Related papers: An inhomogeneous contact process model for speciat…

We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a…

A birth-death-sampling model gives rise to phylogenetic trees with samples from the past and the present. Interpreting "birth" as branching speciation, "death" as extinction, and "sampling" as fossil preservation and recovery, this model --…

We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are…

A wide variety of stochastic models of cladogenesis (based on speciation and extinction) lead to an identical distribution on phylogenetic tree shapes once the edge lengths are ignored. By contrast, the distribution of the tree's edge…

We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in…

We consider contact processes on the hierarchical group, where sites infect other sites at a rate depending on their hierarchical distance, and sites become healthy with a constant recovery rate. If the infection rates decay too fast as a…

Many species see their range shifted poleward in response to global warming and need to keep pace in order to survive. To understand the effect of climate change on species ranges and its consequences on population dynamics, we consider a…

We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…

We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results…

This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…

Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…

Given that extinction in a bisexual population is certain, we study a way to approximate the time when this extinction occurs. Our study is based on standard tools from Extreme Value Theory, which in practice are very easy to implement. We…

Neutral speciation mechanisms based on isolation by distance and sexual selection, termed topopatric, have recently been shown to describe the observed patterns of abundance distributions and species-area relationships. Previous works have…

The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…

We present a stochastic model for the size of a taxon in paleobiology, in which we allow for the evolution of new taxon members, and both individual and catastrophic extinction events. The model uses ideas from the theory of birth and death…

Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process…

We introduce a method to prove metastability of the contact process on Erd\H{o}s-R\'enyi graphs and on configuration model graphs. The method relies on uniformly bounding the total infection rate from below, over all sets with a fixed…

The extinction transition on a one dimensional heterogeneous substrate with diffusive correlations is studied. Diffusively correlated heterogeneity is shown to affect the location of the transition point, as the reactants adapt to the…

Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many research topics such as quantifying species sizes in ecological populations, describing…

This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…