RESUMEN
When mortality (µ), aging rate (γ) and age (t) are treated according to the Gompertz model µ(t) = µ0eγt (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+µ0eγt (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.
Asunto(s)
Envejecimiento , Longevidad , Modelos Biológicos , Mortalidad , Animales , HumanosRESUMEN
Melatonin was administered at the dose of 1,2 mcg per capita (an equivalent to pediatric dosages) at days 1, 3 and 5 postpartum to 129/Sv mice, which were followed thereafter till their natural deaths. In adult males, findings included a decrease in body weight and an increase in the contribution of pulmonary lesions, which were revealed upon postmortem examinations, to the overall mortality. In adult females, no changes in body weight occurred, the proportion of middle- and late-age mice having irregular estrous cycles increased, and mortality associated with uterine hemangiomas was accelerated. Trends in malignant tumor yields were different: a decrease in males and an increase in females. Tends in survival patterns were expressed as significant increases or decreases in the lifespans of the last 25% and 10% of male or female survivors respectively. An analysis of the complete survivorships curves in terms of the Gompertz model showed that changes in the initial mortality and aging rate were within the limits determined by the artifactual component of the Strehler-Mildvan correlation between these parameters. On a whole, the trends found in the present work were opposite in males and females being mostly favorable for the former and adverse for the latter. Gender specificity should be kept in mind upon considering the use of melatonin by children and their mothers.
Asunto(s)
Antioxidantes , Longevidad , Melatonina , Animales , Antioxidantes/farmacología , Peso Corporal , Niño , Femenino , Humanos , Recién Nacido , Masculino , Melatonina/farmacología , Ratones , Ratones Endogámicos , Factores SexualesRESUMEN
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.
Asunto(s)
Envejecimiento/genética , Envejecimiento/fisiología , Factor I del Crecimiento Similar a la Insulina/genética , Factor I del Crecimiento Similar a la Insulina/fisiología , Longevidad/genética , Longevidad/fisiología , Timo/patología , Envejecimiento/patología , Animales , Femenino , Queratina-14/genética , Ratones , Ratones Transgénicos , Regiones Promotoras Genéticas , Receptor IGF Tipo 1/genética , Receptor IGF Tipo 1/fisiología , Transducción de Señal , Factor Tímico Circulante/metabolismoRESUMEN
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.
Asunto(s)
Envejecimiento , Experimentación Animal/estadística & datos numéricos , Longevidad , Modelos Estadísticos , Animales , Grupos Control , Humanos , Esperanza de Vida , Mortalidad , Murinae , SobrevidaRESUMEN
Gompertz empirical law of mortality is often used in practical research to parametrize survival fraction as a function of age with the help of just two quantities: the Initial Mortality Rate (IMR) and the Gompertz exponent, inversely proportional to the Mortality Rate Doubling Time (MRDT). The IMR is often found to be inversely related to the Gompertz exponent, which is the dependence commonly referred to as Strehler-Mildvan (SM) correlation. In this paper, we address fundamental uncertainties of the Gompertz parameters inference from experimental Kaplan-Meier plots and show, that a least squares fit often leads to an ill-defined non-linear optimization problem, which is extremely sensitive to sampling errors and the smallest systematic demographic variations. Therefore, an analysis of consequent repeats of the same experiments in the same biological conditions yields the whole degenerate manifold of possible Gompertz parameters. We find that whenever the average lifespan of species greatly exceeds MRDT, small random variations in the survival records produce large deviations in the identified Gompertz parameters along the line, corresponding to the set of all possible IMR and MRDT values, roughly compatible with the properly determined value of average lifespan in experiment. The best fit parameters in this case turn out to be related by a form of SM correlation. Therefore, we have to conclude that the combined property, such as the average lifespan in the group, rather than IMR and MRDT values separately, may often only be reliably determined via experiments, even in a perfectly homogeneous animal cohort due to its finite size and/or low age-sampling frequency, typical for modern high-throughput settings. We support our findings with careful analysis of experimental survival records obtained in cohorts of C. elegans of different sizes, in control groups and under the influence of experimental therapies or environmental conditions. We argue that since, SM correlation may show up as a consequence of the fitting degeneracy, its appearance is not limited to homogeneous cohorts. In fact, the problem persists even beyond the simple Gompertz mortality law. We show that the same degeneracy occurs exactly in the same way, if a more advanced Gompertz-Makeham aging model is employed to improve the modeling. We explain how SM type of relation between the demographic parameters may still be observed even in extremely large cohorts with immense statistical power, such as in human census datasets, provided that systematic historical changes are weak in nature and lead to a gradual change in the mean lifespan.
Asunto(s)
Modelos Estadísticos , Mortalidad/tendencias , Análisis de Supervivencia , Factores de Edad , Animales , Caenorhabditis elegans , Humanos , Tamaño de la MuestraRESUMEN
The Gompertz mortality model is often used to evaluate evolutionary theories of ageing, such as the Medawar-Williams' hypothesis that high extrinsic mortality leads to faster ageing. However, fits of the Gompertz mortality model to data often find the opposite result that mortality is negatively correlated with the rate of ageing. This negative correlation has been independently discovered in several taxa and is known in actuarial studies of ageing as the Strehler-Mildvan correlation. We examine the role of mortality selection in determining late-life variation in susceptibility to death, which has been suggested to be the cause of this negative correlation. We demonstrate that fixed-frailty models that account for heterogeneity in frailty do not remove the correlation and that the correlation is an inherent statistical property of the Gompertz distribution. Linking actuarial and biological rates of ageing will continue to be a pressing challenge, but the Strehler-Mildvan correlation itself should not be used to diagnose any biological, physiological, or evolutionary process. These findings resolve some key tensions between theory and data that affect evolutionary and biological studies of ageing and mortality. Tests of evolutionary theories of ageing should include direct measures of physiological performance or condition.
Asunto(s)
Envejecimiento , Evolución Biológica , Modelos Estadísticos , Animales , Biometría , Humanos , Mortalidad , Acondicionamiento Físico HumanoRESUMEN
OBJECTIVES: In paleodemography, the Bayesian approach has been suggested to provide an effective means by which mortality profiles of past populations can be adequately estimated, and thus avoid problems of "age-mimicry" inherent in conventional approaches. In this study, we propose an application of the Gompertz model using an "informative" prior probability distribution by revising a recent example of the Bayesian approach based on an "uninformative" distribution. METHODS: Life-table data of 134 human populations including those of contemporary hunter-gatherers were used to determine the Gompertz parameters of each population. In each population, we used both raw life-table data and the Gompertz parameters to calculate some demographic values such as the mean life-span, to confirm representativeness of the model. Then, the correlation between the two Gompertz parameters (the Strehler-Mildvan correlation) was re-established. We incorporated the correlation into the Bayesian approach as an "informative" prior probability distribution, and tested its effectiveness using simulated data. RESULTS: Our analyses showed that the mean life-span (≥ age 15) and the proportion of living persons aging over 45 were well-reproduced by the Gompertz model. The simulation showed that using the correlation as an informative prior provides a narrower estimation range in the Bayesian approach than does the uninformative prior. CONCLUSIONS: The Gompertz model can be assumed to accurately estimate the mean life-span and/or the proportion of old people in a population. We suggest that the Strehler-Mildvan correlation can be used as a useful constraint in demographic reconstructions of past human populations.