Related papers: Equilibrium in Wright-Fisher models of population …
We introduce a meta-population version of models of asymmetric exclusion models, consisting of a spatial arrangement of patches. Patches are of a specific size, indicating the maximal number of particles they can hold. We use an expansion…
We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
Non-equilibrium stationary fluctuations may exhibit a special symmetry called fluctuation relations (FR). Here, we show that this property is always satisfied by the subtraction of two random and independent variables related by a…
We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…
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…
We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equation and admits a continuous solution. We establish the…
We investigate the properties of a Wright-Fisher diffusion process started from frequency x at time 0 and conditioned to be at frequency y at time T. Such a process is called a bridge. Bridges arise naturally in the analysis of selection…
In both population genetics and forensic genetics it is important to know how haplotypes are distributed in a population. Simulation of population dynamics helps facilitating research on the distribution of haplotypes. In forensic genetics,…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
We examine deviations from Boltzmann-Gibbs statistics for partially equilibrated systems of finite size. We find that such systems are characterized by the Levy distribution whose non-extensivity parameter is related to the number of…
We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through…
We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain…
In this paper we study the equilibrium energy fluctuation field of a one-dimensional reversible non gradient model. We prove that the limit fluctuation process is governed by a generalized Ornstein- Uhlenbeck process, which covariances are…
Extending the stochastic mean-field model by including pairing, an approach is proposed for describing evolutions of complex many-body systems in terms of an ensemble of Time-Dependent Hartree-Fock Bogoliubov trajectories which is…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
Fluctuations in biodiversity, large and small, are pervasive in the fossil record, yet we do not understand the processes generating them. Here we extend theory from non-equilibrium statistical physics to describe the previously unaccounted…
In this paper we analyze the equilibrium properties of a large class of stochastic processes describing the fundamental biological process within bacterial cells, {\em the production process of proteins}. Stochastic models classically used…
One of the fundamental mathematical models for studying random genetic drift is the Kimura equation, derived as the large-population limit of the discrete Wright-Fisher model. However, due to the degeneracy of the diffusion coefficient, it…