Toward reconciling inferences concerning genetic variation in senescence in Drosophila melanogaster.

Standard models for senescence predict an increase in the additive genetic variance for log mortality rate late in the life cycle. Variance component analysis of age-specific mortality rates of related cohorts is problematic. The actual mortality rates are not observable and can be estimated only crudely at early ages when few individuals are dying and at late ages when most are dead. Therefore, standard quantitative genetic analysis techniques cannot be applied with confidence. We present a novel and rigorous analysis that treats the mortality rates as missing data following two different parametric senescence models. Two recent studies of Drosophila melanogaster, the original analyses of which reached different conclusions, are reanalyzed here. The two-parameter Gompertz model assumes that mortality rates increase exponentially with age. A related but more complex three-parameter logistic model allows for subsequent leveling off in mortality rates at late ages. We find that while additive variance for mortality rates increases for late ages under the Gompertz model, it declines under the logistic model. The results from the two studies are similar, with differences attributable to differences between the experiments.     

Quantitative genetic tests of recent senescence theory: age-specific mortality and male fertility in Drosophila melanogaster

Quantitative genetic models of aging predict that additive genetic variance for fitness components should increase with age. However, recent studies have found that at very late ages, the genetic variance components decline. This decline may be due to an age-related drop in reproductive effort. If genetic variance in reproductive effort affects the genetic variance in mortality, the decline in reproductive effort at late ages should lead to a decrease in the genetic variance in mortality. To test this, we carried out a large-scale quantitative genetic analysis of age-specific mortality and fertility in virgin male Drosophila melanogaster. As in earlier studies, we found that the additive variance for age-specific mortality and fertility declined at late ages. Also, recent theoretical developments provide new predictions to distinguish between the mutation accumulation (MA) and antagonistic pleiotropy (AP) models of senescence. The deleterious effects of inbreeding are expected to increase with age under MA, but not under AP. This prediction was supported for both age-specific mortality and male fertility. Under AP, the ratio of dominance to additive variance is expected to decline with age. This predicition, too, was supported by the data analyzed here. Taken together, these analyses provide support for both the models playing a role in the aging process. We argue that the time has come to move beyond a simple comparison of these genetic models, and to think more deeply about the evolutionary causes and consequences of senescence.     

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.     

EXPERIMENTAL EVOLUTION OF SENESCENCE: AN ANALYSIS USING A “HETEROGENEITY” MORTALITY MODEL

A long-term laboratory selection experiment has produced replicated populations of fruit flies that differ in mean life span by more than twofold. An analysis of age-specific mortality rates indicated that differences in mean life span have been achieved principally by evolution of patterns of senescence. These results provide empirical confirmation that senescence can be modified within species by appropriate forms of natural selection, which is a fundamental prediction of theories regarding the genetic basis and evolution of senescence. Mortality data were fit to a model that accounts for the leveling off of cohort mortality rates at older ages, but that does not necessarily imply that very old individuals cease to senesce.     

MORTALITY PLATEAUS AND THE EVOLUTION OF SENESCENCE: WHY ARE OLD-AGE MORTALITY RATES SO LOW?

Age-specific mortality rates level off far below 100% at advanced ages in experimental populations of Drosophila melanogaster and other organisms. This observation is inconsistent with the equilibrium predictions of both the antagonistic pleiotropy and mutation accumulation models of senescence, which, under a wide variety of assumptions, predict a “wall” of mortality rates near 100% at postreproductive ages. Previous models of age-specific mortality patterns are discussed in light of recent demographic data concerning late-age mortality deceleration and age-specific properties of new mutations. The most recent theory (Mueller and Rose 1996) argues that existing evolutionary models can easily and robustly explain the demographic data. Here we discuss the sensitivity of that analysis to different types of mutational effects, and demonstrate that its conclusion is very sensitive to assumptions about mutations. A legitimate resolution of evolutionary theory and demographic data will require experimental observations on the age-specificity of mutational effects for new mutations and the degree to which mortality rates in adjacent ages are constrained to be similar (positive pleiotropy), as well as consideration of redundancy and heterogeneity models from demographic theory.     

