Related papers: Mutations as Levy flights
The data we analyze derives from the observation of numerous cells of the bacterium Escherichia coli (E. coli) growing and dividing. Single cells grow and divide to give birth to two daughter cells, that in turn grow and divide. Thus, a…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We study Markovian continuous-time random walk models for L\'evy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in…
In a short article submitted to ArXiv [1], Maddamsetti et al. argue that the variation in the neutral mutation rate among genes in Escherichia coli that we recently reported [2] might be explained by horizontal gene transfer (HGT). To…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
Replication of genetic material is an important process for all living organisms. Origins of replication initiate the copying of DNA at many points on a chromosome, and it is the distribution of these points that is relevant here, as it…
A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the…
In this work, the dynamics of fluctuations in gene expression time series is investigated. By using collected data of gene expression from yeast and human organisms, we found that the fluctuations of gene expression level and its average…
Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the…
Spatial constraints such as rigid barriers affect the dynamics of cell populations, potentially altering the course of natural evolution. In this paper, we investigate the population genetics of Escherichia coli proliferating in…
Recent observations as well as theoretical studies of YSO jets suggest the presence of two steady components: a disk wind type outflow needed to explain the observed high mass loss rates and a stellar wind type outflow probably accounting…
Once recognizing that point particles moving inside the extended version of the rippled billiard perform L\'evy flights characterized by a L\'evy-type distribution $P(\ell)\sim \ell^{-(1+\alpha)}$ with $\alpha=1$, we derive a generalized…
We study macroevolutionary dynamics by extending microevolutionary competition models to long time scales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary…
DNA migration in topologically structured microchannels with periodic cavities is investigated experimentally and with Brownian dynamics simulations of a simple bead-spring model. The results are in very good agreement with one another. In…
The evolution in coding DNA sequences brings new flexibility and freedom to the codon words, even as the underlying nucleotides get significantly ordered. These curious contra-rules of gene organisation are observed from the distribution of…
We study symmetric L\'evy flights in a semi-infinite domain $[0,\infty)$ with a reflecting and absorbing boundary at 0. To this end, we use the fractional differential equation that governs the L\'evy process. Incorporating the boundary…
We have simulated the evolution of age structured populations whose individuals represented by their diploid genomes were distributed on a square lattice. The environmental conditions on the whole territory changed simultaneously in the…
We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it…
Mutation is a critical mechanism by which evolution explores the functional landscape of proteins. Despite our ability to experimentally inflict mutations at will, it remains difficult to link sequence-level perturbations to systems-level…
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a L\'evy flight on a line. After a brief survey of the theory of records for independent and…