Related papers: A periodic Kingman model for the balance between m…
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…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study 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.…
Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis.…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
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…
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the…
The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts have been previously conjectured and…
Biological evolution depends on the passing down to subsequent generations of genetic information encoding beneficial traits, and on the removal of unfit individuals by a selection mechanism. However, selection acts on phenotypes, and is…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
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…
We consider integro-differential models describing the evolution of a population structured by a quantitative trait. Individuals interact competitively, creating a strong selection pressure on the population. On the other hand, mutations…
We establish convergence to the Kingman coalescent for a class of age-structured population models with time-constant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother's age.
We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and removed from the system with a uniform…
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…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation.…