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.     

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.     

Age-specific properties of spontaneous mutations affecting mortality in Drosophila melanogaster.

An analysis of the effects of spontaneous mutations affecting age-specific mortality was conducted using 29 lines of Drosophila melanogaster that had accumulated spontaneous mutations for 19 generations. Divergence among the lines was used to estimate the mutational variance for weekly mortality rates and the covariance between weekly mortality rates at different ages. Significant mutational variance was observed in both males and females early in life (up to approximately 30 days of age). Mutational variance was not significantly different from zero for mortality rates at older ages. Mutational correlations between ages separated by 1 or 2 wk were generally positive, but they declined monotonically with increasing separation such that mutational effects on early-age mortality were uncorrelated with effects at later ages. Analyses of individual lines revealed several instances of mutation-induced changes in mortality over a limited range of ages. Significant age-specific effects of mutations were identified in early and middle ages, but surprisingly, mortality rates at older ages were essentially unaffected by the accumulation procedure. Our results provide strong evidence for the existence of a class of polygenic mutations that affect mortality rates on an age-specific basis. The patterns of mutational effects measured here relate directly to recently published estimates of standing genetic variance for mortality in Drosophila, and they support mutation accumulation as a viable mechanism for the evolution of senescence.     

Why ageing stops: heterogeneity explains late-life mortality deceleration in nematodes

While ageing is commonly associated with exponential increase in mortality with age, mortality rates paradoxically decelerate late in life resulting in distinct mortality plateaus. Late-life mortality plateaus have been discovered in a broad variety of taxa, including humans, but their origin is hotly debated. One hypothesis argues that deceleration occurs because the individual probability of death stops increasing at very old ages, predicting the evolution of earlier onset of mortality plateaus under increased rate of extrinsic mortality. By contrast, heterogeneity theory suggests that mortality deceleration arises from individual differences in intrinsic lifelong robustness and predicts that variation in robustness between populations will result in differences in mortality deceleration. We used experimental evolution to directly test these predictions by independently manipulating extrinsic mortality rate (high or low) and mortality source (random death or condition-dependent) to create replicate populations of nematodes, Caenorhabditis remanei that differ in the strength of selection in late-life and in the level of lifelong robustness. Late-life mortality deceleration evolved in response to differences in mortality source when mortality rate was held constant, while there was no consistent response to differences in mortality rate. These results provide direct experimental support for the heterogeneity theory of late-life mortality deceleration.     

The evolution of age-specific mortality rates in Drosophila melanogaster: genetic divergence among unselected lines.

Age-specific effects of spontaneous mutations on mortality rates in Drosophila are inferred from three large demographic experiments. Data were collected from inbred lines that were allowed to accumulate spontaneous mutations for 10, 19, and 47 generations. Estimates of age-specific mutational variance for mortality were based on data from all three experiments, totalling approximately 225,000 flies, using a model developed for genetic analysis of age-dependent traits (the character process model). Both within- and among-generation analyses suggest that the input of genetic variance is greater for early life mortality rates than for mortality at older ages. In females, age-specific mutational variances ranged over an order of magnitude from 5.96 x 10(-3) at 2 wk posteclosion to 0.02 x 10(-3) at 7 wk. The male data show a similar pattern. Age-specific genetic variances were substantially less at generation 47 than at generation 19-an unexplained observation that is likely due to block effects. Mutational correlations among mortality rates at different ages tend to increase with the accumulation of new mutations. Comparison of the mutation-accumulation lines at generations 19 and 47 with their respective control lines suggests little age-specific mutational bias.     

