Related papers: Muller's ratchet clicks in finite time
Eigen's quasi-species model describes viruses as ensembles of different mutants of a high fitness "master" genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…
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 study a model of growing population that competes for resources. At each time step, all existing particles reproduce and the offspring randomly move to neighboring sites. Then at any site with more than one offspring, the particles are…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
If deleterious mutations near a fitness maximum in a spatially distributed population are sufficiently frequent or detrimental, the population can undergo a fitness collapse, similarly to the Muller's ratchet effect in well-mixed…
We study the dynamics of an age-structured population in which the life expectancy of an offspring may be mutated with respect to that of its parent. When advantageous mutation is favored, the average fitness of the population grows…
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…
Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as…
We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the…
We introduce a toy model for interacting populations connected by mutations and limited by a shared resource. We study the presence of Eigen's error threshold and mutational meltdown. The phase diagram of the system shows that the…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
We study the posterior contraction behavior of the latent population structure that arises in admixture models as the amount of data increases. We adopt the geometric view of admixture models - alternatively known as topic models - as a…
The effects of inbreeding on human health depend critically on the number and severity of recessive, deleterious mutations carried by individuals. In humans, existing estimates of these quantities are based on comparisons between…
We introduce the following discrete time model. Each natural number represents an ecological niche and is assigned a fitness in $(0,1)$. All the sites are updated simultaneously at every discrete time. At any given time the environment may…
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…
We consider an approximating sequence of interacting population models with branching, mutation and competition. Each individual is characterized by its trait and the traits of its ancestors. Birth- and death-events happen at exponential…