Related papers: A comparison between the quasi-species evolution a…
In this paper, we study the equilibrium behavior of Eigen's quasispecies equations for an arbitrary gene network. We consider a genome consisting of $ N $ genes, so that each gene sequence $ \sigma $ may be written as $ \sigma = \sigma_1…
The Waxman-Peck theory of the population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central aim is the calculation of the probability density with respect to…
I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
We study a general class of birth-and-death processes with state space $\mathbb{N}$ that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
We propose a microscopic stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. It is shown that, for small amplitude fluctuations, the proposed model gives a result for the…
RNA viruses are known to replicate with extremely high mutation rates. These rates are actually close to the so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
Developmental dynamics of multicellular organism is a process that takes place in a multi-stable system in which each attractor state represents a cell type and attractor transitions correspond to cell differentiation paths. This new…
The Price equation partitions the change in the expected value of a population measure. The first component describes the partial change caused by altered frequencies. The second component describes the partial change caused by altered…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
In this paper, we study the asymptotic (large time) behavior of a selection-mutation-competition model for a population structured with respect to a phenotypic trait, when the rate of mutation is very small. We assume that the reproduction…
Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents…
We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…
We consider species tree estimation under a standard stochastic model of gene tree evolution that incorporates incomplete lineage sorting (as modeled by a coalescent process) and gene duplication and loss (as modeled by a branching…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Ecological interactions can dramatically alter evolutionary outcomes in complex communities. Yet, the framework of population genetics largely neglects interactions from a species-rich community. Here, we bridge this gap by using dynamical…
We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into…