogaster, Caenorhabditis elegans, medflies, yeasts and humans. Species evolved in silico especially differ in their population diversity of maintenance strategies, which itself emerges as an adaptation to the environment over generations. Based on this integrative framework, we also derive predictions and interpretations concerning the effects of diet changes and heat-shock treatments on mortality patterns.

How evolving heterogeneity distributions of resource allocation strategies shape mortality patterns

It is well established that individuals age differently. Yet the nature of these inter-individual differences is still largely unknown. For humans, two main hypotheses have been recently formulated: individuals may experience differences in aging rate or aging timing. This issue is central because it directly influences predictions for human lifespan and provides strong insights into the biological determinants of aging. In this article, we propose a model which lets population heterogeneity emerge from an evolutionary algorithm. We find that whether individuals differ in (i) aging rate or (ii) timing leads to different emerging population heterogeneity. Yet, in both cases, the same mortality patterns are observed at the population level. These patterns qualitatively reproduce those of yeasts, flies, worms and humans. Such findings, supported by an extensive parameter exploration, suggest that mortality patterns across species and their potential shapes belong to a limited and robust set of possible curves. In addition, we use our model to shed light on the notion of subpopulations, link population heterogeneity with the experimental results of stress induction experiments and provide predictions about the expected mortality patterns. As biology is moving towards the study of the distribution of individual-based measures, the model and framework we propose here paves the way for evolutionary interpretations of empirical and experimental data linking the individual level to the population level.

A new cultivation system for studying chemical effects on the lifespan of the fruit fly

A side-by-side comparison was made between a conventional vial system and a novel bottle system for cultivating flies and testing the effect of chemical exposure on the lifespan of the flies. While the two cultivation systems yielded very similar results for the effect of DEHP (di[2-ethylhexyl] phthalate) on reducing the lifespan of fruit fly Drosophila melanogaster, the new bottle system has many advantages over the conventional vial system. The bottle system allowed long-term cultivation of flies in the same bottle and thus eliminated the need for transferring of flies between vials. Foods/nutrients were provided as fresh moisture medium coated on a glass slide vertically hanged in the center of the bottle. Fly discharges and dead flies were collected onto a draw horizontally inserted into the bottom of the bottle. These features have resulted in great convenience for cultivating flies and reduced labor and media cost. The effective separation of food from discharge may allow accurate mass balance measurement and thus yield more definitive observations for understanding the actual role of calorie restriction (CR) or dietary-restriction (DR) in fly metabolism and longevity.

Hamilton's forces of natural selection after forty years

In 1966, William D. Hamilton published a landmark paper in evolutionary biology: "The Moulding of Senescence by Natural Selection." It is now apparent that this article is as important as his better-known 1964 articles on kin selection. Not only did the 1966 article explain aging, it also supplied the basic scaling forces for natural selection over the entire life history. Like the Lorentz transformations of relativistic physics, Hamilton's Forces of Natural Selection provide an overarching framework for understanding the power of natural selection at early ages, the existence of aging, the timing of aging, the cessation of aging, and the timing of the cessation of aging. His twin Forces show that natural selection shapes survival and fecundity in different ways, so their evolution can be somewhat distinct. Hamilton's Forces also define the context in which genetic variation is shaped. The Forces of Natural Selection are readily manipulable using experimental evolution, allowing the deceleration or acceleration of aging, and the shifting of the transition ages between development, aging, and late life. For these reasons, evolutionary research on the demographic features of life history should be referred to as "Hamiltonian."

An evolutionary heterogeneity model of late-life fecundity in Drosophila

There is now a significant body of research that establishes the deceleration of mortality rates in late life and their ultimate leveling off on a late-life plateau. Natural selection has been offered as one mechanism responsible for these plateaus. The force of natural selection should also exert such effects on female fecundity. We have already developed a model of female fecundity in late life that incorporates the general predictions of the evolutionary model. The original evolutionary model predicts a decline in fecundity from a peak in early life, followed by a plateau with non-zero fecundity in late life. However, in Drosophila there is also a well-defined decline in fecundity among dying flies, here called the "death spiral". This effect produces heterogeneity between dying and non-dying flies. Here a hybrid evolutionary heterogeneity model is developed to accommodate both the evolutionary plateau prediction and the death spiral. It is shown that this evolutionary heterogeneity model gives a much better fit to late-life fecundity data.

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.

Evolution of late-life fecundity in Drosophila melanogaster

Late-life fecundity has been shown to plateau at late ages in Drosophila analogously to late-life mortality rates. In this study, we test an evolutionary theory of late life based on the declining force of natural selection that can explain the occurrence of these late-life plateaus in Drosophila. We also examine the viability of eggs laid by late-age females and test a population genetic mechanism that may be involved in the evolution of late-life fecundity: antagonistic pleiotropy. Together these experiments demonstrate that (i) fecundity plateaus at late ages, (ii) plateaus evolve according to the age at which the force of natural selection acting on fecundity reaches zero, (iii) eggs laid by females in late life are viable and (iv) antagonistic pleiotropy is involved in the evolution of late-life fecundity. This study further supports the evolutionary theory of late life based on the age-specific force of natural selection.

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.

Protein networks, pleiotropy and the evolution of senescence

The number of interactions, or connectivity, among proteins in the yeast protein interaction network follows a power law. I compare patterns of connectivity for subsets of yeast proteins associated with senescence and with five other traits. I find that proteins associated with ageing have significantly higher connectivity than expected by chance, a pattern not seen for most other datasets. The pattern holds even when controlling for other factors also associated with connectivity, such as localization of protein expression within the cell. I suggest that these observations are consistent with the antagonistic pleiotropy theory for the evolution of senescence. In further support of this argument, I find that a protein's connectivity is positively correlated with the number of traits it influences or its degree of pleiotropy, and further show that the average degree of pleiotropy is greatest for proteins associated with senescence. I explain these results with a simple mathematical model combining assumptions of the antagonistic pleiotropy theory for the evolution of senescence with data on network topology. These findings integrate molecular and evolutionary models of senescence, and should aid in the search for new ageing genes.

Dissociation between functional senescence and oxidative stress resistance in Drosophila

Many studies strongly suggest a causal link between oxidative stress and determination of life span. The relationship between oxidative stress and age-related functional declines, however, is less clear. Additionally, the full spectrum of functional declines associated with aging has not been systematically evaluated in the fruit fly, Drosophila melanogaster, one of the leading models for aging research. Toward a more comprehensive assessment of functional senescence in Drosophila, we evaluated a series of behaviors in control flies of increasing ages. Our studies reveal a novel age-dependent functional decline in the olfactory system and confirm previous reports of age-related locomotor defects in flies. Behavioral responses to electric shock and light are maintained in aged flies. Thus, some sensory systems senesce during the first several weeks of life while others do not. Interestingly, the age-dependent functional declines in olfactory and locomotor systems are indistinguishable in control flies and methuselah, a mutant with enhanced resistance to oxidative stress and increased life span. Our results indicate that enhanced resistance to oxidative stress and extension of life span do not necessarily confer protection from age-related functional declines.

A test of evolutionary theories of aging

Senescence is a nearly universal feature of multicellular organisms, and understanding why it occurs is a long-standing problem in biology. The two leading theories posit that aging is due to (i) pleiotropic genes with beneficial early-life effects but deleterious late-life effects ("antagonistic pleiotropy") or (ii) mutations with purely deleterious late-life effects ("mutation accumulation"). Previous attempts to distinguish these theories have been inconclusive because of a lack of unambiguous, contrasting predictions. We conducted experiments with Drosophila based on recent population-genetic models that yield contrasting predictions. Genetic variation and inbreeding effects increased dramatically with age, as predicted by the mutation theory. This increase occurs because genes with deleterious effects with a late age of onset are unopposed by natural selection. Our findings provide the strongest support yet for the mutation theory.

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.

Male genotype affects female longevity in Drosophila melanogaster

Several recent studies suggest that interactions with conspecific males can reduce the longevity of female Drosophila melanogaster or support the idea that male and female fitness components are involved in antagonistic interactions. Here we report that males from third-chromosome isogenic lines demonstrated significant genetic variation in male reproductive performance and in the longevity of their mates. Increased male performance was marginally significantly associated with one measure of increased female survival rate. However, there was no indication of tradeoffs or negative correlations between male reproductive success and female survival. We discuss alternative hypotheses for the cause of the induced variation in female longevity.

Ageing and immortality

The concept of the force of natural selection was developed to explain the evolution of ageing. After ageing, however, comes a period in which mortality rates plateau and some individual organisms could, in theory, live forever. This late-life immortality has no presently agreed upon explanation. Two main theories have been offered. The first is heterogeneity within ageing cohorts, such that only extremely robust individuals survive ageing. This theory can be tested by comparisons of more and less robust cohorts. It can also be tested by fitting survival data to its models. The second theory is that late-life plateaus in mortality reflect the inevitable late-life plateau in the force of natural selection. This theory can be tested by changing the force of natural selection in evolving laboratory populations, particularly the age at which the force plateaus. This area of research has great potential for elucidating the overall structure of life-history evolution, particularly the interrelationship between the three life-history phases of development, ageing and immortality.

Age-specific decrease in aerobic efficiency associated with increase in oxygen free radical production in Drosophila melanogaster

This study was designed to test the free radical theory of aging by using Drosophila melanogaster as a model system. Oxygen free radicals are generated by mitochondria during the process of normal oxidative metabolism. Age-specific measurements of oxygen consumption, heat production and anti-oxidant enzyme activity were obtained from two inbred lines of male flies, one selected for longevity and one normal-lived. The findings of this study demonstrate that although oxygen consumption remains relatively constant over the majority of the life span of each line of flies, aerobic efficiency declines with advancing age. This loss of aerobic efficiency manifests itself as a decline in total body metabolism as measured by heat production, and appears to be associated with an age-specific increase in damage inflicted upon mitochondria by oxygen free radicals.

Heterogeneity in Individual Mortality Risk and Its Importance for Evolutionary Studies of Senescence

Mortality was simulated under the assumption of heterogeneity in individual age-specific mortality risk. Heterogeneity was modeled by assigning each individual its own Gompertz mortality function. Means and variances of the Gompertz intercept and slope parameters were based on published data for Drosophila melanogaster. Simulations of large cohorts reproduced mortality plateaus similar to those observed for actual cohorts of flies. Catastrophic late-age mortality was not observed except when heterogeneity was very low and rates of senescence were very high. A second set of simulations was designed to mimic experiments that have investigated age-specific patterns of genetic variance in mortality rates. Within-genotype heterogeneity in mortality risk resulted in a decline in genetic variance of mortality rates at old ages. That result suggests that the decline in genetic variance at old ages that has been observed in some experiments is an artifact of heterogeneity. Mortality rate plateaus, decrease in genetic variance of mortality rates at old ages, and absence of catastrophic late-age mortality all appear to contradict predictions of the evolutionary theory of senescence. Heterogeneity in mortality risk may explain those contradictions.

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.