Biological implications of the Weibull and Gompertz models of aging

Optimizing Medical Care during a Nerve Agent Mass Casualty Incident Using Computer Simulation

INTRODUCTION

Chemical mass casualty incidents (MCIs) pose a substantial threat to public health and safety, with the capacity to overwhelm healthcare infrastructure and create societal disorder. Computer simulation systems are becoming an established mechanism to validate these plans due to their versatility, cost-effectiveness and lower susceptibility to ethical problems.

METHODS

We created a computer simulation model of an urban subway sarin attack analogous to the 1995 Tokyo sarin incident. We created and combined evacuation, dispersion and victim models with the SIMEDIS computer simulator. We analyzed the effect of several possible approaches such as evacuation policy ('Scoop and Run' vs. 'Stay and Play'), three strategies (on-site decontamination and stabilization, off-site decontamination and stabilization, and on-site stabilization with off-site decontamination), preliminary triage, victim distribution methods, transport supervision skill level, and the effect of search and rescue capacity.

RESULTS

Only evacuation policy, strategy and preliminary triage show significant effects on mortality. The total average mortality ranges from 14.7 deaths in the combination of off-site decontamination and Scoop and Run policy with pretriage, to 24 in the combination of onsite decontamination with the Stay and Play and no pretriage.

CONCLUSION

Our findings suggest that in a simulated urban chemical MCI, a Stay and Play approach with on-site decontamination will lead to worse outcomes than a Scoop and Run approach with hospital-based decontamination. Quick transport of victims in combination with on-site antidote administration has the potential to save the most lives, due to faster hospital arrival for definitive care.

Exploring Patterns of Human Mortality and Aging: A Reliability Theory Viewpoint

The most important manifestation of aging is an increased risk of death with advancing age, a mortality pattern characterized by empirical regularities known as mortality laws. We highlight three significant ones: the Gompertz law, compensation effect of mortality (CEM), and late-life mortality deceleration and describe new developments in this area. It is predicted that CEM should result in declining relative variability of mortality at older ages. The quiescent phase hypothesis of negligible actuarial aging at younger adult ages is tested and refuted by analyzing mortality of the most recent birth cohorts. To comprehend the aging mechanisms, it is crucial to explain the observed empirical mortality patterns. As an illustrative example of data-directed modeling and the insights it provides, we briefly describe two different reliability models applied to human mortality patterns. The explanation of aging using a reliability theory approach aligns with evolutionary theories of aging, including idea of chronic phenoptosis. This alignment stems from their focus on elucidating the process of organismal deterioration itself, rather than addressing the reasons why organisms are not designed for perpetual existence. This article is a part of a special issue of the journal that commemorates the legacy of the eminent Russian scientist Vladimir Petrovich Skulachev (1935-2023) and his bold ideas about evolution of biological aging and phenoptosis.

Multiparameter analysis of timelapse imaging reveals kinetics of megakaryocytic erythroid progenitor clonal expansion and differentiation

Single-cell assays have enriched our understanding of hematopoiesis and, more generally, stem and progenitor cell biology. However, these single-end-point approaches provide only a static snapshot of the state of a cell. To observe and measure dynamic changes that may instruct cell fate, we developed an approach for examining hematopoietic progenitor fate specification using long-term (> 7-day) single-cell time-lapse imaging for up to 13 generations with in situ fluorescence staining of primary human hematopoietic progenitors followed by algorithm-assisted lineage tracing. We analyzed progenitor cell dynamics, including the division rate, velocity, viability, and probability of lineage commitment at the single-cell level over time. We applied a Markov probabilistic model to predict progenitor division outcome over each generation in culture. We demonstrated the utility of this methodological pipeline by evaluating the effects of the cytokines thrombopoietin and erythropoietin on the dynamics of self-renewal and lineage specification in primary human bipotent megakaryocytic-erythroid progenitors (MEPs). Our data support the hypothesis that thrombopoietin and erythropoietin support the viability and self-renewal of MEPs, but do not affect fate specification. Thus, single-cell tracking of time-lapse imaged colony-forming unit assays provides a robust method for assessing the dynamics of progenitor self-renewal and lineage commitment.

Floral phenology of an Andean bellflower and pollination by buff-tailed sicklebill hummingbird

The Andean bellflowers comprise an explosive radiation correlated with shifts to specialized pollination. One diverse clade has evolved with extremely curved floral tubes and is predicted to be pollinated exclusively by one of two parapatric species of sicklebill hummingbirds (Eutoxeres). In this study, we focused on the floral biology of Centropogon granulosus, a bellflower thought to be specialized for pollination by Eutoxeres condamini, in a montane cloud forest site in southeastern Peru. Using camera traps and a pollination exclusion experiment, we documented E. condamini as the sole pollinator of C. granulosus. Visitation by E. condamini was necessary for fruit development. Flowering rates were unequivocally linear and conformed to the "steady-state" phenological type. Over the course of >1800 h of monitoring, we recorded 12 E. condamini visits totaling 42 s, indicating traplining behavior. As predicted by its curved flowers, C. granulosus is exclusively pollinated by buff-tailed sicklebill within our study area. We present evidence for the congruence of phenology and visitation as a driver of specialization in this highly diverse clade of Andean bellflowers.

