Mortality equation characterizes the dynamics of an aging population

It is shown that if the computer model of biological ageing proposed by Stauffer is modified such that the late reproduction is privileged then the Gompertz law of exponential increase of mortality can be retrieved.

Author's early work on aging is developed to yield a relationship between life spans and the velocity of aging. The mathematical analysis shows that the mean extent of the advancement of aging throughout one's life is conserved, or equivalently, the product of the mean life span, and the mean rate of aging is constant. The result is in harmony with our experiences: It accounts for the unlimited replicability of tumor cells, and predicts the prolonged life spans of hibernating...

Mortality is an instrument of natural selection. Evolutionary motivated theories imply its irreversibility and life history dependence. This is inconsistent with mortality data for protected populations. Accurate analysis yields mortality law, which is specific for their evolutionary unprecedented conditions, yet universal for species as evolutionary remote as humans and flies. The law is exact, instantaneous, reversible, stepwise, and allows for a rapid (within less than two...

Existing theories for the evolution of aging and death treat senescence as a side-effect of strong selection for fertility. These theories are well-developed mathematically, but fit poorly with emerging experimental data. The data suggest that aging is an adaptation, selected for its own sake. But aging contributes only negatively to fitness of the individual. What kind of selection model would permit aging to emerge as a population-level adaptation? I explore the thesis that...

Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented, and their survival far beyond reproductive age may be a byproduct rather than tool of evolution. Physical approach, which takes advantage of their extensively quantified mortality, establishes that its dominant fraction yields the exact law, and suggests its unusual mechanism. The law is universal for all animals, from yeast to humans, despite their drastically diffe...

Evolution is faced with a formidable challenge: refining the already highly optimised design of biological species, a feat accomplished through all preceding generations. In such a scenario, the impact of random changes (the method employed by evolution) is much more likely to be harmful than advantageous, potentially lowering the chances of reproduction of the affected individuals. The proposition of ageing as a nonadaptive phenomenon is robust and nearly universally acknowl...

We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour of the solution to a renewal type equation, and then to derive properties that illustrate the adaptive dynamics of such a population. We begin with a simplified model by discarding the effect of mutations, which allows us to introduce the ...

The aim of this study is to compare the growth speed of different cell populations measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of cells all aging or growing at the same rate $\bar v$. A second population (with variability) is composed of cells each aging or growing at a rate $v$ drawn according to a non-degenerated distribution $\rho$ with mean $\bar v$. In a first part, ...

Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented. Physical approach, which takes advantage of their extensively quantified mortality, establishes that its dominant fraction yields the exact law, whose universality from yeast to humans is unprecedented, and suggests its unusual mechanism. Singularities of the law demonstrate new kind of stepwise adaptation. The law proves that universal mortality is an evolutionary b...

We present, solve and numerically simulate a simple model that describes the consequences of increased longevity on fertility rates, population growth and the distribution of wealth in developed societies. We look at the consequences of the repeated use of life extension techniques and show that they represent a novel commodity whose introduction will profoundly influence key aspects of economy and society in general. In particular, we uncover two phases within our simplified...