Adaptive evolution in a spatially structured asexual population

We study the process of adaptation in a spatially structured asexual haploid population. The model assumes a local competition for replication, where each organism interacts only with its nearest neighbors. We observe that the substitution rate of beneficial mutations is smaller for a spatially structured population than that seen for populations without structure. The difference between structured and unstructured populations increases as the adaptive mutation rate increases. Furthermore, the substitution rate decreases as the number of neighbors for local competition is reduced. We have also studied the impact of structure on the distribution of adaptive mutations that fix during adaptation.The original version is available at www.springerlink.co

Sex and deleterious mutations

For access the publication please visit the following link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2390638/The evolutionary advantage of sexual reproduction has been considered as one of the most pressing questions in evolutionary biology. While a pluralistic view of the evolution of sex and recombination has been suggested by some, here we take a simpler view and try to quantify the conditions under which sex can evolve given a set of minimal assumptions. Since real populations are finite and also subject to recurrent deleterious mutations, this minimal model should apply generally to all populations. We show that the maximum advantage of recombination occurs for an intermediate value of the deleterious effect of mutations. Furthermore we show that the conditions under which the biggest advantage of sex is achieved are those that produce the fastest fitness decline in the corresponding asexual population and are therefore the conditions for which Muller's ratchet has the strongest effect. We also show that the selective advantage of a modifier of the recombination rate depends on its strength. The quantification of the range of selective effects that favors recombination then leads us to suggest that, if in stressful environments the effect of deleterious mutations is enhanced, a connection between sex and stress could be expected, as it is found in several specie

Scaling, genetic drift and clonal interference in the extinction pattern of asexual populations

We investigate the dynamics of loss of favorable mutations in an asexual haploid population. In the current work, we consider homogeneous as well as spatially structured population models. We focus our analysis on statistical measurements of the probability distribution of the maximum population size N(sb) achieved by those mutations that have not reached fixation. Our results show a crossover behavior which demonstrates the occurrence of two evolutionary regimes. In the first regime, which takes place for small N(sb) , the probability distribution is described by a power law with characteristic exponent theta(d) =1.8 +/- 0.01. This power law is not influenced by the rate of beneficial mutations. The second regime, which occurs for intermediate to large values of N(sb), has a characteristic exponent theta(c) which increases as the rate of beneficial mutations grows. These results establish where genetic drift and clonal interference become the main underlying mechanism in the extinction of advantageous mutations

The effect of spatial structure in adaptive evolution

We study the dynamics of adaptation in a spatially structured population. The model assumes local competition for replication, where each organism interacts only with its nearest neighbors and is inspired by experimental methods that can be used to study the process of adaptive evolution in microbes. In such experiments microbial populations are grown on petri dishes and allowed to adapt by serial passage. We compare the rate of adaptation in a structured population where the structure is maintained intact to those where movement of individuals can occur. We observe that the rate of adaptive evolution is higher and the mean effect of fixed beneficial mutations is lower in intact structures than in structures with mixing.The original version is available at www.springerlink.co

Muller's ratchet in random graphs and scale free networks

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of mitochondria, the degeneration of the Y chromosome, the evolution of sex and recombination and the evolution of microbes. Here we study the speed of Muller's ratchet in a population subdivided into many small subpopulations connected by migration, and distributed on a network. We compare the speed of the ratchet in two distinct types of topologies: scale free networks and random graphs. The difference between the topologies is noticeable when the average connectivity of the network and the migration rate is large. In this situation we observe that the ratchet clicks faster in scale free networks than in random graphs. So contrary to intuition, scale free networks are more prone to loss of genetic information than random graphs. On the other hand, we show that scale free networks are more robust to the random extinction than random graphs. Since these complex networks have been shown to describe well real-life systems, our results open a framework for studying the evolution of microbes and disease epidemics

On the structure pf genealogical trees in the presence of selection

We investigate through numerical simulations the effect of selection on two summary statistics for nucleotide variation in a sample of two genes from a population of N asexually reproducing haploid individuals. One is the mean time since two individuals had their most recent common ancestor ($\bar{T_s}$), and the other is the mean number of nucleotide differences between two genes in the sample ($\bar{d_s}$). In the case of diminishing epistasis, in which the deleterious effect of a new mutation is attenuated, we find that the scale of $\bar{d_s}$ with the population size depends on the mutation rate, leading then to the onset of a sharp threshold phenomenon as N becomes large.Comment: 6 page

Survival-extinction phase transition in a bit-string population with mutation

A bit-string model for the evolution of a population of haploid organisms, subject to competition, reproduction with mutation and selection is studied, using mean field theory and Monte Carlo simulations. We show that, depending on environmental flexibility and genetic variability, the model exhibits a phase transtion between extinction and survival. The mean-field theory describes the infinite-size limit, while simulations are used to study quasi-stationary properties.Comment: 11 pages, 5 figure

The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $\sigma_{via}$, yields a viable organism with first order growth rate constant $k > 1$ if it is equal to some target ``master'' sequence $\sigma_{via, 0}$. The second gene, denoted by $\sigma_{rep}$, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $\sigma_{rep, 0}$. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on \mu \equiv L\eps , the product of sequence length and per base pair replication error probability, and \eps_r , the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As \eps_r exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds \ln k/\eps_r , while above the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds $\ln k/f_{del}$, where $f_{del}$ denotes the fraction of deleterious mutations.Comment: 14 pages, 3 figures. Submitted to Physical Review

Small-word networks decrease the speed of Muller's ratchet

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of non-recombining genomes, such as the mitochondria, the degeneration of the Y chromosome, and the evolution of sex and recombination. Here we study the speed of Muller's ratchet in a spatially structured population which is subdivided into many small populations (demes) connected by migration, and distributed on a graph. We studied different types of networks: regular networks (similar to the stepping-stone model), small-world networks and completely random graphs. We show that at the onset of the small-world network - which is characterized by high local connectivity among the demes but low average path length - the speed of the ratchet starts to decrease dramatically. This result is independent of the number of demes considered, but is more pronounced the larger the network and the stronger the deleterious effect of mutations. Furthermore, although the ratchet slows down with increasing migration between demes, the observed decrease in speed is smaller in the stepping-stone model than in small-world networks. As migration rate increases, the structured populations approach, but never reach, the result in the corresponding panmictic population with the same number of individuals. Since small-world networks have been shown to describe well the real contact networks among people, we discuss our results in the light of the evolution of microbes and disease epidemic

Small-word networks decrease the speed of Muller's ratchet

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of non-recombining genomes, such as the mitochondria, the degeneration of the Y chromosome, and the evolution of sex and recombination. Here we study the speed of Muller's ratchet in a spatially structured population which is subdivided into many small populations (demes) connected by migration, and distributed on a graph. We studied different types of networks: regular networks (similar to the stepping-stone model), small-world networks and completely random graphs. We show that at the onset of the small-world network - which is characterized by high local connectivity among the demes but low average path length - the speed of the ratchet starts to decrease dramatically. This result is independent of the number of demes considered, but is more pronounced the larger the network and the stronger the deleterious effect of mutations. Furthermore, although the ratchet slows down with increasing migration between demes, the observed decrease in speed is smaller in the stepping-stone model than in small-world networks. As migration rate increases, the structured populations approach, but never reach, the result in the corresponding panmictic population with the same number of individuals. Since small-world networks have been shown to describe well the real contact networks among people, we discuss our results in the light of the evolution of microbes and disease epidemic