Age-Specific Patterns of Genetic Variance in Drosophila Melanogaster. I. Mortality

PETER MEDAWAR proposed that senescence arises from an age-related decline in the force of selection, which allows late-acting deleterious mutations to accumulate. Subsequent workers have suggested that mutation accumulation could produce an age-related increase in additive genetic variance (V(A)) for fitness traits, as recently found in Drosophila melanogaster. Here we report results from a genetic analysis of mortality in 65,134 D. melanogaster. Additive genetic variance for female mortality rates increases from 0.007 in the first week of life to 0.325 by the third week, and then declines to 0.002 by the seventh week. Males show a similar pattern, though total variance is lower than in females. In contrast to a predicted divergence in mortality curves, mortality curves of different genotypes are roughly parallel. Using a three-parameter model, we find significant V(A) for the slope and constant term of the curve describing age-specific mortality rates, and also for the rate at which mortality decelerates late in life. These results fail to support a prediction derived from MEDAWAR's ``mutation accumulation' theory for the evolution of senescence. However, our results could be consistent with alternative interpretations of evolutionary models of aging.     

Probing the evolution of senescence inDrosophila melanogaster withP-element tagging

Natural populations host a wealth of genetic variation in longevity and age-specific schedules of reproduction. This variation provides critical information for inferring the evolutionary origin of senescence. Patterns of mutational effects on age-specific fecundity and survival provide additional insight to distinguish alternative models of senescence. In this study,P-elements bearing thewhite minigene were inserted at random into a common genetic background, generating lines ofD. melanogaster with single, stable transposon inserts. A series of 48 single-P-element lines revealed statistically significant heterogeneity in both longevity and fecundity. Longevity and early fecundity were only weakly positively correlated (r=0.286,P=0.0398). Both the pooled sample and 30 of the individual lines exhibited a leveling of age-specific mortality at advanced ages, in opposition to the classical demographic models. To the extent that these mutational effects are representative of naturally-occurring mutations in heterogeneous populations, this result presents a problem for the evolutionary theory of senescence. Natural selection is inefficient at removing deleterious mutations that are expressed only at late ages, and selection may not differentiate between mutations whose effects on longevity are post-reproductive. A leveling of the mortality rate would also be seen if mutations whose expression is delayed until very late simply do not occur. A simulation of mutation-selection balance among the 48P-element tagged lines shows that the mean longevity declines monotonically with increasing mutation rate, consistent with the mutation-accumulation model.     

The influence of environmentally induced heterogeneity on age-specific genetic variance for mortality rates

Using parametric models that describe the increase in mortality rates with age, we demonstrate that environmentally induced heterogeneity among genetically identical individuals is sufficient to generate biased estimates of age-specific genetic variance. Although the magnitude of the bias may change with age, one general trend emerges: the true genetic variance at the oldest ages is likely to be dramatically underestimated. Our results are robust to different manifestations of heterogeneity and suggest that such a bias is a general feature of these models. We note that age-dependent estimates of genetic variance for characters that are correlated with mortality (either genetically or environmentally) can be expected to be similarly affected. The results are independent of sample size and suggest that the bias may be more widespread in the literature than is currently appreciated. Our results are discussed with reference to existing data on mortality variance in Drosophila melanogaster.     

Stage dynamics, period survival, and mortality plateaus

Mortality plateaus at advanced ages have been found in many species, but their biological causes remain unclear. Here, we exploit age-from-stage methods for organisms with stage-structured demography to study cohort dynamics, obtaining age patterns of mortality by weighting one-period stage-specific survivals by expected age-specific stage structure. Cohort dynamics behave as a killed Markov process. Using as examples two African grasses, one pine tree, a temperate forest perennial herb, and a subtropical shrub in a hurricane-driven forest, we illustrate diverse patterns that may emerge. Age-specific mortality always reaches a plateau at advanced ages, but the plateau may be reached rapidly or slowly, and the trajectory may follow positive or negative senescence along the way. In variable environments, birth state influences mortality at early but not late ages, although its effect on the level of survivorship persists. A new parameter micro omega summarizes the risk of mortality averaged over the entire lifetime in a variable environment. Recent aging models for humans that employ nonobservable abstract states of "vitality" are also known to produce diverse trajectories and similar asymptotic behavior. We discuss connections, contrasts, and implications of our results to these models for the study of aging.     

Evolution of late-life mortality in Drosophila melanogaster

Abstract.— 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.     

