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Chan, Durrett, and Lanchier introduced a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into two seasons. They proved that there is an…

Populations and Evolution · Quantitative Biology 2023-09-12 Hwai-Ray Tung , Rick Durrett

It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…

Probability · Mathematics 2010-03-02 Nicolas Lanchier

Neuhauser [Probab. Theory Related Fields 91 (1992) 467--506] considered the two-type contact process and showed that on $\mathbb{Z}^2$ coexistence is not possible if the death rates are equal and the particles use the same dispersal…

Probability · Mathematics 2007-05-23 Benjamin Chan , Richard Durrett

We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their boundaries. Each site of the space may contain only one…

Probability · Mathematics 2007-05-23 George Kordzakhia , Steven P. Lalley

We study two one-dimensional variants of the contact process: the contact-and-barrier process, where the population evolves in a region delimited by a randomly moving barrier, and the multitype contact process, in which two species compete…

Probability · Mathematics 2026-02-27 Isabella Alvarenga , Daniel Valesin

Coexistence of individuals with different species or phenotypes is often found in nature in spite of competition between them. Stable coexistence of multiple types of individuals have implications for maintenance of ecological biodiversity…

Disordered Systems and Neural Networks · Physics 2007-05-23 Naoki Masuda , Norio Konno

In the multitype contact process, vertices of a graph can be empty or occupied by a type 1 or a type 2 individual; an individual of type $i$ dies with rate 1 and sends a descendant to a neighboring empty site with rate $\lambda_i$. We study…

Probability · Mathematics 2018-03-06 Thomas Mountford , Pedro Luis Barrios Pantoja , Daniel Valesin

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of…

Populations and Evolution · Quantitative Biology 2011-03-09 Jacek Wendykier , Adam Lipowski , Antonio Luis Ferreira

I examine the effect of exogenous spatial heterogeneity on the coexistence of competing species using a simple model of non-hierarchical competition for site occupancy on a lattice. The sites on the lattice are divided into two types…

Populations and Evolution · Quantitative Biology 2011-10-17 Ilmari Karonen

This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are…

This paper considers a natural variant of the $d$-dimensional multitype contact process in which individuals can be fertile or sterile. Fertile individuals of type $i$ give birth to an offspring of their own type at rate $\lambda_i$, the…

Probability · Mathematics 2025-10-08 Nicolas Lanchier , Max Mercer , Hyunsik Yun

We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on $\mathbb{Z}$ a single mutant cannot survive while on…

Probability · Mathematics 2018-01-08 Idan Alter , Gideon Amir

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a…

Probability · Mathematics 2007-05-23 Thomas M. Liggett , Rinaldo B. Schinazi , Jason Schweinsberg

In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka-Volterra type competition terms in heterogeneous media. We first find various conditions on the parameters which guarantee the global…

Analysis of PDEs · Mathematics 2018-06-11 Tahir Bachar Issa , Wenxian Shen

A two-species spatially extended system of hosts and parasitoids is studied. There are two distinct kinds of coexistence; one with populations distributed homogeneously in space and another one with spatiotemporal patterns. In the latter…

Populations and Evolution · Quantitative Biology 2009-02-19 Matti Peltomaki , Martin Rost , Mikko Alava

We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an…

Populations and Evolution · Quantitative Biology 2015-06-12 Shlomit Weisman , David A. Kessler

We study coexistence in discrete time multi-type frog models. We first show that for two types of particles on $\mathbb{Z}^d$, for $d\geq2$, for any jumping parameters $p_1, p_2 \in (0,1)$, coexistence occurs with positive probability for…

Probability · Mathematics 2024-02-23 Rishideep Roy , Kumarjit Saha

The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the $d$-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at…

Probability · Mathematics 2014-10-16 Nicolas Lanchier , Yuan Zhang

We consider a spatial stochastic model for a pathogen population growing inside a host that attempts to eliminate the pathogens through its immune system. The pathogen population is divided into different types. A pathogen can either…

Probability · Mathematics 2026-02-03 Fábio Lopes , Alejandro Roldán-Correa

It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…

Analysis of PDEs · Mathematics 2014-07-22 François Castella , Sten Madec , Yvan Lagadeuc
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