Does Good Mutation Help You Live Longer?

In large asexual populations, beneficial mutations have to compete with each other for fixation. Here, I derive explicit analytic expressions for the rate of substitution and the mean beneficial effect of fixed mutations, under the assumptions that the population size N is large, that the mean effect of new beneficial mutations is smaller than the mean effect of new deleterious mutations, and that new beneficial mutations are exponentially distributed. As N increases, the rat...

This paper shows that differentiating the lifetimes of two phenotypes independently from their fertility can lead to a qualitative change in the equilibrium of a population: since survival and reproduction are distinct functional aspects of an organism, this observation contributes to extend the population-genetical characterisation of biological function. To support this statement a mathematical relation is derived to link the lifetime ratio T_1/T_2, which parametrizes the d...

We consider a model of a population with fixed size $N$, which is subjected to an unlimited supply of beneficial mutations at a constant rate $\mu_N$. Individuals with $k$ beneficial mutations have the fitness $(1+s_N)^k$. Each individual dies at rate 1 and is replaced by a random individual chosen with probability proportional to its fitness. We show that when $\mu_N \ll 1/(N \log N)$ and $N^{-\eta} \ll s_N \ll 1$ for some $\eta < 1$, large numbers of beneficial mutations ar...

We consider a model of asexually reproducing individuals with random mutations and selection. The rate of mutations is proportional to the population size, $N$. The mutations may be either beneficial or deleterious. In a paper by Yu, Etheridge and Cuthbertson (2009) it was conjectured that the average rate at which the mean fitness increases in this model is $O(\log N/(\log\log N)^2)$. In this paper we show that for any time $t > 0$ there exist values $\epsilon_N \rightarrow ...

The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these `amplifiers of natural selection' typically increase fixation time. Here we study population structures that achieve a trade-off between high fixation probability and short fixation time. First, we show that no amplifiers can hav...

Understanding why we age is a long-lived open problem in evolutionary biology. Aging is prejudicial to the individual and evolutionary forces should prevent it, but many species show signs of senescence as individuals age. Here, I will propose a model for aging based on assumptions that are compatible with evolutionary theory: i) competition is between individuals; ii) there is some degree of locality, so quite often competition will between parents and their progeny; iii) op...

We consider a model of asexually reproducing individuals. The birth and death rates of the individuals are affected by a fitness parameter. The rate of mutations that cause the fitnesses to change is proportional to the population size, N. The mutations may be either beneficial or deleterious. In a paper by Yu, Etheridge and Cuthbertson [Ann. Appl. Probab. 20 (2010) 978-1004] it was shown that the average rate at which the mean fitness increases in this model is bounded below...

There has been a recent surge of interest in what causes aging. This has been matched by unprecedented research investment in the field from tech companies. But, despite considerable effort from a broad range of researchers, we do not have a rigorous mathematical theory of programmed aging. To address this, we recently derived a mortality equation that governs the transition matrix of an evolving population with a given maximum age. Here, we characterize the spectrum of eigen...

Lifespan distributions of populations of quite diverse species such as humans and yeast seem to surprisingly well follow the same empirical Gompertz-Makeham law, which basically predicts an exponential increase of mortality rate with age. This empirical law can for example be grounded in reliability theory when individuals age through the random failure of a number of redundant essential functional units. However, ageing and subsequent death can also be caused by the accumula...

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. I...