Related papers: Discrete versus continuous models in evolutionary …

We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…

In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the…

When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to…

A variety of genome transformations can occur as a microbial population adapts to a large environmental change. In particular, genomic surveys indicate that, following the transition to an obligate, host-dependent symbiont, the density of…

We study the large population limit of a multi-strategy discrete-time Moran process in the weak selection regime. We show that the replicator dynamics is interpreted as the large-population limit of the Moran process. This result is…

We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…

Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete…

We consider integro-differential models describing the evolution of a population structured by a quantitative trait. Individuals interact competitively, creating a strong selection pressure on the population. On the other hand, mutations…

Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…

The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire…

The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…

In genetics the Moran model describes the neutral evolution of a bi-allelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on…

Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…

We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We…

This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…

We construct a simple dynamical model of the massive globular cluster Omega Cen. The model includes simple treatments of dynamical evolution in a galactic tide, and evolution of single stars. Binary stars and rotation are neglected. The…

We model a general, hierarchically organized tissue by a multi compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single…