Related papers: Cumulants, Moments and Selection: The Connection B…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
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…
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without…
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.…
Factorial moments and cumulants are usually defined with respect to the unconditioned Poisson process. Conditioning a sample by selecting events of a given overall multiplicity $N$ necessarily introduces correlations. By means of Edgeworth…
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…
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…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
The purpose of this Note is twofold: First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete-time. In the process, we…
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and…
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…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
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…
Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population…
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak…