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We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length $L$. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant…
These notes introduce probabilistic landscape models defined on high-dimensional discrete sequence spaces. The models are motivated primarily by fitness landscapes in evolutionary biology, but links to statistical physics and computer…
Darwinian evolution can be illustrated as an uphill walk in a landscape, where the surface consists of genotypes, the height coordinates represent fitness, and each step corresponds to a point mutation. Epistasis, roughly defined as the…
The mechanisms by which adaptive phenotypes spread within an evolving population after their emergence are understood fairly well. Much less is known about the factors that influence the evolutionary accessibility of such phenotypes, a…
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 fitness landscape defines the relationship between genotypes and fitness in a given environment, and underlies fundamental quantities such as the distribution of selection coefficient, or the magnitude and type of epistasis. A better…
Natural genomes sometimes encode two different proteins in staggered reading frames of the same DNA sequence. Despite the prevalence of these 'overlapping genes' across the tree of life, it remains unknown whether arbitrary protein pairs…
We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which…
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…
The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is…
In this paper we study a variation of the accessibility percolation model, this is also motivated by evolutionary biology and evolutionary computation. Consider a tree whose vertices are labeled with random numbers. We study the probability…
The fitness landscape - the mapping between genotypes and fitness - determines properties of the process of adaptation. Several small genetic fitness landscapes have recently been built by selecting a handful of beneficial mutations and…
We investigate an simple evolutionary game of sequences and demonstrate on this example the structure of fitness landscapes in discrete problems. We show the smoothing action of the genotype-phenotype mapping which still makes it feasible…
We study the accessibility percolation model on infinite trees. The model is defined by associating an absolute continuous random variable $X_v$ to each vertex $v$ of the tree. The main question to be considered is the existence or not of…
The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of…
We show that higher order epistasis has a substantial impact on evolutionary dynamics by analyzing peaks in the fitness landscapes. There are 193,270,310 fitness graphs, or cube orientations, for 4-locus systems, distributed on 511, 863…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
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…
Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness…
Mutational robustness quantifies the effect of random mutations on fitness. When mutational robustness is high, most mutations do not change fitness or have only a minor effect on it. From the point of view of fitness landscapes, robust…