An explanation for negligible senescence in animals

Negligible or negative senescence occurs when mortality risk is stable or decreases with age, and has been observed in some wild animals. Age-independent mortality in animals may lead to an abnormally long maximum individual lifespans and be incompatible with evolutionary theories of senescence. The reason why there is no evidence of senescence in these animals has not been fully understood. Recovery rates are usually very low for wild animals with high dispersal ability and/or small body size (e.g., bats, rodents, and most birds). The only information concerning senescence for most of these species is the reported lifespan when individuals are last seen or caught. We deduced the probability density function of the reported lifespan based on the assumption that the real lifespan corresponding to Weibull or Gompertz distribution. We show that the magnitude of the increase in mortality risk is largely underestimated based on the reported lifespans with low recovery probability. The risk of mortality can aberrantly appear to have a negative correlation with age when it actually increases with increasing lifespan. We demonstrated that the underestimated aging rate for wild animals with low recovery probability can be generalizable to any aging models. Our work provides an explanation for the appearance of negligible senescence in many wild animals. Humans attempt to obtain insights from other creatures to better understand our own biology and its gain insight into how to enhance and extended human health. Our advice is to take a second glance before admiring the negligible senescence in other animals. This ability to escape from senescence is possibly only as beautiful illusion in animals.

Brown Rot Disease in Stored Nectarines: Modeling the Combined Effects of Preharvest and Storage Conditions

Brown rot in stored stone fruits, caused by Monilinia spp., may be due to preharvest and storage factors, but the combined effect of these factors has yet to be investigated. We set up two experiments to monitor the progression of brown rot during the storage of nectarines subjected to various preharvest and storage conditions. We assessed the effects of different agricultural practices (irrigation regimen × fruit load) and harvest dates on brown rot progress during storage in 2018 and the effect of different storage temperatures in 2019. We found that the cumulative incidence of brown rot during storage increased with individual fruit mass, which was influenced by agricultural practices, and for later harvest dates. It also increased with storage temperature. We observed that during storage no secondary infections developed in nectarines not in direct contact with fruits infected with Monilinia laxa. These findings led to the identification of candidate variables describing the brown rot risk on nectarines during storage, such as individual fruit mass, meteorological conditions before fruit harvest, prevalence of brown rot at harvest, and storage temperature. We used these variables to build a mathematical model for estimating the time-to-appearance of brown rot symptoms in stored nectarines. This model fitted the experimental data well, highlighting the need to pay greater attention to the interaction between preharvest and storage conditions. This model could be used to evaluate management strategies for reducing the impact of brown rot in nectarines during storage.

Senescence: why and where selection gradients might not decline with age

Patterns of ageing across the tree of life are much more diverse than previously thought. Yet, we still do not adequately understand how, why and where across the tree of life a particular pattern of ageing will evolve. An ability to predict ageing patterns requires a firmer understanding of how and why different ecological and evolutionary factors alter the sensitivity of fitness to age-related changes in mortality and reproduction. From this understanding, we can ask why and where selection gradients might not decline with age. Here, we begin by summarizing the recent breadth of literature that is unearthing, empirically and theoretically, the mechanisms that drive variation in patters of senescence. We focus on the relevance of two key parameters, population structure and reproductive value, as key to understanding selection gradients, and therefore senescence. We discuss how growth form, individual trade-offs, stage structure and social interactions may all facilitate differing distributions of these two key parameters than those predicted by classical theory. We argue that these four key aspects can help us understand why patterns of negligible and negative senescence can actually be explained under the same evolutionary framework as classical senescence.

A joint explanation of infant and old age mortality

Infant deaths and old age deaths are very different. The former are mostly due to severe congenital malformations of one or a small number of specific organs. On the contrary, old age deaths are largely the outcome of a long process of deterioration which starts in the 20s and affects almost all organs. In terms of age-specific death rates, there is also a clear distinction: the infant death rate falls off with age, whereas the adult and old age death rate increases exponentially with age in conformity with Gompertz's law. An additional difference is that whereas aging and old age death have been extensively studied, infant death received much less attention. To our knowledge, the two effects have never been inter-connected. Clearly, it would be satisfactory to explain the two phenomena as being two variants within the same explanatory framework. In other words, a mechanism providing a combined explanation for the two forms of mortality would be welcome. This is the purpose of the present paper. We show here that the same biological effects can account for the two cases provided there is a difference in their severity: death triggered by isolated lethal anomalies in one case and widespread wear-out anomalies in the second. We show that quite generally this mechanism leads indeed, respectively, to a declining and an upgoing death rate. Moreover, this theoretical framework leads to the conjecture that the severity of the death effects, whether in infancy or old age, is higher for organisms which comprised a larger number of organs. Finally, let us observe that the main focus of the paper is the drastic difference of the age-specific death rates (i.e., decreasing versus increasing) because this difference is found in many species, whereas the question of the best fit (e.g., Gompertz versus Weibull) is rather specific to human mortality.

Linking the maximum reported life span to the aging rate in wild birds

Dozens of surrogates have been used to reflect the rate of aging in comparative biology. For wild organisms, the maximum reported life span is often considered a key metric. However, the connection between the maximum reported life span for a single individual and the aging rate of that species is far from clear. Our objective was to identify a pragmatic solution to calculate the aging rate from the maximum reported life span of wild birds. We explicitly linked the maximum reported life span to the aging process by employing a Weibull distribution and calculating the shape parameter in this model, which reflects the change in mortality across ages and be used as a surrogate for the aging rate. From simulated data, we demonstrated that the percentile estimator is suitable for calculating the aging rate based on the maximum reported life span. We also calculated the aging rate in 246 bird species based on published information from EURING and tested its relationship with body mass. Our study constitutes a new approach for using maximum reported life span in aging research. The aging rate calculated in the study is based on numerous assumptions/prerequisites and can be improved as more is learned about these assumptions/prerequisites.

