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On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial "uphill" mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the…

Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been…

Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional…

Due to stochastic fluctuations arising from finite population size, known as genetic drift, the ability of a population to explore a rugged fitness landscape depends on its size. In the weak mutation regime, while the mean steady-state…

We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation…

We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to…

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…

We consider the adaptation dynamics of an asexual population that walks uphill on a rugged fitness landscape which is endowed with large number of local fitness peaks. We work in a parameter regime where only those mutants that are single…

Within the framework of population genetics we consider the evolution of an asexual haploid population under the effect of a rapidly varying natural selection (microevolution). We focus on the case in which the environment exerting…

We consider a fixed size population that undergoes an evolutionary adaptation in the weak mutuation rate limit, which we model as a biased Langevin process in the genotype space. We show analytically and numerically that, if the fitness…

Organisms that exploit different environments may experience a stochastic delay in adjusting their fitness when they switch habitats. We study two species whose fitness is determined by the species composition of the local environment, as…

We investigate the exploration of rugged fitness landscapes by spatially structured populations with demes on the nodes of a graph, connected by migrations. In the rare migration regime, we find that finite structures can adapt more…

We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation. Biologically motivated by the influence of seasons or the variation of drug concentration during medical treatment,…

In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other…

We study the evolution of asexual microorganisms with small mutation rate in fluctuating environments, and develop techniques that allow us to expand the formal solution of the evolution equations to first order in the mutation rate. Our…

We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…

In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of more fit individuals. The right selection pressure is critical in ensuring sufficient…

A major aim of evolutionary biology is to explain the respective roles of adaptive versus non-adaptive changes in the evolution of complexity. While selection is certainly responsible for the spread and maintenance of complex phenotypes,…

We investigate the evolution of populations of random Boolean networks under selection for robustness of the dynamics with respect to the perturbation of the state of a node. The fitness landscape contains a huge plateau of maximum fitness…

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…