Related papers: An inhomogeneous contact process model for speciat…
We study a contact process running in a random environment in $\mathbb {Z}^d$ where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by…
We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model's infection rates are varied through a control parameter, for which…
We study a two dimensional version of Neuhauser's long range sexual reproduction model and prove results that give bounds on the critical values $\lambda_f$ for the process to survive from a finite set and $\lambda_e$ for the existence of a…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective…
We finely describe the "coming down from infinity" for birth and death processes which eventually become extinct. Our biological motivation is to study the decrease of regulated populations which are initially large. Under general…
In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the…
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…
We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on $\mathbb{Z}$ with time varying and possible state-dependent…
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…
We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate that provides a stochastic changing of lengthes by a free diffusion law. The birth and death rates are length dependent which…
We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean…
The process of speciation, where an ancestral species divides in two or more new species, involves several geographic, environmental and genetic components that interact in a complex way. Understanding all these elements at once is…
We consider a birth-death process with the birth rates $i\lambda$ and death rates $i\mu +i(i-1)\theta$, where $i$ is the current state of the process. A positive competition rate $\theta$ is assumed to be small. In the supercritical case…
We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes.
We consider the contact process with infection rate $\lambda$ on a random $(d+1)$-regular graph with $n$ vertices, $G_n$. We study the extinction time $\tau_{G_n}$ (that is, the random amount of time until the infection disappears) as $n$…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
A simulation model of a population having internal (genetic) structure is presented. The population is subject to selection pressure coming from the environment which is the same in the whole system but changes in time. Reproduction has a…
Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,\infty)$.…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…