Data-driven identification of ageing-related diseases from electronic health records

Reducing the burden of late-life morbidity requires an understanding of the mechanisms of ageing-related diseases (ARDs), defined as diseases that accumulate with increasing age. This has been hampered by the lack of formal criteria to identify ARDs. Here, we present a framework to identify ARDs using two complementary methods consisting of unsupervised machine learning and actuarial techniques, which we applied to electronic health records (EHRs) from 3,009,048 individuals in England using primary care data from the Clinical Practice Research Datalink (CPRD) linked to the Hospital Episode Statistics admitted patient care dataset between 1 April 2010 and 31 March 2015 (mean age 49.7 years (s.d. 18.6), 51% female, 70% white ethnicity). We grouped 278 high-burden diseases into nine main clusters according to their patterns of disease onset, using a hierarchical agglomerative clustering algorithm. Four of these clusters, encompassing 207 diseases spanning diverse organ systems and clinical specialties, had rates of disease onset that clearly increased with chronological age. However, the ages of onset for these four clusters were strikingly different, with median age of onset 82 years (IQR 82–83) for Cluster 1, 77 years (IQR 75–77) for Cluster 2, 69 years (IQR 66–71) for Cluster 3 and 57 years (IQR 54–59) for Cluster 4. Fitting to ageing-related actuarial models confirmed that the vast majority of these 207 diseases had a high probability of being ageing-related. Cardiovascular diseases and cancers were highly represented, while benign neoplastic, skin and psychiatric conditions were largely absent from the four ageing-related clusters. Our framework identifies and clusters ARDs and can form the basis for fundamental and translational research into ageing pathways.

Male mortality rates mirror mortality rates of older females

Women on average live longer than men, which seems to suggest that women also age slower than men. However, the potential difference in the pace of aging between the sexes is a relatively controversial topic, and both positions, i.e. "men age faster" and "men and women age at the same pace", have found some support. We therefore employ parametric models previously established in model organisms as well as two nonparametric approaches to compare the pace of aging between the sexes using freely available mortality data from 13 high-income countries. Our results support the hypothesis that men age faster than women while also suggesting that the difference is small and that from a practical standpoint male mortality rates behave similarly to the mortality rates of women approximately eight years their senior.

Field estimates of fitness costs of the pace-of-life in an endangered damselfly

Theory predicts that within-population differences in the pace-of-life can lead to cohort splitting and produce marked intraspecific variation in body size. Although many studies showed that body size is positively correlated with fitness, many argue that selection for the larger body is counterbalanced by opposing physiological and ecological selective mechanisms that favour smaller body. When a population split into cohorts with different paces of life (slow or fast cohort), one would expect to detect the fitness-size relationship among and within cohorts, that is, (a) slower-developing cohort has larger body size and higher fitness than faster-developing cohort, and (b) larger individuals within each cohort show higher fitness than smaller individuals. Here, we test these hypotheses in capture-mark-recapture field surveys that assess body size, lifespan, survival and lifetime mating success in two consecutive generations of a partially bivoltine aquatic insect, Coenagrion mercuriale, where the spring cohort is slower-developing than the autumn cohort. As expected, body size was larger in the slow-developing cohort, which is consistent with the temperature-size rule and also with the duration of development. Body size seasonal variation was greater in slow-developing cohort most likely because of the higher variation in age at maturity. Concordant with theory, survival probability, lifespan and lifetime mating success were higher in the slow-developing cohort. Moreover, individual body size was positively correlated with survival and mating success in both cohorts. Our study confirms the fitness costs of fast pace-of-life and the benefits of larger body size to adult fitness.

The Effect of Gaussian Noise on Maximum Likelihood Fitting of Gompertz and Weibull Mortality Models with Yeast Lifespan Data

Background/study context: Empirical lifespan data sets are often studied with the best-fitted mathematical model for aging. Here, we studied how experimental noises can influence the determination of the best-fitted aging model. We investigated the influence of Gaussian white noise in lifespan data sets on the fitting outcomes of two-parameter Gompertz and Weibull mortality models, commonly adopted in aging research.

METHODS

To un-equivocally demonstrate the effect of Gaussian white noises, we simulated lifespans based on Gompertz and Weibull models with added white noises. To gauge the influence of white noise on model fitting, we defined a single index, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> , for the difference between the maximal log-likelihoods of the Weibull and Gompertz model fittings. We then applied the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> approach using experimental replicative lifespan data sets for the laboratory BY4741 and BY4742 wildtype reference strains.

RESULTS

We systematically evaluated how Gaussian white noise can influence the maximal likelihood-based comparison of the Gompertz and Weibull models. Our comparative study showed that the Weibull model is generally more tolerant to Gaussian white noise than the Gompertz model. The effect of noise on model fitting is also sensitive to model parameters.

CONCLUSION

Our study shows that Gaussian white noise can influence the fitting of an aging model for yeast replicative lifespans. Given that yeast replicative lifespans are hard to measure and are often pooled from different experiments, our study highlights that interpreting model fitting results should take experimental procedure variation into account, and the best fitting model may not necessarily offer more biological insights.

