Related papers: Eigen's Error Threshold and Mutational Meltdown in…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We present stochastic, finite-population formulations of the Crow-Kimura and Eigen models of quasispecies theory, for fitness functions that depend in an arbitrary way on the number of mutations from the wild type. We include back mutations…
The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual…
Here we present extinction, extirpation and coexistence conditions where / when two communities combine. We consider one specific model where two communities coalesce, and another model where the communities coexist side by side, blending…
We study general properties of the leading eigenvalue $\overline{w}(q)$ of Eigen's evolutionary matrices depending on the probability $q$ of faithful reproduction. This is a linear algebra problem that has various applications in…
After reviewing the general scaling properties of aging systems, we present a numerical study of the slow evolution induced in the zeta urn model by a quench from a high temperature to a lower one where a condensed equilibrium phase exists.…
We introduce a model of molecular evolution in which the fitness of an individual depends both on its own and on the parent's genotype. The model can be solved by means of a nonlinear mapping onto the standard quasispecies model. The…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
We study Eigen's model of quasi-species, characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum…
Motivated by the climate crisis that is currently ravaging the planet, we propose and analyze a novel framework for the evolution of anthropogenic climate impact in which the evolution of human environmental behavior and environmental…
A non-local toy-model is proposed for the purpose of modelling the ``wave function collapse'' of a two-state quantum system. The collapse is driven by a nonlinear evolution equation with an extreme sensitivity to absolute phase. It is…
We propose a variation of the GMS model of evolution of species. In this version, as in the GMS model, at each birth, the new species in the system is labeled with a random fitness mark, but in our variation, to each extinction event is…
This paper extends Eigen's quasispecies equations to account for the semiconservative nature of DNA replication. We solve the equations in the limit of infinite sequence length for the simplest case of a static, sharply peaked fitness…
Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner's Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as…
We consider a nonlocal bistable reaction-diffusion equation, which serves as a model for a population structured by a phenotypic trait, subject to mutation, trait-dependent fitness, and nonlocal competition. Within this replicator-mutator…
In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a…
A multi-type neutral Cannings population model with mutation and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a…
This paper develops an analytically tractable model for determining the equilibrium distribution of mismatch repair deficient strains in unicellular populations. The approach is based on the single fitness peak (SFP) model, which has been…