Related papers: The quasispecies distribution
In 1991 J.F. Aarnes introduced the concept of quasi-measures in a compact topological space $\Omega$ and established the connection between quasi-states on $C (\Omega)$ and quasi-measures in $\Omega$. This work solved the linearity problem…
A central issue in ecology today is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to the problem of species abundance…
We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…
We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet of…
We prove that a Moran model converges in probability to Eigen's quasispecies model in the infinite population limit.
George Williams defined an evolutionary unit as hereditary information for which the selection bias between competing units dominates the informational decay caused by imperfect transmission. In this article, I extend Williams' approach to…
Stirling permutations were introduced by Gessel and Stanley, who used their enumeration by the number of descents to give a combinatorial interpretation of certain polynomials related to Stirling numbers. Quasi-Stirling permutations, which…
We use finite-size scaling to investigate the critical behavior of the quasiespecies model of molecular evolution in the single-sharp-peak replication landscape. This model exhibits a sharp threshold phenomenon at Q=Q_c=1/a, where Q is the…
We study an abstract model for the co-evolution between mutating viruses and the adaptive immune system. In sequence space, these two populations are localized around transiently dominant strains. Delocalization or error thresholds exhibit…
Subcritical population processes are attracted to extinction and do not have non-trivial stationary distributions, which prompts the study of quasi-stationary distributions (QSDs) instead. In contrast to what generally happens for…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
The experimental discovery of quasicrystals by D Shechtman, D Gratias, I Blech, and J W Cahn in 1984 provided the paradigm for a new type of long-range order of solid matter in nature. This discovery stimulated an explosion of new…
We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…
In this paper we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985)…
The quasispherical Szekeres metric is an exact solution to Einstein's equations describing an inhomogeneous and anisotropic cosmology. Though its governing equations are well-known, there are subtle, often-overlooked details in how the…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…
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…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…