Translating the biology of aging into novel therapeutics for Alzheimer disease

Aging is the leading risk factor for most chronic illnesses of old age, including Alzheimer disease (AD), a progressive neurodegenerative disease with currently no therapies that prevent, slow, or halt disease progression. Like other chronic diseases of old age, the progressive pathology of AD begins decades before the onset of symptoms. Many decades of research in biological gerontology have revealed common processes that are relevant to understanding why the aging brain is vulnerable to AD. In this review, we frame the development of novel therapeutics for AD in the context of biological gerontology. The many therapies currently in development based on biological gerontology principles provide promise for the development of a new generation of therapeutics to prevent and treat AD.

Actuarial senescence in a dimorphic bird: different rates of ageing in morphs with discrete reproductive strategies

It is often hypothesized that intra-sexual competition accelerates actuarial senescence, or the increase in mortality rates with age. However, an alternative hypothesis is that parental investment is more important to determining senescence rates. We used a unique model system, the white-throated sparrow (Zonotrichia albicollis), to study variation in actuarial senescence. In this species, genetically determined morphs display discrete mating strategies and disassortative pairing, providing an excellent opportunity to test the predictions of the above hypotheses. Compared to tan-striped males, white-striped males are more polygynous and aggressive, and less parental. Tan-striped females receive less parental support, and invest more into parental care than white-striped females, which are also more aggressive. Thus, higher senescence rates in males and white-striped birds would support the intra-sexual competition hypothesis, whereas higher senescence rates in females and tan-striped birds would support the parental investment hypothesis. White-striped males showed the lowest rate of actuarial senescence. Tan-striped females had the highest senescence rate, and tan-striped males and white-striped females showed intermediate, relatively equal rates. Thus, results were inconsistent with sexual selection and competitive strategies increasing senescence rates, and instead indicate that senescence may be accelerated by female-biased parental care, and lessened by sharing of parental duties.

Early and Adult Social Environments Shape Sex-Specific Actuarial Senescence Patterns in a Cooperative Breeder

Sociality modulates life-history traits through changes in resource allocation to fitness-related traits. However, how social factors at different stages of the life cycle modulate senescence remains poorly understood. To address this question, we assessed the influence of social environment in both early life and adulthood on actuarial senescence in the Alpine marmot, a cooperative breeder. The influence of helpers on actuarial senescence strongly differed depending on when help was provided and on the sex of the dominant. Being helped when adult slowed down senescence in both sexes. However, the effect of the presence of helpers during the year of birth of a dominant was sex specific. Among dominants helped during adulthood, females born in the presence of helpers senesced slower, whereas males senesced faster. Among dominants without helpers during adulthood, females with helpers at birth senesced faster. Social environment modulates senescence but acts differently between sexes and life stages.

Early mortality saves energy: estimating the energetic cost of excess offspring in a seabird

Offspring are often produced in excess as insurance against stochastic events or unpredictable resources. This strategy may result in high early-life mortality, yet age-specific mortality before offspring independence and its associated costs have rarely been quantified. In this study, we modelled age-specific survival from hatching to fledging using 24 years of data on hatching order (HO), growth and age of mortality of more than 15 000 common tern (Sterna hirundo) chicks. We found that mortality peaked directly after hatching, after which it declined rapidly. Mortality hazard was best described with the Gompertz function, and was higher with later HO, mainly due to differences in baseline mortality hazard, rather than age-dependent mortality. Based on allometric mass-metabolism relationships and detailed growth curves of starving chicks, we estimated that the average metabolizable energy intake of non-fledged chicks was only 8.7% of the metabolizable energy intake of successful chicks during the nestling phase. Although 54% of hatchlings did not fledge, our estimates suggest them to have consumed only 9.3% of the total energy consumption of all hatched chicks in the population before fledging. We suggest that rapid mortality of excess offspring is part of an adaptive brood reduction strategy to the benefit of the parents.

The generational scalability of single-cell replicative aging

Despite the identification of numerous genes able to modulate lifespan, it remains unknown whether these genes interact to form a regulatory network that governs aging. Here we show that genetic interventions that extend or shorten replicative lifespan in Saccharomyces cerevisiae elicit proportional scaling of survival curve dynamics. The scalable nature of replicative lifespan distributions indicates that replicative aging is governed by a global state variable that determines cell survival by integrating effects from different risk factors. We also show that the Weibull survival function, a scale-invariant mathematical form, is capable of accurately predicting experimental survival distributions. We demonstrate that a drift-diffusion model of aging state with random challenge arrival effectively captures mortality risk. Measuring single-cell generation durations during aging, we uncover power-law dynamics with strain-specific speeds of increase in generation durations. Our application of quantitative modeling approaches to high-precision replicative aging data offers novel insights into aging dynamics and lifespan determinants in single cells.

The Smurf transition: new insights on ageing from end-of-life studies in animal models

PURPOSE OF REVIEW

Over the past 5 years, many articles were published concerning the prediction of high risk of mortality in apparently healthy adults, echoing the first description in 2011 of the Smurf phenotype, a harbinger of natural death in drosophila.

RECENT FINDINGS

These recent findings suggest that the end-of-life is molecularly and physiologically highly stereotyped, evolutionarily conserved and predictable.

SUMMARY

Taken altogether, these results from independent teams using multiple organisms including humans draw the lines of future directions in ageing research. The ability to identify and study individuals about to die of natural causes with no apparent diseases is a game-changer in this field. In addition, the public health applications are potentially of tremendous impact in our ageing societies and raise important ethical questions.

Density-dependence interacts with extrinsic mortality in shaping life histories

The role of extrinsic mortality in shaping life histories is poorly understood. However, substantial evidence suggests that extrinsic mortality interacts with density-dependence in crucial ways. We develop a model combining Evolutionarily Stable Strategies with a projection matrix that allows resource allocation to growth, tissue repairs, and reproduction. Our model examines three cases, with density-dependence acting on: (i) mortality, (ii) fecundity, and (iii) production rate. We demonstrate that density-independent extrinsic mortality influences the rate of aging, age at maturity, growth rate, and adult size provided that density-dependence acts on fertility or juvenile mortality. However, density-independent extrinsic mortality has no effect on these life history traits when density-dependence acts on survival. We show that extrinsic mortality interacts with density-dependence via a compensation mechanism: the higher the extrinsic mortality the lower the strength of density-dependence. However, this compensation fully offsets the effect of extrinsic mortality only if density-dependence acts on survival independently of age. Both the age-pattern and the type of density-dependence are crucial for shaping life history traits.

Latitudinal and age-specific patterns of larval mortality in the damselfly Lestes sponsa: Senescence before maturity?

Latitudinal differences in life history traits driven by differences in seasonal time constraints have been widely documented. Yet, latitudinal patterns in (age-specific) mortality rates have been poorly studied. Here, we studied latitudinal differences in pre-adult age-specific mortality patterns in the strictly univoltine damselfly Lestes sponsa. We compared individuals from three latitudes reared from the egg stage in the laboratory at temperatures and photoperiods simulating those at the latitude of origin (main experiment) and under common-garden conditions at a fixed temperature and photoperiod (supplementary experiment). Results from the main experiment showed that the high-latitude population exhibited higher mortality rates than the central and southern populations, likely reflecting a cost of their faster development. Age-specific mortality patterns, also indicated higher ageing rates in the high-latitude compared to the low-latitude population, which likely had a genetic basis. The strong within-population variation in hatching dates in the low-latitude population caused variation in mortality rates; individuals that hatched later showed higher mortality rates presumably due to their shorter development times compared to larvae that hatched earlier. In both experiments, larvae from all three latitudes showed accelerated mortality rates with age, which is consistent with a pattern of senescence before adulthood.

Different Mechanisms of Longevity in Long-Lived Mouse and Caenorhabditis elegans Mutants Revealed by Statistical Analysis of Mortality Rates

Mouse and Caenorhabditis elegans mutants with altered life spans are being used to investigate the aging process and how genes determine life span. The survival of a population can be modeled by the Gompertz function, which comprises two parameters. One of these parameters ("G") describes the rate at which mortality accelerates with age and is often described as the "rate of aging." The other parameter ("A") may correspond to the organism's baseline vulnerability to deleterious effects of disease and the environment. We show that, in mice, life-span-extending mutations systematically fail to affect the age-dependent acceleration of mortality (G), but instead affect only baseline vulnerability (A). This remains true even when comparing strains maintained under identical environmental conditions. In contrast, life-span-extending mutations in C. elegans were associated with decreases in G These observations on mortality rate kinetics suggest that the mechanisms of aging in mammals might fundamentally differ from those in nematodes.

Invariant death

In nematodes, environmental or physiological perturbations alter death’s scaling of time. In human cancer, genetic perturbations alter death’s curvature of time. Those changes in scale and curvature follow the constraining contours of death’s invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death’s scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.

Effects of maternal age on euploidy rates in a large cohort of embryos analyzed with 24-chromosome single-nucleotide polymorphism-based preimplantation genetic screening

OBJECTIVE

To determine the effect of maternal age on the average number of euploid embryos retrieved during oocyte harvest as part of an in vitro fertilization (IVF) cycle, including the probability of retrieving at least one euploid embryo in a cohort (PrE).

DESIGN

Retrospective study.

SETTING

Preimplantation genetic screening (PGS) laboratory.

PATIENT(S)

Women aged 18 to 48 years undergoing IVF treatment.

INTERVENTION(S)

Use of 24-chromosome single-nucleotide polymorphism (SNP)-based PGS of day-3 and day-5 embryo biopsies.

MAIN OUTCOME MEASURE(S)

Relationships between maternal age and the rate of embryos that tested as euploid (hereafter referred to as "euploid embryos"), the average number and proportion of euploid embryos per IVF cycle, and PrE.

RESULT(S)

We analyzed 22,599 day-3 embryos and 15,112 day-5 embryos. In women aged 27 to 35 years, the median proportion of euploid embryos in each cycle remained constant at ∼35% in day-3 biopsies and ∼55% in day-5 biopsies, but it decreased rapidly after age 35. On average, women in their late 20s had four euploid embryos (day 3 or day 5) per cycle, but this number decreased linearly (R(2) ≥ 0.983) after 35 years of age. The effect of maternal age on PrE was similar, with a rapid exponential decline (R(2) = 0.986). Across all maternal ages, the euploid proportion and number of embryos per cycle were counterbalanced, so the number of euploid embryos per cycle was the same for day-3 and day-5 biopsies. This suggests that the loss of embryos from day 3 to day 5 was primarily due to aneuploidy.

CONCLUSION(S)

Our results confirm the known inverse relationship between advanced maternal age (>35 years) and embryo euploidy, demonstrating that equal numbers of euploid embryos are available at day 3 and day 5.

