Evolutionary theory of ageing and the problem of correlated Gompertz parameters

Using a penalized likelihood to detect mortality deceleration

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

Trends in Human Species-Specific Lifespan and Actuarial Aging Rate

The compensation effect of mortality (CEM) was tested and species-specific lifespan was estimated using data on one-year age-specific death rates from the Human Mortality Database (HMD). CEM was confirmed using this source of the data and human species-specific lifespan estimates were obtained, which were similar to the estimates published before. Three models (Gompertz-Makeham, Gompertz-Makeham with mean-centered age, and Gompertz) produced similar estimates of the species-specific lifespan. These estimates demonstrated some increase over time. Attempts to measure aging rates through the Gompertz slope parameter led to the conclusion that actuarial aging rates were stable during most of the 20th century, but recently demonstrated an increase over time in the majority (74%) of studied populations. This recent phenomenon is most likely caused by more rapid historical decline of mortality at the younger adult age groups compared to the older age groups, thus making the age gradient in mortality steeper over time. There is no biomedical reason to believe that human aging rates accelerated recently, so that the actuarial aging rate is probably not a good measure of true aging rate (rate of functional loss). Therefore, better measures of aging rate need to be developed.

Survival with Random Effect

The article focuses on mortality models with a random effect applied in order to evaluate human mortality more precisely. Such models are called frailty or Cox models. The main assertion of the paper shows that each positive random effect transforms the initial hazard rate (or density function) to a new absolutely continuous survival function. In particular, well-known Weibull and Gompertz hazard rates and corresponding survival functions are analyzed with different random effects. These specific models are presented with detailed calculations of hazard rates and corresponding survival functions. Six specific models with a random effect are applied to the same data set. The results indicate that the accuracy of the model depends on the data under consideration.

The mechanism between mortality, population growth and ageing of the population in the European lower and upper middle income countries

This paper analyses the effect of mortality rates (under-five and adult mortality) and population growth on the population ageing in a pooled sample of nine lower and upper middle European countries. Therefore, the main goal of this research is to investigate the ageing process of the population in the context of mortality mechanisms (under five and adult mortality) and of population growth in nine European LUMIs. The analysis is implemented in terms of Pooled least squares with cross-section fixed effects methodology. The novelty used within this research is White two-way cluster standard errors & covariance. This study is based on a database from the World Bank and UN covering the period 1995-2019. The expected results are making available quantitative analysis and insights in the context of mechanisms between the ageing process of population, mortality and population growth across these European LUMIs. Results are consistent with the notion that the increasing ageing process within these countries may be a consequence of the negative impact of population growth and from the influence of adult mortality for both sexes. The research results confirm the presence of solid ties of the mechanism between mortality, population growth and population ageing. Therefore, a clear point was provided that mortality acceleration will depend primarily on the level of population growth.

Exponential increase in mortality with age is a generic property of a simple model system of damage accumulation and death

The risk of dying increases exponentially with age, in humans as well as in many other species. This increase is often attributed to the "accumulation of damage" known to occur in many biological structures and systems. The aim of this paper is to describe a generic model of damage accumulation and death in which mortality increases exponentially with age. The damage-accumulation process is modeled by a stochastic process know as a queue, and risk of dying is a function of the accumulated damage, i.e., length of the queue. The model has four parameters and the main characteristics of the model are: (i) damage occurs at random times with a constant high rate; (ii) the damage is repaired at a limited rate, and consequently damage can accumulate; (iii) the efficiency of the repair mechanism decays linearly with age; (iv) the risk of dying is a function of the accumulated damage. Using standard results from the mathematical theory of queues it is shown that there is an exponential dependence between risk of dying and age in these models, and that this dependency holds irrespective of how the damage-accumulation process is modeled. Furthermore, the ways in which this exponential dependence is shaped by the model parameters are also independent of the details of the damage accumulation process. These generic features suggest that the model could be useful when interpreting changes in the relation between age and mortality in real data. To exemplify, historical mortality data from Sweden are interpreted in the light of the model. The decrease in mortality seen between cohorts born in 1905, compared to those born in 1885, can be accounted for by higher threshold to damage. This fits well with the many advances made in public health during the 20th century.

Antipsychotic agents deteriorate brain and retinal function in schizophrenia patients with combined auditory and visual hallucinations: A pilot study and secondary follow-up study

INTRODUCTION

Schizophrenia patients often experience auditory hallucinations (AHs) and visual hallucinations (VHs). However, the degree and type of brain and retinal alterations associated with combined AHs and VHs in schizophrenia patients remain unknown. There is an urgent need for a study that investigates the trajectory of brain and retinal alterations in patients with first-episode untreated schizophrenia accompanied by combined AHs and VHs (FUSCHAV).

