Related papers: A maximum principle for the mutation-selection equ…
We reformulate the eigenvalue problem for the selection--mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
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…
The interplay between mutation and selection plays a fundamental role in the behaviour of evolutionary algorithms (EAs). However, this interplay is still not completely understood. This paper presents a rigorous runtime analysis of a…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
We study the stationary state of a population evolving under the action of random genetic drift, selection and recombination in which both deleterious and reverse beneficial mutations can occur. We find that the equilibrium fraction of…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be…
In this paper, we discuss the fitness landscape evolution of permanent replicator systems using a hypothesis that the specific time of evolutionary adaptation of the system parameters is much slower than the time of internal evolutionary…
A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and removed from the system with a uniform…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
Mitochondrial and nuclear genomes must be co-adapted to ensure proper cellular respiration and energy production. Mito-nuclear incompatibility reduces individual fitness and induces hybrid infertility, suggesting a possible role in…
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…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…