A theoretical model of the evolution of actuarial senescence under environmental stress

Free-living organisms are exposed to a wide range of stressors, all of which can disrupt components of stress-related and detoxification physiology. The subsequent accumulation of somatic damage is widely believed to play a major role in the evolution of senescence. Organisms have evolved sophisticated physiological regulatory mechanisms to maintain homeostasis in response to environmental perturbations, but these systems are likely to be constrained in their ability to optimise robustness to multiple stressors due to functional correlations among related traits. While evolutionary change can accelerate due to human ecological impacts, it remains to be understood how exposure to multiple environmental stressors could affect senescence rates and subsequently population dynamics and fitness. We used a theoretical evolutionary framework to quantify the potential consequences for the evolution of actuarial senescence in response to exposure to simultaneous physiological stressors – one versus multiple and additive versus synergistic – in a hypothetical population of avian “urban adapters”. In a model in which multiple stressors have additive effects on physiology, species may retain greater capacity to recover, or respond adaptively, to environmental challenges. However, in the presence of high synergy, physiological dysregulation suddenly occurs, leading to a rapid increase in age-dependent mortality and subsequent population collapse. Our results suggest that, if the synergistic model is correct, population crashes in environmentally-stressed species could happen quickly and with little warning, as physiological thresholds of stress resistance are overcome.

•

Environmental stressors challenge physiological systems linked to senescence.

•

Various scenarios of stress exposure were simulated on a hypothetical “urban adapter”.

•

Actuarial senescence increased rapidly in synergistic models of stress.

•

Wild populations may be at greater risk of collapse than demography alone suggests.

•

An explicit model of how stressors affect physiology underlying ageing is required.

Do Insect Populations Die at Constant Rates as They Become Older? Contrasting Demographic Failure Kinetics with Respect to Temperature According to the Weibull Model

Temperature implies contrasting biological causes of demographic aging in poikilotherms. In this work, we used the reliability theory to describe the consistency of mortality with age in moth populations and to show that differentiation in hazard rates is related to extrinsic environmental causes such as temperature. Moreover, experiments that manipulate extrinsic mortality were used to distinguish temperature-related death rates and the pertinence of the Weibull aging model. The Newton-Raphson optimization method was applied to calculate parameters for small samples of ages at death by estimating the maximum likelihoods surfaces using scored gradient vectors and the Hessian matrix. The study reveals for the first time that the Weibull function is able to describe contrasting biological causes of demographic aging for moth populations maintained at different temperature regimes. We demonstrate that at favourable conditions the insect death rate accelerates as age advances, in contrast to the extreme temperatures in which each individual drifts toward death in a linear fashion and has a constant chance of passing away. Moreover, slope of hazard rates shifts towards a constant initial rate which is a pattern demonstrated by systems which are not wearing out (e.g. non-aging) since the failure, or death, is a random event independent of time. This finding may appear surprising, because, traditionally, it was mostly thought as rule that in aging population force of mortality increases exponentially until all individuals have died. Moreover, in relation to other studies, we have not observed any typical decelerating aging patterns at late life (mortality leveling-off), but rather, accelerated hazard rates at optimum temperatures and a stabilized increase at the extremes.In most cases, the increase in aging-related mortality was simulated reasonably well according to the Weibull survivorship model that is applied. Moreover, semi log- probability hazard rate model illustrations and maximum likelihoods may be usefully in defining periods of mortality leveling off and provide clear evidence that environmental variability may affect parameter estimates and insect population failure rate. From a reliability theory standpoint, failure rates vary according to a linear function of age at the extremes indicating that the life system (i.e., population) is able to eliminate earlier failure and/or to keep later failure rates constant. The applied model was able to identify the major correlates of extended longevity and to suggest new ideas for using demographic concepts in both basic and applied population biology and aging.

Intrinsic and extrinsic mortality reunited

Intrinsic and extrinsic mortality are often separated in order to understand and measure aging. Intrinsic mortality is assumed to be a result of aging and to increase over age, whereas extrinsic mortality is assumed to be a result of environmental hazards and be constant over age. However, allegedly intrinsic and extrinsic mortality have an exponentially increasing age pattern in common. Theories of aging assert that a combination of intrinsic and extrinsic stressors underlies the increasing risk of death. Epidemiological and biological data support that the control of intrinsic as well as extrinsic stressors can alleviate the aging process. We argue that aging and death can be better explained by the interaction of intrinsic and extrinsic stressors than by classifying mortality itself as being either intrinsic or extrinsic. Recognition of the tight interaction between intrinsic and extrinsic stressors in the causation of aging leads to the recognition that aging is not inevitable, but malleable through the environment.

Calculating the Rate of Senescence From Mortality Data: An Analysis of Data From the ERA-EDTA Registry

The rate of senescence can be inferred from the acceleration by which mortality rates increase over age. Such a senescence rate is generally estimated from parameters of a mathematical model fitted to these mortality rates. However, such models have limitations and underlying assumptions. Notably, they do not fit mortality rates at young and old ages. Therefore, we developed a method to calculate senescence rates from the acceleration of mortality directly without modeling the mortality rates. We applied the different methods to age group-specific mortality data from the European Renal Association-European Dialysis and Transplant Association Registry, including patients with end-stage renal disease on dialysis, who are known to suffer from increased senescence rates (n = 302,455), and patients with a functioning kidney transplant (n = 74,490). From age 20 to 70, senescence rates were comparable when calculated with or without a model. However, when using non-modeled mortality rates, senescence rates were yielded at young and old ages that remained concealed when using modeled mortality rates. At young ages senescence rates were negative, while senescence rates declined at old ages. In conclusion, the rate of senescence can be calculated directly from non-modeled mortality rates, overcoming the disadvantages of an indirect estimation based on modeled mortality rates.