METHODS

FUSCHAV patients (n = 120), divided into four groups according to AH and VH symptom severity (severe AHs combined with severe VHs [FUSCHSASV, 20 patients]; middle-to-moderate AHs combined with severe VHs [FUSCHMASV, 23 patients]; severe AHs combined with middle-to-moderate VHs [FUSCHSAMV, 28 patients]; and middle-to-moderate AHs combined with middle-to-moderate VHs [FUSCHMAMV, 26 patients]), were compared to healthy controls (n = 30). Gray matter volume (GMV) was adopted for brain structural alteration assessment. Total retinal thickness was adopted as a measure of retinal thickness impairment.

RESULTS

In the pilot study, the rate of GMV reduction showed an inverted U-shaped pattern across the different FUSCHAV patient groups according to AH and VH severity. The degree of retinal impairment remained stable across the groups. More notably, in the secondary follow-up study, we observed that, after 6 months of treatment with antipsychotic agents, all the GMV reduction-related differences across the different patient groups disappeared, and both GMV and retinal thickness demonstrated a tendency to deteriorate.

CONCLUSIONS

These findings indicate the need for heightened alertness on brain and retinal impairments in patients with FUSCHAV. Further deteriorations induced by antipsychotic agent treatment should be monitored in clinical practice.

Human ageing, longevity and evolution: can ageing be programmed?

Understanding the proximate and ultimate causes of ageing is one of the key challenges in current biology and medicine. These problems are so important that they are sometimes referred to as the Holy Grail of biology and the Great Conundrum in biogerontology. From an evolutionary perspective, ageing is due to a failure of selection that is caused either by declining strength of selection after the onset of sexual reproduction (Medawar’s theory and Charlesworth’s model) or pleiotropic constraints (Williams’ theory). According to the disposable soma theory, which was proposed by Kirkwood and Holliday, ageing is driven by the accumulation of damage during life and failures of defensive and repair mechanisms as the more an animal expends on sexual reproduction, the less it can expend on bodily maintenance, and vice versa. Although these standard models rule out the possibility that ageing is programmed, there is no consensus about the nature of ageing within the life history in current biogerontology. Interestingly, empirical studies show that there are molecular instructions for ageing and evolutionarily conserved mechanisms for ageing, which seems inconsistent with the idea that ageing is a matter of neglect or a consequence of a failure of selection due to pleiotropic constraints. Here, selected arguments for programmed (i.e. either determined and adaptive or prearranged but non-adaptive) and non-programmed ageing are discussed. Recent advances in biogerontology that cast new light on these problems are outlined here in the context of the idea that the pace of ageing can act as an adaptation in nature, even though ageing is non-programmed and non-adaptive.

Revamping the evolutionary theories of aging

Radical lifespan disparities exist in the animal kingdom. While the ocean quahog can survive for half a millennium, the mayfly survives for less than 48 h. The evolutionary theories of aging seek to explain why such stark longevity differences exist and why a deleterious process like aging evolved. The classical mutation accumulation, antagonistic pleiotropy, and disposable soma theories predict that increased extrinsic mortality should select for the evolution of shorter lifespans and vice versa. Most experimental and comparative field studies conform to this prediction. Indeed, animals with extreme longevity (e.g., Greenland shark, bowhead whale, giant tortoise, vestimentiferan tubeworms) typically experience minimal predation. However, data from guppies, nematodes, and computational models show that increased extrinsic mortality can sometimes lead to longer evolved lifespans. The existence of theoretically immortal animals that experience extrinsic mortality - like planarian flatworms, panther worms, and hydra - further challenges classical assumptions. Octopuses pose another puzzle by exhibiting short lifespans and an uncanny intelligence, the latter of which is often associated with longevity and reduced extrinsic mortality. The evolutionary response to extrinsic mortality is likely dependent on multiple interacting factors in the organism, population, and ecology, including food availability, population density, reproductive cost, age-mortality interactions, and the mortality source.

