Related papers: Equations of Evolutionary Dynamics in High Dimensi…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
When mutations are rampant, quasispecies theory or Eigen's model predicts that the fittest type in a population may not dominate. Beyond a critical mutation rate, the population may even be delocalized completely from the peak of the…
We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…
We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed…
In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a Win-Stay-Lose-Shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average…
The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
We show that, in the periodic homogenization of uniformly elliptic Hamilton-Jacobi equations in any dimension, the effective Hamiltonian does not necessarily inherit the quasiconvexity property (in the momentum variables) of the original…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behavior using numerical simulations. The proposed numerical approach can handle also density dependent fitness,…
We study the long-time behavior of almost periodic solutions to stochastic scalar conservation laws in any space dimension, under the assumption of Lipschitz continuity of the flux functions and a non-degeneracy condition. We show the…
Biodiversity and extinction are central issues in evolution. Dynamical balance among different species in ecosystems is often described by deterministic replicator equations with moderate success. However, fluctuations are inevitable,…
We reconsider the Eigen's quasi-species model for competing self-reproductive macromolecules in populations characterized by a single-peaked fitness landscape. The use of ideas and tools borrowed from polymers theory and statistical…
We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the…
A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The…
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
We study the long-time dynamics of the time-evolutionary Boltzmann equation with hard sphere collisions in the three-dimensional half-space \( \mathbb{R}^2 \times \mathbb{R}^+\), subject to diffuse reflection boundary conditions and small…
It is well-known that quasi-one-dimensional superconductors suffer from the pairing fluctuations that significantly reduce the superconducting temperature or even completely suppress any coherent behavior. Here we demonstrate that a…