Differential evolution of asexual and sexual females in a benign culture environment

Here we report one of the first investigations of evolvability of lifespan and reproduction in metazoans, examining both extrinsic and intrinsic factors. We tested effects on senescence of an environmental variable (simulated lake hydroperiod, the length of time an aquatic habitat is inundated), female reproductive physiology (asexual females that reproduce by ameiosis, versus sexual females reproducing by meiosis), and time in a benign culture environment (minimal, if any, external mortality factors). To do this we established chemostat cultures of the rotifer Brachionus plicatilis s.s., and maintained the cultures for 385 d. Hydroperiod alone or in interaction with the effects of time in the benign environment (season) or reproductive physiology had no significant effect on the net reproductive rate, generation time, or rate of aging. Yet combining animals from both ephemeral and permanent hydroperiods revealed a 26% increase in asexual female lifespan across seasons (23% decrease in the rate of aging) and a 56% increase in asexual fecundity, suggesting that maintenance in benign laboratory conditions leads to slower aging. The relative stasis of traits for sexual females implies an impact of reproductive physiology on evolvability. In addition we found a positive correlation between fecundity and lifespan, suggesting an absence of trade-offs in life history traits in the benign laboratory environment.

Lifespan extension and delay of age-related functional decline caused by Rhodiola rosea depends on dietary macronutrient balance

Background

This study was conducted to evaluate the effects of rhizome powder from the herb Rhodiola rosea, a traditional Western Ukraine medicinal adaptogen, on lifespan and age-related physiological functions of the fruit fly Drosophila melanogaster.

Results

Flies fed food supplemented with 5.0 mg/ml and 10.0 mg/ml of R. rosea rhizome powder had a 14% to 17% higher median lifespan, whereas at 30.0 mg/ml lifespan was decreased by 9% to 12%. The preparation did not decrease fly fecundity.

The effect of R. rosea supplement on lifespan was dependent on diet composition. Lifespan extension by 15% to 21% was observed only for diets with protein-to-carbohydrate ratios less than 1. Lifespan extension was also dependent on total concentration of macronutrients. Thus, for the diet with 15% yeast and 15% sucrose there was no lifespan extension, while for the diet with protein-to-carbohydrate ratio 20:1 R. rosea decreased lifespan by about 10%.

Flies fed Rhodiola preparation were physically more active, less sensitive to the redox-cycling compound menadione and had a longer time of heat coma onset compared with controls. Positive effects of Rhodiola rhizome on stress resistance and locomotor activity were highest at the ‘middle age’.

Conclusions

The present data show that long-term food supplementation with R. rosea rhizome not only increases D. melanogaster lifespan, but also delays age-related decline of physical activity and increases stress resistance, what depends on protein-to-carbohydrate ratio of the diet.

The size-life span trade-off decomposed: why large dogs die young

Large body size is one of the best predictors of long life span across species of mammals. In marked contrast, there is considerable evidence that, within species, larger individuals are actually shorter lived. This apparent cost of larger size is especially evident in the domestic dog, where artificial selection has led to breeds that vary in body size by almost two orders of magnitude and in average life expectancy by a factor of two. Survival costs of large size might be paid at different stages of the life cycle: a higher early mortality, an early onset of senescence, an elevated baseline mortality, or an increased rate of aging. After fitting different mortality hazard models to death data from 74 breeds of dogs, we describe the relationship between size and several mortality components. We did not find a clear correlation between body size and the onset of senescence. The baseline hazard is slightly higher in large dogs, but the driving force behind the trade-off between size and life span is apparently a strong positive relationship between size and aging rate. We conclude that large dogs die young mainly because they age quickly.

Skew-t fits to mortality data--can a Gaussian-related distribution replace the Gompertz-Makeham as the basis for mortality studies?

Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies.

A comparative assessment of univariate longevity measures using zoological animal records

Comparative biogerontology evaluates cellular, molecular, physiological, and genomic properties that distinguish short-lived from long-lived species. These studies typically use maximum reported lifespan (MRLS) as the index with which to compare traits, but there is a general awareness that MRLS is not ideal owing to statistical shortcomings that include bias resulting from small sample sizes. Nevertheless, MRLS has enough species-specific information to show strong associations with many other species-specific traits, such as body mass, stress resistance, and codon usage. The major goal of this study was to see if we could identify surrogate measures with better statistical properties than MRLS but that still capture inter-species differences in extreme lifespan. Using zoological records of 181 bird and mammal species, we evaluated 16 univariate metrics of aging and longevity, including nonparametric quantile-based measures and parameters derived from demographic models of aging, for three desirable statistical properties. We wished to identify those measures that: (i) correlated well with MRLS when the biasing effects of sample size were removed; (ii) correlated weakly with population size; and (iii) were highly robust to the effects of sampling error. Nonparametric univariate descriptors of the distribution of lifespans clearly outperformed the measures derived from demographic analyses. Mean adult lifespan and quantile-based measures, and in particular the 90th quantile of longevity, performed particularly well, demonstrating far less sensitivity to small sample size effects than MRLS while preserving much of the information contained in the maximum lifespan measure. These measures should take the place of MRLS in comparative studies of lifespan.

