Related papers: Selection-recombination-mutation dynamics: Gradien…
Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix…
Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies…
The population dynamics in a modified Leslie-Gower model with an additive Allee effect are highly sensitive to both parameters and initial population densities, leading to outcomes ranging from coextinction to sustained multistable steady…
A system of replicators with Hebbian random couplings is studied using dynamical methods. The self-reproducing species are here characterized by a set of binary traits and interact based on complementarity. In the case of an extensive…
We analyze the replicator-mutator equations for the Rock-Paper-Scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating…
The replicator-mutator dynamic was originally derived to model the evolution of language, and since the model was derived in such a general manner, it has been applied to the dynamics of social behavior and decision making in multi-agent…
There are 512 two-locus, two-allele, two-phenotype, fully-penetrant disease models. Using the permutation between two alleles, between two loci, and between being affected and unaffected, one model can be considered to be equivalent to…
The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population…
This paper investigates the long-term behavior of a class of $\Lambda$-Wright--Fisher processes incorporating frequency-dependent selection, coordinated (bidirectional) selection, as well as individual and coordinated mutation. Our primary…
We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the…
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…
The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per-capita growth rate at low densities is reduced. We examine…
The mutant allele frequencies in oncogenes peak around 0.40 and rapidly decrease. In this article, we explain why this is the case. Invoking a key result from mathematical analysis in our model, namely, the inverse function theorem, we…
In social dilemmas self-interested learning agents face the choice between the societal benefit of cooperation and the immediate reward of defection. Significant evidence exists on the benefits of assortment mechanisms such as partner…
The well-known replicator equation in evolutionary game theory describes how population-level behaviors change over time when individuals make decisions using simple imitation learning rules. In this paper, we study evolutionary dynamics…
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…
Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently it has been introduced into evolutionary game theory. In evolutionary game dynamics, the…
Background: Speciation corresponds to the progressive establishment of reproductive barriers between groups of individuals derived from an ancestral stock. Since Darwin did not believe that reproductive barriers could be selected for, he…