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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…
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 $NK$ model, introduced by Kauffman, Levin, and Weinberger, is a random field used to describe the fitness landscape of certain species with $N$ genetic loci, each interacting with $K$ others. The model has wide applications in…
A fitness landscape is a mapping from the space of genetic sequences, which is modeled here as a binary hypercube of dimension $L$, to the real numbers. We consider random models of fitness landscapes, where fitness values are assigned…
The factors that influence genetic architecture shape the structure of the fitness landscape, and therefore play a large role in the evolutionary dynamics. Here the NK model is used to investigate how epistasis and pleiotropy -- key…
We study how correlations in the random fitness assignment may affect the structure of fitness landscapes. We consider three classes of fitness models. The first is a continuous phenotype space in which individuals are characterized by a…
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…
Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here we discuss probabilistic models of…
A fitness landscape is a genetic space -- with two genotypes adjacent if they differ in a single locus -- and a fitness function. Evolutionary dynamics produce a flow on this landscape from lower fitness to higher; reaching equilibrium only…
In this paper we present two modifications of traditional $NK$ fitness landscapes, the $\theta NK$ and $HNK$ models, and explore these modifications via accessibility and ruggedness. The $\theta NK$ model introduces a parameter $\theta$ to…
Simulated landscapes have been used for decades to evaluate search strategies whose goal is to find the landscape location with maximum fitness. Applications include modeling the capacity of enzymes to catalyze reactions and the clinical…
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…
The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts have been previously conjectured and…
We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of…
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…
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…
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…
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…
Darwinian evolution is driven by random mutations, genetic recombination (gene shuffling) and selection that favors genotypes with high fitness. For systems where each genotype can be represented as a bitstring of length $L$, an overview of…
We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent…