Flowers of immortality

We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the fitness and age characteristics exhibit counter-intuitive behavior as a function of the mutational bias. By analytical and numerical study of the underlying rate equations, we show that if deleterious mutations are favored, the average fitness of...

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...

We study an equation structured by age and a phenotypic trait describing the growth process of a population subject to aging, competition between individuals, and mutations. This leads to a renewal equation which occurs in many evolutionary biology problems. We aim to describe precisely the asymp-totic behavior of the solution, to infer properties that illustrate the concentration and adaptive dynamics of such a population. This work is a continuation of [38] where the case w...

Aging, as defined in terms of the slope of the probability of death versus time (hazard curve), is a generic phenomenon observed in nearly all complex systems. Theoretical models of aging predict hazard curves that monotonically increase in time, in discrepancy with the peculiar ups and downs observed in empirically. Here we introduce the concept of co-aging, where the demographic trajectories of multiple cohorts couple together, and show that co-aging dynamics can account fo...

Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates. Individuals reproduce and die with a rate that is a property of each state, not necessarily related to its stability, and the offspring is born on the parent's state. The total population is limited by resources or space, as for example in a...

Biological aging is characterized by an age-dependent increase in the probability of death and by a decrease in the reproductive capacity. Individual age-dependent rates of survival and reproduction have a strong impact on population dynamics, and the genetic elements determining survival and reproduction are under different selective forces throughout an organism lifespan. Here we develop a highly versatile numerical model of genome evolution --- both asexual and sexual --- ...

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...

Based on the study of cellular aging using the single-cell model organism of budding yeast and corroborated by other studies, we propose the Emergent Aging Model (EAM). EAM hypothesizes that aging is an emergent property of complex biological systems, exemplified by biological networks such as gene networks. An emergent property refers to traits that a system has at the system level but which its low-level components do not. EAM is based on a quantitative definition of aging ...

In general or normal random matrix ensembles, the support of eigenvalues of large size matrices is a planar domain (or several domains) with a sharp boundary. This domain evolves under a change of parameters of the potential and of the size of matrices. The boundary of the support of eigenvalues is a real section of a complex curve. Algebro-geometrical properties of this curve encode physical properties of random matrix ensembles. This curve can be treated as a limit of a spe...

We study the dynamics of an age-structured population in which the life expectancy of an offspring may be mutated with respect to that of its parent. When advantageous mutation is favored, the average fitness of the population grows linearly with time $t$, while in the opposite case the average fitness is constant. For no mutational bias, the average fitness grows as t^{2/3}. The average age of the population remains finite in all cases and paradoxically is a decreasing funct...