Related papers: The long-tail distribution function of mutations i…
This thesis is aimed at studying mutations, understood as trajectories in the DNA configuration space. An evolutive model of mutations in terms of Levy flights is proposed. The parameters of the model are estimated by means of data from the…
Data from a long time evolution experiment with Escherichia Coli and from a large study on copy number variations in subjects with european ancestry are analyzed in order to argue that mutations can be described as Levy flights in the…
Taking into account an evolutionary model of mutations in term of Levy Fights that was previously constructed, we designed an algorithm to reproduce the evolutionary dynamics of the Long-Term Evolution Experiment (LTEE) with E. Coli…
Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large…
Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing…
Unraveling bacterial strategies for spatial exploration is crucial for understanding the complexity in the organization of life. Bacterial motility determines the spatio-temporal structure of microbial communities, controls infection…
Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such…
We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics…
The Lenski experiment is a long term daily reproduction of Escherichia coli, that has evidenced phenotypic and genetic evolutions along the years. Some mathematical models, that could be usefull in understanding the results of that…
We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…
The extent of parallel evolution at the genotypic level is quantitatively linked to the distribution of beneficial fitness effects (DBFE) of mutations. The standard view, based on light-tailed distributions (i.e. distributions with finite…
This chapter gives a synopsis of recent approaches to model and analyse the evolution of microbial populations under selection. The first part reviews two population genetic models of Lenski's long-term evolution experiment with Escherichia…
We describe the evolution of $E.coli$ populations through a Bak-Sneppen type model which incorporates random mutations. We show that, for a value of the mutation level which coincides with the one estimated from experiments, this model…
We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus" and/or "max"…
Unraveling the evolutionary forces shaping bacterial diversity can today be tackled using a growing amount of genomic data. While the genome of eukaryotes is highly stable, bacterial genomes from cells of the same species highly vary in…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
Genetic interactions can strongly influence the fitness effects of individual mutations, yet the impact of these epistatic interactions on evolutionary dynamics remains poorly understood. Here we investigate the evolutionary role of…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
Various rod-shaped bacteria such as the canonical gram negative Escherichia coli or the well-studied gram positive Bacillus subtilis divide symmetrically after they approximately double their volume. Their size at division is not constant,…
Although the role of lateral gene transfer is well recognized in the evolution of bacteria, it is generally assumed that it has had less influence among eukaryotes. To explore this hypothesis we compare the dynamics of genome evolution in…