Related papers: Coexistence for a multitype contact process with s…
We investigate the evolution of competing languages, a subject where much previous literature suggests that the outcome is always the domination of one language over all the others. Since coexistence of languages is observed in reality, we…
A stochastic comparison result that makes progress towards understanding the classical multitype contact process with unequal death rates is given. It has long been conjectured that the particle type with the largest birth to death rate…
Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder.…
D. discoideum has been recently suggested as an example of bet-hedging. Upon starvation a population of unicellular amoebae splits between aggregators, which form a fruiting body made of a stalk and resistant spores, and non-aggregators.…
Multicomponent phase separation is a routine occurrence in both living and synthetic systems. Thermodynamics provides a straightforward path to determine the phase boundaries that characterize these transitions for systems at equilibrium.…
We establish the criterion for the phase coexistence in a mixture of nonreciprocally interacting scalar densities. For an arbitrary number of components the active pressure exists for a specific class of interactions, and when the free…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
In this paper, we introduce a two-sex controlled branching model to describe the interaction between predator and prey populations with sexual reproduction. This process is a two-type branching process, where the first type corresponds to…
We study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
Extending previous rigorous results, we prove existence of an ordering transition at finite temperature for a class of nematogenic lattice models, where spins are associated with a one- or two-dimensional lattice, and interact via…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended…
We study the competition for space between two cell lines that differ only in the expression of the Ras oncogene. The two cell populations are initially separated and set to migrate antagonistically towards an in-between stripe of free…
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed by balls connected with thin corridors, we show the occurrence of pattern…
Ecosystems are formed by networks of species and their interactions. Traditional models of such interactions assume a constant interaction strength between a given pair of species. However, there is often significant trait variation among…
In order to model real ecological systems one has to consider many species that interact in complex ways. However, most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions. The few…
Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…
We study numerically domain growth and interface fluctuations in one- and two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on…