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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…
In a co-evolutionary context, the survive probability of individual elements of a system depends on their relation with their neighbors. The natural selection process depends on the whole population, which is determined by local events…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…
A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of more fit individuals. The right selection pressure is critical in ensuring sufficient…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
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 derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a…
We study the population genetics of Evolution in the important special case of weak selection, in which all fitness values are assumed to be close to one another. We show that in this regime natural selection is tantamount to the…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
We consider a model of a population with fixed size $N$, which is subjected to an unlimited supply of beneficial mutations at a constant rate $\mu_N$. Individuals with $k$ beneficial mutations have the fitness $(1+s_N)^k$. Each individual…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…