Related papers: Kingman's model with random mutation probabilities…
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 a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original model, the fitness distribution of the population is modeled by…
Kingman's House-of-Cards model is a simple and celebrated model to describe the evolution of population under the competition of selection and mutation. Letting mutation probabilities vary on generations makes the model more realistic and…
We describe the onset of condensation in the simple model for the balance between selection and mutation given by Kingman in terms of a scaling limit theorem. Loosely speaking, this shows that the wave moving towards genes of maximal…
Kingman's model of selection and mutation studies the limit type value distribution in an asexual population of discrete generations and infinite size undergoing selection and mutation. This paper generalizes the model to analyse the…
We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability…
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…
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…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
When an advantageous mutation occurs in a population, the favorable allele may spread to the entire population in a short time, an event known as a selective sweep. As a result, when we sample $n$ individuals from a population and trace…
We establish convergence to the Kingman coalescent for the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may…
This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions…
The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the $\Lambda$-coalescent. In particular we formulate the…
We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman's coalescent process, which produces a binary tree, universally emerges from many microscopic models in which the…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…
Multiple-merger coalescents, e.g. $\Lambda$-$n$-coalescents, have been proposed as models of the genealogy of $n$ sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's…