Fitness versus Longevity in Age-Structured Population Dynamics

We generalize the standard Penna bit-string model of biological ageing by assuming that each deleterious mutation diminishes the survival probability in every time interval by a small percentage. This effect is added to the usual lethal but age-dependent effect of the same mutation. We then find strong advantages or disadvantages of sexual reproduction (with males and females) compared to asexual cloning, depending on parameters.

In this paper we consider a generalization to the asexual version of the Penna model for biological aging, where we take a continuous time limit. The genotype associated to each individual is an interval of real numbers over which Dirac $\delta$--functions are defined, representing genetically programmed diseases to be switched on at defined ages of the individual life. We discuss two different continuous limits for the evolution equation and two different mutation protocols,...

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...

The adaptive evolution of large asexual populations is generally characterized by competition between clones carrying different beneficial mutations. This interference phenomenon slows down the adaptation speed and makes the theoretical description of the dynamics more complex with respect to the successional occurrence and fixation of beneficial mutations typical of small populations. A simplified modeling framework considering multiple beneficial mutations with equal and co...

A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model, genetic information is represented by the fraction of defective genes in the population, the population numbers for each specific individual's age are represented by exactly the same functions of age in both models. This gives us a new possibilit...

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...

The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured po...

We present some analytic results for the steady states of the Penna model of sen escence, generalised to allow genetically identical individuals to die at differ ent ages via an arbitrary survival function. Modelling this with a Fermi functio n (of modest width) we obtain a clear mortality plateau late in life: something that has so far eluded explanation within such mutation accumulation models. This suggests that factors causing variable mortality withi n genetically identi...

In this paper we study the effect of rare mutations, driven by a marked point process, on the evolutionary behavior of a population. We derive a Kolmogorov equation describing the expected values of the different frequencies and prove some rigorous analytical results about their behavior. Finally, in a simple case of two different quasispecies, we are able to prove that the rarity of mutations increases the survival opportunity of the low fitness species.

W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full non-linear demographic model for mutation accumulation of Evans et al. (2007), we find surprising differences. Non-linear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine pr...