Patterns of age-specific means and genetic variances of mortality rates predicted by the mutation-accumulation theory of ageing

A general quantitative genetic model of mutations with age-specific deleterious effects is developed. It is shown that, for the simplest case of a species with age-independent reproductive rates and extrinsic adult mortality rates, and no pleiotropic effects of age-specific mutations, exponential increases with age of both the mean and additive genetic variance of age-specific mortality rates are expected. Models where age-specific mutations have pleiotropic effects on mortality that extend either throughout adult life, or are confined to juvenile stages, produce equilibria with exponential increases in the mean and additive variance of mortality rates during much of adult life. However, the rates of increase diminish late in life, and can even become zero. Predictions concerning the additive genetic correlations in mortality rates between different ages are also developed. The predictions of the models are compared with data on humans and Drosophila.     

Quantitative trait loci with age-specific effects on fecundity in Drosophila melanogaster

Life-history theory and evolutionary theories of aging assume the existence of alleles with age-specific effects on fitness. While various studies have documented age-related changes in the genetic contribution to variation in fitness components, we know very little about the underlying genetic architecture of such changes. We used a set of recombinant inbred lines to map and characterize the effects of quantitative trait loci (QTL) affecting fecundity of Drosophila melanogaster females at 1 and 4 weeks of age. We identified one QTL on the second chromosome and one or two QTL affecting fecundity on the third chromosome, but these QTL affected fecundity only at 1 week of age. There was more genetic variation for fecundity at 4 weeks of age than at 1 week of age and there was no genetic correlation between early and late-age fecundity. These results suggest that different loci contribute to the variation in fecundity as the organism ages. Our data provide support for the mutation accumulation theory of aging as applied to reproductive senescence. Comparing the results from this study with our previous work on life-span QTL, we also find evidence that antagonistic pleiotropy may contribute to the genetic basis of senescence in these lines as well.     

The reliability theory of aging and longevity.

Reliability theory is a general theory about systems failure. It allows researchers to predict the age-related failure kinetics for a system of given architecture (reliability structure) and given reliability of its components. Reliability theory predicts that even those systems that are entirely composed of non-aging elements (with a constant failure rate) will nevertheless deteriorate (fail more often) with age, if these systems are redundant in irreplaceable elements. Aging, therefore, is a direct consequence of systems redundancy. Reliability theory also predicts the late-life mortality deceleration with subsequent leveling-off, as well as the late-life mortality plateaus, as an inevitable consequence of redundancy exhaustion at extreme old ages. The theory explains why mortality rates increase exponentially with age (the Gompertz law) in many species, by taking into account the initial flaws (defects) in newly formed systems. It also explains why organisms "prefer" to die according to the Gompertz law, while technical devices usually fail according to the Weibull (power) law. Theoretical conditions are specified when organisms die according to the Weibull law: organisms should be relatively free of initial flaws and defects. The theory makes it possible to find a general failure law applicable to all adult and extreme old ages, where the Gompertz and the Weibull laws are just special cases of this more general failure law. The theory explains why relative differences in mortality rates of compared populations (within a given species) vanish with age, and mortality convergence is observed due to the exhaustion of initial differences in redundancy levels. Overall, reliability theory has an amazing predictive and explanatory power with a few, very general and realistic assumptions. Therefore, reliability theory seems to be a promising approach for developing a comprehensive theory of aging and longevity integrating mathematical methods with specific biological knowledge.     

Age-independent and age-dependent decreases in reproduction of females

The terminal allocation and senescence hypotheses make opposite predictions about how age-specific reproductive effort should vary during old age. There is empirical support for both hypotheses, although reports on senescence are more numerous. Individual heterogeneity and selective mortality, however, decrease our ability to measure how reproductive effort varies during late life. The damage accumulation model proposes that terminal allocation and senescence could be partly age-independent. Using a reverse-age approach, we analysed an unusually complete record of annual reproductive success for 90 bighorn ewes that died between 7 and 18years of age. We estimated age-specific and age-independent variation of reproductive effort in late-life. Reproductive effort decreased in the two last reproductions, independently of age at death. Fecundity also decreased in the last 2years of life, with a steeper decline for older individuals. Our study reveals that reproductive senescence includes both age-dependent and age-independent components.