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Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…
Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a…
We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
All possible phenotypes are not equally accessible to evolving populations. In fact, only phenotypes of large size, i.e. those resulting from many different genotypes, are found in populations of sequences, presumably because they are…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context…
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly…
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 the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic…
The importance of mutator clones in the adaptive evolution of asexual populations is not fully understood. Here we address this problem by using an ab initio microscopic model of living cells, whose fitness is derived directly from their…
We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic…
Due to stochastic fluctuations arising from finite population size, known as genetic drift, the ability of a population to explore a rugged fitness landscape depends on its size. In the weak mutation regime, while the mean steady-state…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist…
We consider the accumulation of beneficial and deleterious mutations in large asexual populations. The rate of adaptation is affected by the total mutation rate, proportion of beneficial mutations and population size $N$. We show that…