Evolution in random fitness landscapes: the infinite sites model

Abstract

We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability distribution g(w). This is the finite population version of Kingman's house of cards model [J.F.C. Kingman, J. Appl. Probab. 15, 1 (1978)]. In contrast to Kingman's work, the focus here is on unbounded distributions g(w) which lead to an indefinite growth of the population fitness. The model is solved analytically in the limit of infinite population size N → ∞ and simulated numerically for finite N . When the genomewide mutation probability U is small, the long time behavior of the model reduces to a point process of fixation events, which is referred to as a diluted record process (DRP). The DRP is similar to the standard record process except that a new record candidate (a number that exceeds all previous entries in the sequence) is accepted only with a certain probability that depends on the values of the current record and the candidate. We develop a systematic analytic approximation scheme for the DRP. At finite U the fitness frequency distribution of the population decomposes into a stationary part due to mutations and a traveling wave component due to selection, which is shown to imply a reduction of the mean fitness by a factor of 1 − U compared to the U → 0 limit.

The dynamics of adaptation on correlated fitness landscapes

“…Φ x (y)dy denotes the probability that a mutation arising in an individual of fitness x will have a fitness in [y, y+dy]. The space of fitness-parametrized landscapes includes, among others, such well-known (2,5,6,20,27,(29)(30)(31) landscapes as (i) the "house of cards" (HOC) or the uncorrelated landscapes, for which all genotypes have the same NFD Φ x (y) = Ψ(y); (ii) the non-epistatic (NEPI) landscapes, for which the distribution of fitness effects of mutations is the same for all genotypes, so that the NFD is given by Φ x (y) = Ψ(y − x), and (iii) the "stairway to heaven" (STH) landscapes, for which the distribution of selection coefficients is the same for all genotypes, so that the NFD is given by…”

“…But neutral networks (14,25,26) or mutations with equal effect but different evolutionary potential fall outside of the scope of fitness-parametrized landscapes. Nevertheless, the space of fitness-parametrized landscapes is very large and contains most of the landscapes studied in previous literature.To understand this space better, we will first explore three classical fitness landscapes: the uncorrelated landscape (2,5,6,20,27), the (additive) nonepistatic landscape (28,29), and the landscape …”

“…To understand this space better, we will first explore three classical fitness landscapes: the uncorrelated landscape (2,5,6,20,27), the (additive) nonepistatic landscape (28,29), and the landscape with a constant distribution of selection coefficients (30,31). We will demonstrate how the choice of landscape influences the dynamics of adaptation.…”

Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

“…For example, in long-term evolution experiments the speed of adaptation usually slows down (Lenski and Travisano 1994;Barrick et al 2009), which is attributed to the decreasing supply of beneficial mutations. In this context, the house-of-cards model, in which fitness values are assigned randomly to genotypes, could provide a more realistic description (Kingman 1978;Park and Krug 2008). In the framework of this model one cannot, however, explain the advantage of sex, because the fitness of a recombinant genotype is uncorrelated with the parental fitnesses and therefore beneficial mutations cannot accumulate through recombination.…”

Modeling microevolution in a changing environment: the evolving quasispecies and the diluted champion process

“…However, in contrast with the case of compact support, the dynamics for a finite population with N 1 individuals can now be substantially different from the infinite population limit. In fact, the evolution process can be described as a non stationary record process where condensates of a given fitness are replaced by ones of higher fitness ( [18]), with persistence times that becomes longer and longer as the fitness increases. It has been noticed in [17] that, however, an uncondensed phase can be metastable for long times.…”