Gompertz' survivorship law as an intrinsic principle of aging

We defend the hypothesis that life-spanning population survivorship curves, as described by Gompertz' law and composed from cross-sectional data (here mortality), reflect an intrinsic aging principle active in each subject of that population. In other words Gompertz' law reflects aging of a prototypical subject, provided minimal (or no) external causes of death (i.e. fatal infections, starvation, accidents). Our approach deviates from the traditional (exponential) Gompertz' hazard function. For instance, the here formulated Gompertz' law accurately describes old-age deceleration of both all-cause mortality and the incidence of some ageing-associated cancers, as illustrated for the Dutch population. We consider the possibility that the old-age expression and progression of cancer and other pathologies becomes suppressed, because of random (and exponential) accumulation of damage during life. Gompertz' law may trigger new concepts and models describing life-spanning physiological and pathological processes of aging. We discuss (and reject) various aging models (e.g. a predominant role of individual variations at birth; reliability theory) and point to the explanatory potential of network models and systemic regulatory models.

Modeling physiological processes that relate toxicant exposure and bacterial population dynamics

Quantifying effects of toxicant exposure on metabolic processes is crucial to predicting microbial growth patterns in different environments. Mechanistic models, such as those based on Dynamic Energy Budget (DEB) theory, can link physiological processes to microbial growth.Here we expand the DEB framework to include explicit consideration of the role of reactive oxygen species (ROS). Extensions considered are: (i) additional terms in the equation for the "hazard rate" that quantifies mortality risk; (ii) a variable representing environmental degradation; (iii) a mechanistic description of toxic effects linked to increase in ROS production and aging acceleration, and to non-competitive inhibition of transport channels; (iv) a new representation of the "lag time" based on energy required for acclimation. We estimate model parameters using calibrated Pseudomonas aeruginosa optical density growth data for seven levels of cadmium exposure. The model reproduces growth patterns for all treatments with a single common parameter set, and bacterial growth for treatments of up to 150 mg(Cd)/L can be predicted reasonably well using parameters estimated from cadmium treatments of 20 mg(Cd)/L and lower. Our approach is an important step towards connecting levels of biological organization in ecotoxicology. The presented model reveals possible connections between processes that are not obvious from purely empirical considerations, enables validation and hypothesis testing by creating testable predictions, and identifies research required to further develop the theory.

Human actuarial aging increases faster when background death rates are lower: a consequence of differential heterogeneity?

Many analyses of human populations have found that age-specific mortality rates increase faster across most of adulthood when overall mortality levels decline. This contradicts the relationship often expected from Williams' classic hypothesis about the effects of natural selection on the evolution of senescence. More likely, much of the within-species difference in actuarial aging is not due to variation in senescence, but to the strength of filters on the heterogeneity of frailty in older survivors. A challenge to this differential frailty hypothesis was recently posed by an analysis of life tables from historical European populations and traditional societies that reported variation in actuarial aging consistent with Williams' hypothesis after all. To investigate the challenge, we reconsidered those cases and aging measures. Here we show that the discrepancy depends on Ricklefs' aging rate measure, ω, which decreases as mortality levels drop because it is an index of mortality level itself, not the rate of increase in mortality with age. We also show unappreciated correspondence among the parameters of Gompertz-Makeham and Weibull survival models. Finally, we compare the relationships among mortality parameters of the traditional societies and the historical series, providing further suggestive evidence that differential heterogeneity has strong effects on actuarial aging.

Senescence rates in patients with end-stage renal disease: a critical appraisal of the Gompertz model

The most frequently used model to describe the exponential increase in mortality rate over age is the Gompertz equation. Logarithmically transformed, the equation conforms to a straight line, of which the slope has been interpreted as the rate of senescence. Earlier, we proposed the derivative function of the Gompertz equation as a superior descriptor of senescence rate. Here, we tested both measures of the rate of senescence in a population of patients with end-stage renal disease. It is clinical dogma that patients on dialysis experience accelerated senescence, whereas those with a functional kidney transplant have mortality rates comparable to the general population. Therefore, we calculated the age-specific mortality rates for European patients on dialysis (n=274 221; follow-up=594 767 person-years), for European patients with a functioning kidney transplant (n=61 286; follow-up=345 024 person-years), and for the general European population. We found higher mortality rates, but a smaller slope of logarithmic mortality curve for patients on dialysis compared with both patients with a functioning kidney transplant and the general population (P<0.001). A classical interpretation of the Gompertz model would imply that the rate of senescence in patients on dialysis is lower than in patients with a functioning transplant and lower than in the general population. In contrast, the derivative function of the Gompertz equation yielded the highest senescence rates for patients on dialysis, whereas the rate was similar in patients with a functioning transplant and the general population. We conclude that the rate of senescence is better described by the derivative function of the Gompertz equation.

Dynamic energy budget approaches for modelling organismal ageing

Ageing is a complex multifactorial process involving a progressive physiological decline that, ultimately, leads to the death of an organism. It involves multiple changes in many components that play fundamental roles under healthy and pathological conditions. Simultaneously, every organism undergoes accumulative 'wear and tear' during its lifespan, which confounds the effects of the ageing process. The scenario is complicated even further by the presence of both age-dependent and age-independent competing causes of death. Various manipulations have been shown to interfere with the ageing process. Calorie restriction, for example, has been reported to increase the lifespan of a wide range of organisms, which suggests a strong relation between energy metabolism and ageing. Such a link is also supported within the main theories for ageing: the free radical hypothesis, for instance, links oxidative damage production directly to energy metabolism. The Dynamic Energy Budgets (DEB) theory, which characterizes the uptake and use of energy by living organisms, therefore constitutes a useful tool for gaining insight into the ageing process. Here we compare the existing DEB-based modelling approaches and, then, discuss how new biological evidence could be incorporated within a DEB framework.