Mortality Plateaus Research Articles

Three Editorials—Three Historical Allusions

University of Toronto, Sunnybrook Health Science Centre, Toronto, Ontario, Canada. beverley.orser@utoronto.caIn Reply:— I thank Dr. Roy for his thoughtful integration of the three editorials.1–3His broad overview of the evolution of anesthetic practice highlights two important points. As a result of the hard work of our forefathers, we have developed a remarkable understanding of “what anesthetics do.” These insights have produced unprecedented advances in patient safety, primarily as a result of improved monitoring and drug delivery systems. However, we are also reminded that we still don't understand “how anesthetics work.” This lack of knowledge has resulted in a paucity of radically new anesthetic drugs which, in turn, has contributed to a plateau in anesthesia-related mortality.4The specialty of anesthesiology must be ambitious and relentless in its efforts to develop safer anesthetic drugs and improved drug administration strategies. This effort will require a firm commitment to train young investigators who will bring the best science to bear on this important goal.University of Toronto, Sunnybrook Health Science Centre, Toronto, Ontario, Canada. beverley.orser@utoronto.ca

The vitality model: A way to understand population survival and demographic heterogeneity

A four-parameter model describing mortality as the first passage of an abstract measure of survival capacity, vitality, is developed and used to explore four classic problems in demography: (1) medfly demographic paradox, (2) effect of diet restriction on longevity, (3) cross-life stage effects on survival curves and (4) mortality plateaus. The model quantifies the sources of mortality in these classical problems into vitality-dependent and independent parts, and characterizes the vitality-dependent part in terms of initial and evolving heterogeneities. Three temporal scales express the balance of these factors: a time scale of death from senescence, a time scale of accidental mortality and a crossover time between evolving vs. initial heterogeneity. The examples demonstrate how the first-passage approach provides a unique and informative perspective into the processes that shape the survival curves of populations.

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.

The evolution of senescence through decelerating selection for system reliability

Senescence is a universal phenomenon in organisms, characterized by increasing mortality and decreasing fecundity with advancing chronological age. Most proximate agents of senescence, such as reactive oxygen species and UV radiation, are thought to operate by causing a gradual build-up of bodily damage. Yet most current evolutionary theories of senescence emphasize the deleterious effects of functioning genes in late life, leaving a gap between proximate and ultimate explanations. Here, we present an evolutionary model of senescence based on reliability theory, in which beneficial genes or gene products gradually get damaged and thereby fail, rather than actively cause harm. Specifically, the model allows organisms to evolve multiple redundant copies of a gene product (or gene) that performs a vital function, assuming that organisms can avoid condition-dependent death so long as at least one copy remains undamaged. We show that organisms with low levels of extrinsic mortality, and high levels of genetic damage, tend to evolve high levels of redundancy, and that mutation-selection balance results in a stable population distribution of the number of redundant elements. In contrast to previous evolutionary models of senescence, the mortality curves that emerge from such populations match empirical senescence patterns in three key respects: they exhibit: (1) an initially low, but rapidly increasing mortality rate at young ages, (2) a plateau in mortality at advanced ages and (3) 'mortality compensation', whereby the height of the mortality plateau is independent of the environmental conditions under which different populations evolved.

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.

Z. Yi, E. M. Crimmins, Y. Carrière and J.-M. Robine, Longer Life and Healthy Aging

Z. Yi, E. M. Crimmins, Y. Carrière and J.-M. Robine, Longer Life and Healthy Aging

The Genetic Architecture of Life Span and Mortality Rates: Gender and Species Differences in Inbreeding Load of Two Seed-Feeding Beetles

We examine the inbreeding load for adult life span and mortality rates of two seed beetle species, Callosobruchus maculatus and Stator limbatus. Inbreeding load differs substantially between males and females in both study populations of C. maculatus--life span of inbred females was 9-13% shorter than the life span of outbred females, whereas the life span of inbred males did not differ from the life span of outbred males. The effect of inbreeding on female life span was largely due to an increase in the slope of the mortality curve. In contrast, inbreeding had only a small effect on the life span of S. limbatus--life spans of inbred beetles were approximately 5% shorter than those of outbred beetles, and there was no difference in inbreeding load between the sexes. The inbreeding load for mean life span was approximately 0.4-0.6 lethal equivalents per haploid gamete for female C. maculatus and approximately 0.2-0.3 for both males and females of S. limbatus, all within the range of estimates commonly obtained for Drosophila. However, contrary to the predictions of mutation-accumulation models, inbreeding load for loci affecting mortality rates did not increase with age in either species, despite an effect of inbreeding on the initial rate of increase in mortality. This was because mortality rates decelerated with age and converged to a mortality plateau for both outbred and inbred beetles.

Seasonal sea turtle mortality risk from forced submergence in bottom trawls

The risk of mortality to sea turtles with increasing trawl tow time was assessed in two seasons, summer and winter. Tows of 10 min or less had negligible mortality in both seasons while intermediate tow times resulted in rapid escalations in mortality before reaching a plateau of high mortality. Mortality increased more quickly in winter than in summer.

Simulations of a mortality plateau in the sexual Penna model for biological aging

The Penna model is a strategy to simulate the genetic dynamics of age-structured populations, in which the individual genomes are represented by bit strings. It provides a simple metaphor for the evolutionary process in terms of the mutation accumulation theory. In its original version, an individual dies due to inherited diseases when its current number of accumulated mutations, n, reaches a threshold value T. Since the mean number of diseases increases with age, the probability to die is zero for very young ages (n < T) and equals 1 for the old ones (n > or = T). Here, instead of using a step function to determine the genetic death age, we test several other functions that may or may not slightly increase the death probability at young ages (n < T), but that decrease this probability at old ones. Our purpose is to study the oldest old effect, that is, a plateau in the mortality curves at advanced ages. By imposing certain conditions, it has been possible to obtain a clear plateau using the Penna model. However, a more realistic one appears when a modified version, that keeps the population size fixed without fluctuations, is used. We also find a relation between the birth rate, the age structure of the population, and the death probability.

Learning curve for laparoscopic Roux-en-Y gastric bypass with totally hand-sewn anastomosis

Laparoscopic Roux-en-Y gastric bypass (LRYGB) is a challenging operation for the treatment of morbid obesity with well-demonstrated effectiveness in weight lost. There are several variations to the technique. From September 2000 to July 2004, 600 consecutive patients underwent surgery for morbid obesity at our institution. The surgical technique employed was LRYGB with totally hand-sewn gastrojejunal anastomosis (GJA). All patients were considered candidates for laparoscopic approach regardless of age, gender, body mass index (BMI), or previous bariatric or digestive surgery. Mean BMI was 44.4 +/- 7.6 kg/m2. Thirty-two patients had undergone previous failed bariatric procedures. Conversion to an open procedure was necessary in three patients. Seventy-two patients (12%) developed early complications, including 23 (3.8%) leaks at the GJA (eight in the first 18 patients). Mortality rate was 1.1% (one death was related to GJA leakage). Early and late reoperation rates were 5.3 and 1.8%, respectively. Rate plateau of morbidity and mortality was reached after the first 18 patients when the surgical technique was fully standardized. LRYGB is a technically demanding procedure for the surgical treatment of morbid obesity with significant morbidity during the learning curve. The learning curve can be soon overcome, reaching a rate plateau of complications after adequate training. Morbidly obese patients should be operated on in expert bariatric surgical laparoscopic units to obtain the best results.

Survival Models Based on the Ornstein-Uhlenbeck Process

When modelling survival data it may be of interest to imagine an underlying process leading up to the event in question. The Ornstein-Uhlenbeck process is a natural model to consider in a biological context because it stabilizes around some equilibrium point. This corresponds to the homeostasis often observed in biology, and also to some extent in the social sciences. First, we study the first-passage time distribution of an Ornstein-Uhlenbeck process, focussing especially on what is termed quasi-stationarity and the various shapes of the hazard rate. Next, we consider a model where the individual hazard rate is a squared function of an Ornstein-Uhlenbeck process. We extend known results on this model. The results on quasi-stationarity are relevant for recent discussions about mortality plateaus. In addition, we point out a connection to models for short-term interest rates in financial modeling.

Solvable senescence model with positive mutations.

We build upon our previous analytical results for the Penna model of senescence to include positive mutations. We investigate whether a small but nonzero positive mutation rate gives qualitatively different results to the traditional Penna model in which no positive mutations are considered. We find that the high-lifespan tail of the distribution is radically changed in structure, but that there is not much effect on the bulk of the population. The mortality plateau that we found previously for a stochastic generalization of the Penna model is stable to a small positive mutation rate.

The Reliability‐Engineering Approach to the Problem of Biological Aging

We applied reliability theory to explain aging of biological species and came to the following conclusions: (1) Redundancy is a key notion for understanding aging and the systemic nature of aging in particular. Systems, which are redundant in numbers of irreplaceable elements, do deteriorate (i.e., age) over time, even if they are built of nonaging elements. (2) An apparent aging rate or expression of aging (measured as age differences in failure rates, including death rates) is higher for systems with higher redundancy levels. (3) Redundancy exhaustion over the course of life explains the observed compensation law of mortality (mortality convergence at later life) as well as the observed late-life mortality deceleration, leveling-off, and mortality plateaus. (4) Living organisms seem to be formed with a high load of initial damage, and therefore their life span and aging patterns may be sensitive to early-life conditions that determine this initial damage load during early development.

Markov mortality models: implications of quasistationarity and varying initial distributions

This paper explains some implications of Markov-process theory for models of mortality. We show that an important qualitative feature common to empirical mortality data, and which has been found in certain models—the convergence to a “mortality plateau”—is, in fact, a generic consequence of the models’ convergence to a “quasistationary distribution”. This phenomenon has been explored extensively in the mathematical literature. Not only does this generalization free important results from specifics of the models, it also suggests a new explanation for the convergence to constant mortality. At the same time that we show that the late behavior of these models—convergence to a finite asymptote—is almost logically immutable, we also point out that the early behavior of the mortality rates can be more flexible than has been generally acknowledged. We show, in particular, that an appropriate choice of initial conditions enables one popular model to approximate any reasonable hazard-rate data. This illustrates how precarious it can be to read a model's vindication from its consilience with a favored hazard-rate function, such as the Gompertz exponential.

A multistage theory of age-specific acceleration in human mortality

BackgroundHumans die at an increasing rate until late in life, when mortality rates level off. The causes of the late-life mortality plateau have been debated extensively over the past few years. Here, I examine mortality patterns separately for each of the leading causes of death. The different causes of death show distinct mortality patterns, providing some clues about the varying acceleration of mortality at different ages.ResultsI examine mortality patterns by first plotting the data of mortality rate versus age on a log-log scale. The slope of the age-specific mortality rate at each age is the age-specific acceleration of mortality. About one-half of total deaths have causes with similar shapes for the age-specific acceleration of mortality: a steady rise in acceleration from midlife until a well-defined peak at 80 years, followed by a nearly linear decline in acceleration. This first group of causes includes heart disease, cerebrovascular disease, and accidental deaths. A second group, accounting for about one-third of all deaths, follows a different pattern of age-specific acceleration. These diseases show an approximately linear rise in acceleration to a peak at 35–45 years of age, followed by a steep and steady decline in acceleration for the remainder of life. This second group includes cancer, chronic respiratory diseases, and liver disease. I develop a multistage model of disease progression to explain the observed patterns of mortality acceleration.ConclusionsA multistage model of disease progression can explain both the early-life increase and late-life decrease in mortality acceleration. An early-life rise in acceleration may be caused by increasing rates of transition between stages as individuals grow older. The late-life decline in acceleration may be caused by progression through earlier stages, leaving only a few stages remaining for older individuals.

The quest for a general theory of aging and longevity.

Extensive studies of phenomena related to aging have produced many diverse findings, which require a general theoretical framework to be organized into a comprehensive body of knowledge. As demonstrated by the success of evolutionary theories of aging, quite general theoretical considerations can be very useful when applied to research on aging. In this theoretical study, we attempt to gain insight into aging by applying a general theory of systems failure known as reliability theory. Considerations of this theory lead to the following conclusions: (i) Redundancy is a concept of crucial importance for understanding aging, particularly the systemic nature of aging. Systems that are redundant in numbers of irreplaceable elements deteriorate (that is, age) over time, even if they are built of elements that do not themselves age. (ii) An apparent aging rate or expression of aging is higher for systems that have higher levels of redundancy. (iii) Redundancy exhaustion over the life course explains a number of observations about mortality, including mortality convergence at later life (when death rates are becoming relatively similar at advanced ages for different populations of the same species) as well as late-life mortality deceleration, leveling off, and mortality plateaus. (iv) Living organisms apparently contain a high load of initial damage from the early stages of development, and therefore their life span and aging patterns may be sensitive to early-life conditions that determine this initial damage load. Thus, the reliability theory provides a parsimonious explanation for many important aging-related phenomena and suggests a number of interesting testable predictions. We therefore suggest adding the reliability theory to the arsenal of methodological approaches applied to research on aging.