Variation in actuarial senescence does not reflect life span variation across mammals

The concept of actuarial senescence (defined here as the increase in mortality hazards with age) is often confounded with life span duration, which obscures the relative role of age-dependent and age-independent processes in shaping the variation in life span. We use the opportunity afforded by the Species360 database, a collection of individual life span records in captivity, to analyze age-specific mortality patterns in relation to variation in life span. We report evidence of actuarial senescence across 96 mammal species. We identify the life stage (juvenile, prime-age, or senescent) that contributes the most to the observed variation in life span across species. Actuarial senescence only accounted for 35%-50% of the variance in life span across species, depending on the body mass category. We computed the sensitivity and elasticity of life span to five parameters that represent the three stages of the age-specific mortality curve-namely, the duration of the juvenile stage, the mean juvenile mortality, the prime-age (i.e., minimum) adult mortality, the age at the onset of actuarial senescence, and the rate of actuarial senescence. Next, we computed the between-species variance in these five parameters. Combining the two steps, we computed the relative contribution of each of the five parameters to the variance in life span across species. Variation in life span was increasingly driven by the intensity of actuarial senescence and decreasingly driven by prime-age adult mortality from small to large species because of changes in the elasticity of life span to these parameters, even if all the adult survival parameters consistently exhibited a canalization pattern of weaker variability among long-lived species than among short-lived ones. Our work unambiguously demonstrates that life span cannot be used to measure the strength of actuarial senescence, because a substantial and variable proportion of life span variation across mammals is not related to actuarial senescence metrics.

A 2D analysis of correlations between the parameters of the Gompertz-Makeham model (or law?) of relationships between aging, mortality, and longevity

When mortality (μ), aging rate (γ) and age (t) are treated according to the Gompertz model μ(t) = μ₀e^γt (GM), any mean age corresponds to a manifold of paired reciprocally changing μ₀ and γ. Therefore, any noisiness of data used to derive GM parameters makes them negatively correlated. Besides this artifactual factor of the Strehler-Mildvan correlation (SMC), other factors emerge when the age-independent mortality C modifies survival according to the Gompertz-Makeham model μ(t) = C+μ₀e^γt (GMM), or body resources are partitioned between survival and protection from aging [the compensation effect of mortality (CEM)]. Theoretical curves in (γ, logμ₀) coordinates show how μ₀ decreases when γ increases upon a constant mean age. Within a species-specific range of γ, such "isoage" curves look as nearly parallel straight lines. The slopes of lines constructed by applying GM to survival curves modeled according to GMM upon changes in C are greater than the isoage slopes. When CEM is modeled, the slopes are still greater. Based on these observations, CEM is shown to contribute to SMC associated with sex differences in lifespan, with the effects of several life-extending drugs, and with recent trends in survival/mortality patterns in high-life-expectancy countries; whereas changes in C underlie differences between even high-life-expectancy countries, not only between high- and low-life-expectancy countries. Such interpretations make sense only if GM is not merely a statistical model, but rather reflects biological realities. Therefore, GM is discussed as derivable by applying certain constraints to a natural law termed the generalized Gompertz-Makeham law.

Does grandparental care select for a longer lifespan in non-human mammals?

Several non-human mammalian species provide grandparental care but remain fertile until death, unlike our species. This might call into question the ‘grandmother hypothesis’ that the ability to provide grandparental care, associated with an increase in the cost of breeding with age, promote the early cessation of reproduction. Here, we analyse individual longevity records from non-human mammals to determine whether the few species with grandparental care also stand out among mammals in terms of age-specific survival patterns. Indeed, females of species with grandparental care lived on average 43% longer than males (range: 24–61%), compared with 12% in other polygynous species (95% quantile: −8 to 30%), because of low baseline mortality rates and delayed onset of actuarial senescence. We discuss this finding with respect to the ‘stopping early’ vs. ‘living longer’ debate. We review the role of the environmental context and of the decrease in offspring performance with maternal age (Lansing effect). We formalize the idea of a continuum of parental–grandparental allocation instead of a discrete switch to grandparental care only. Lastly, we suggest that the evolution of menopause has been driven by different forces in different species.

In mice transgenic for IGF1 under keratin-14 promoter, lifespan is decreased and the rates of aging and thymus involution are accelerated

IGF1 signaling is supposedly a key lifespan determinant in metazoans. However, controversial lifespan data were obtained with different means used to modify IGF1 or its receptor (IGF1R) expression in mice. The emerging puzzle lacks pieces of evidence needed to construct a coherent picture. We add to the available evidence by using the Gompertz model (GM), with account for the artifactual component of the Strehler-Mildvan correlation between its parameters, to compare the survival patterns of female FVB/N and FVB/N-derived K14/mIGF1 mice. In K14/mIGF1 vs. FVB/N mice, the rate of aging (γ) is markedly increased without concomitant changes in the initial mortality (μ₀). In published cases where IGF1 signaling was altered by modifying liver or muscle IGF1 or whole body IGF1R expression, lifespan changes are attributable to μ₀. The accelerated aging and associated tumor yield in K14/mIGF1 mice are consistent with the finding that the age-associated decreases in thymus weight and serum thymulin are accelerated in K14/mIGF1 mice. Our results underscore the importance of accounting for the mathematical artifacts of data fitting to GM in attempts to resolve discrepancies in survival data and to differentiate the contributions of the initial mortality and the rate of aging to changes in lifespan.

