Related papers: Bistability in two-locus models with selection, mu…

We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the…

This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and…

Numerous traits under migration-selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be…

Dominance is usually considered a constant value that describes the relative difference in fitness or phenotype between heterozygotes and the average of homozygotes at a focal polymorphic locus. However, the observed dominance can vary with…

We study the asymptotic behavior of an integro-dierential equation describing the evolutionary adaptation of a population structured by a phenotypic trait. The model takes into account mutation, selection, horizontal gene transfer and…

Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…

In the context of multistability driven diseases, like cancer, spatiotemporal plasticity plays a significant role to achieve a spectrum of phenotypic variations. The interplay between gene regulatory networks and environmental factors, such…

In evolution, the effects of a single deleterious mutation can sometimes be compensated for by a second mutation which recovers the original phenotype. Such epistatic interactions have implications for the structure of genome space -…

The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is…

The mutation rate of a well adapted population is prone to reduction so as to have a lower mutational load. We aim to understand the role of epistatic interactions between the fitness affecting mutations in this process. Using a multitype…

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…

We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…

Feedback loops are essential for regulating cell proliferation and maintaining the delicate balance between cell division and cell death. Thanks to the exact solution of a few simple models of cell growth it is by now clear that stochastic…

Fitting models to data is an important part of the practice of science. Advances in machine learning have made it possible to fit more -- and more complex -- models, but have also exacerbated a problem: when multiple models fit the data…

Darwinian evolution can be illustrated as an uphill walk in a landscape, where the surface consists of genotypes, the height coordinates represent fitness, and each step corresponds to a point mutation. Epistasis, roughly defined as the…

Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of…

We study the evolution of allele frequencies in a large population where random mating is violated in a particular way that is related to recent works on speciation. Specifically, we consider non-random encounters in haploid organisms…

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…

Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small…

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…