Analytical solution of a generalized Penna model

In 1995 Penna introduced a simple model of biological aging. A modified Penna model has been demonstrated to exhibit behavior of real-life systems including catastrophic senescence in salmon and a mortality plateau at advanced ages. We present a general steady-state, analytic solution to the Penna model which is able to deal with arbitrary birth and survivability functions. This solution is employed to solve standard variant Penna models studied by simulation. Different Verhulst factors regulating both the birth rate and external death rate are considered.

Solvable senescence model showing a mortality plateau.

We present some analytic results for the steady states of the Penna model of senescence, generalized to allow genetically identical individuals to die at different ages via an arbitrary survival function. Modeling this with a Fermi function (of modest width) we obtain a clear mortality plateau late in life: something that has so far eluded explanation within such mutation accumulation models. This suggests that factors causing variable mortality within genetically identical subpopulations, which include environmental effects, may be essential to understanding the mortality plateau seen in many real species.

Dead Last

Yes, graying baby boomers, you can safely and naturally stop aging! Just live until your mid-90s and your body will quit decaying on its own! Few of us get that chance, but the question of why aging stops in the very old has nettled researchers for the last decade. Now, a study of fruit flies backs an evolutionary explanation and reveals that the age at which deterioration stops is more malleable than anyone expected. Far in the future, researchers might be able to halt human aging before people are too feeble to enjoy the extra time. Whoever said that life begins at 50 never read an actuarial table. By that milestone, an individual's risk of dying--a measure of physical decline--is about five times higher than a 20-year-old's and is rising fast. But for people who survive into their 90s, the mortality rate levels off. The fortunate oldsters apparently stop aging. The idea was controversial at first. "Ten years ago, I didn't believe this at all," says Michael Rose, an evolutionary biologist at the University of California, Irvine. But demographers have confirmed the plateaus in organisms as diverse as yeast and wasps. To explain the slowdown, some scientists back the "tough old bastard hypothesis," which ascribes the effect to inborn constitutional differences. Weaker individuals gradually perish, and by advanced ages, only the hardiest remain. Mathematical models of evolution suggest an alternative explanation. Natural selection dictates how fast organisms fall apart. Creatures grow decrepit because natural selection wanes with age, and mortality rates climb as the strength of natural selection falls (see "Aging Research Grows Up" ). Once an organism has reproduced for the last time, selection's strength reaches zero, and it might seem that aging should shift into overdrive. However, the evolutionary explanation predicts that death rates should level off and physical deterioration should cease. Rose and colleagues tested this explanation in fruit flies. It posits a close correspondence between the age of last reproduction and the age when mortality peaks--and that's what the researchers saw in four lines of flies. Although flies of different strains stopped laying eggs at different ages, in each strain the "break day" when death rates began to stabilize closely followed the end of breeding. The researchers then tried to shift the mortality pinnacle in late-reproducing flies whose break day came at 69 days of age. Rose and colleagues collected eggs only from mothers under the age of 15 days to form each succeeding generation. After 24 generations, the break day had slipped back to 48 days. "This is a fascinating result," says Kenneth Wachter, a demographer at the University of California, Berkeley, because the "onset of mortality plateaus evolves so quickly." The age when mortality levels off is changeable, says Rose, but don't expect these fly results to benefit humans soon. Sometime in the future, he predicts, researchers might know enough to halt aging earlier, say at 45 instead of 90. If scientists pull off that feat, saying that life begins at 50 will be more than a comforting fib. --Mitch Leslie; suggested by Donna Holmes M. R. Rose, M. D. Drapeau, P. G. Yazdi, K. H. Shah, D. B. Moise, R. R. Thakar, C. L. Rauser, L. D. Mueller, Evolution of late-life mortality in Drosophila melanogaster . Evolution 56 , 1982-1991 (2002). [Abstract] [Full Text]

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.