A Tale of Two Concepts: Harmonizing the Free Radical and Antagonistic Pleiotropy Theories of Aging

SIGNIFICANCE

The two foremost concepts of aging are the mechanistic free radical theory (FRT) of how we age and the evolutionary antagonistic pleiotropy theory (APT) of why we age. Both date from the late 1950s. The FRT holds that reactive oxygen species (ROS) are the principal contributors to the lifelong cumulative damage suffered by cells, whereas the APT is generally understood as positing that genes that are good for young organisms can take over a population even if they are bad for the old organisms. Recent Advances: Here, we provide a common ground for the two theories by showing how aging can result from the inherent chemical reactivity of many biomolecules, not just ROS, which imposes a fundamental constraint on biological evolution. Chemically reactive metabolites spontaneously modify slowly renewable macromolecules in a continuous way over time; the resulting buildup of damage wrought by the genes coding for enzymes that generate such small molecules eventually masquerades as late-acting pleiotropic effects. In aerobic organisms, ROS are major agents of this damage but they are far from alone.

CRITICAL ISSUES

Being related to two sides of the same phenomenon, these theories should be compatible. However, the interface between them is obscured by the FRT mistaking a subset of damaging processes for the whole, and the APT mistaking a cumulative quantitative process for a qualitative switch.

FUTURE DIRECTIONS

The manifestations of ROS-mediated cumulative chemical damage at the population level may include the often-observed negative correlation between fitness and the rate of its decline with increasing age, further linking FRT and APT. Antioxid. Redox Signal. 29, 1003-1017.

The effect of disease burden on the speed of aging: an analysis of the Sardinian mortality transition

According to the constant senescence hypothesis, senescence cannot be accelerated or decelerated by exogenous factors. Two contrasting theories have been proposed in the literature. According to the inflammaging theory, those individuals who have experienced a higher antigenic load will experience more rapid senescence. Instead, the calorie restriction theory stresses that excessive daily calorie intake can produce an acceleration in senescence.

To test these theories, this paper analyzes the evolution of the rate of aging in Sardinia (Italy). In this population, the epidemiological transition started without any substantial modification in nutritional levels. This allows us to test the constant senescence hypothesis against the inflammaging theory, without the possible confounding effect produced by the nutrition transition.

To accomplish this aim, the longitudinal life tables from 80 years onwards for Sardinian cohorts born between 1866 and 1908 were reconstituted. They were then used to estimate the rate of aging by means of the Gamma-Gompertz model. Coherently with the inflammaging theory, the results show that the Sardinian population experienced a dramatic decrease in the rate of aging that coincided with the onset of the epidemiological transition.

Applying parametric models to survival data: tradeoffs between statistical significance, biological plausibility, and common sense

Parametric models for survival data help to differentiate aging from other lifespan determinants. However, such inferences suffer from small sizes of experimental animal samples and variable animals handling by different labs. We analyzed control data from a single laboratory where interventions in murine lifespan were studied over decades. The minimal Gompertz model (GM) was found to perform best with most murine strains. However, when several control datasets related to a particular strain are fitted to GM, strikingly rigid interdependencies between GM parameters emerge, consistent with the Strehler-Mildvan correlation (SMC). SMC emerges even when survival patterns do not conform to GM, as with cancer-prone HER2/neu mice, which die at a log-normally distributed age. Numerical experiments show that SMC includes an artifact whose magnitude depends on dataset deviation from conformance to GM irrespectively of the noisiness of small datasets, another contributor to SMC. Still another contributor to SMC is the compensation effect of mortality (CEM): a real tradeoff between the physiological factors responsible for initial vitality and the rate of its decline. To avoid misinterpretations, we advise checking experimental results against a SMC based on historical controls or on subgroups obtained by randomization of control animals. An apparent acceleration of aging associated with a decrease in the initial mortality is invalid if it is not greater than SMC suggests. This approach applied to published data suggests that the effects of calorie restriction and of drugs believed to mimic it are different. SMC and CEM relevance to human survival patterns is discussed.