Related papers: Selective advantage of diffusing faster
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…
In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…
Stochastic phenotype switching has been suggested to play a beneficial role in microbial populations by leading to the division of labour among cells, or ensuring that at least some of the population survives an unexpected change in…
We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasi-species. By suggesting an analogy between the competition among strains and the…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The dynamics of this selection is studied using a simple linear model. It has similarities to…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model [1]. In this paper I modify the etching model to perform sequential, instead of random,…
In its simplest form, the competitive exclusion principle states that a number of species competing for a smaller number of resources cannot coexist. However, it has been observed empirically that in some settings it is possible to have…
Single-cell experiments revealed substantial variability in generation times, growth rates but also in birth and division sizes between genetically identical cells. Understanding how these fluctuations determine the fitness of the…
A stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$, is introduced. The growth is driven by outbursts in the infected region, an outburst in the type 1 (2) infected region transmitting the type 1 (2)…
Given an endogenous timescale set by invasion in a constant environment, we introduced periodic temporal variation in competitive superiority by alternating the species' propagation rates. By manipulating habitat size and introduction rate,…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…
We study competition of two non-motile bacterial strains in a three-dimensional channel numerically, and analyze how their configuration evolves in space and time. We construct a lattice model that takes into account self-replication,…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…
A selective sweep describes the reduction of linked genetic variation due to strong positive selection. If s is the fitness advantage of a homozygote for the beneficial allele and h its dominance coefficient, it is usually assumed that…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…