Related papers: On a mathematical relation between the Eigen model…
We develop an iterative global solution scheme for the backward Kolmogorov equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several alleles at the…
We present an extension of Eigen's model for quasi-species including the competition among individuals, proposed as the simplest mechanism for the formation of new species in a smooth fitness landscape. We are able to obtain analytically…
We are interested in the numerical approximation of non-linear stochastic differential equations (SDEs) with solution in a certain domain. Our goal is to construct explicit numerical schemes that preserve that structure. We generalize the…
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…
We consider a model of asexually reproducing individuals with random mutations and selection. The rate of mutations is proportional to the population size, $N$. The mutations may be either beneficial or deleterious. In a paper by Yu,…
We extend a model of community isolation in the d-dimensional lattice onto the case with an imposed imbalance between birth rates of competing communities. We give analytical and numerical evidences that in the asymmetric two-specie model…
This paper develops a simplified set of models describing asexual and sexual replication in unicel- lular diploid organisms. The models assume organisms whose genomes consist of two chromosomes, where each chromosome is assumed to be…
The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a hypersphere is transformed into the diffusion for the Wright-Fisher model with a particular mutation rate. We use the Ito calculus considering stochastic…
In a recent article, Desai and Fisher (2007) proposed that the speed of adaptation in an asexual population is determined by the dynamics of the stochastic edge of the population, that is, by the emergence and subsequent establishment of…
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection…
We derive central limit theorems for the Wasserstein distance between the empirical distributions of Gaussian samples. The cases are distinguished whether the underlying laws are the same or different. Results are based on the (quadratic)…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
Genetic Programming has been very successful in solving a large area of problems but its use as a machine learning algorithm has been limited so far. One of the reasons is the problem of overfitting which cannot be solved or suppresed as…
We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic…
We study the long-time behavior of solutions to a model of sexual populations structured in phenotypes. The model features a nonlinear integral reproduction operator derived from the Fisher infinitesimal operator and a trait-dependent…
Known results on the moments of the distribution generated by the two-locus Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical methods…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
Within the framework of population genetics we consider the evolution of an asexual haploid population under the effect of a rapidly varying natural selection (microevolution). We focus on the case in which the environment exerting…