Related papers: Adaptive walks and extreme value theory
The adaptation rate in theoretical models of biological evolution increases with the mutation rate but only to a point when mutations into lethal states cause extinction. One would expect that removing such states should be beneficial for…
Molecular evolution is often conceptualised as adaptive walks on rugged fitness landscapes, driven by mutations and constrained by incremental fitness selection. It is well known that epistasis shapes the ruggedness of the landscape's…
Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction…
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…
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…
The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of…
Phenotypic evolution implies sequential fixations of new genomic sequences. The speed at which these mutations fixate depends, in part, on the relative fitness (selection coefficient) of the mutant vs. the ancestor. Using a simple…
The adaptive evolution of a population under the influence of mutation and selection is strongly influenced by the structure of the underlying fitness landscape, which encodes the interactions between mutations at different genetic loci.…
The fitness landscape encodes the mapping of genotypes to fitness and provides a succinct representation of possible trajectories followed by an evolving population. Evolutionary accessibility is quantified by the existence of…
It has recently been noted that the relative prevalence of the various kinds of epistasis varies along an adaptive walk. This has been explained as a result of mean regression in NK model fitness landscapes. Here we show that this…
Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in fitness landscapes has triggered a vast amount of research and has led to many important insights about…
We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small…
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 study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
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 consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…