Related papers: Immigration Processes with Binomial Catastrophes a…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by infinite peaks on a coherently constructed potential energy landscape. It is then important to ask what such…
In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…
We consider the setting of either a general non-local branching particle process or a general non-local superprocess, in both cases, with and without immigration. Under the assumption that the mean semigroup has a Perron-Frobenious type…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…
In this paper we consider two branching processes living in a joint random environment. Assuming that both processes are critical we address the following question: What is the probability that both populations survive up to a large time…
The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A…
We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS…
We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q]=1, and where the birth rate if the population is currently in state…
We consider a bilateral birth-death process characterized by a constant transition rate $\lambda$ from even states and a possibly different transition rate $\mu$ from odd states. We determine the probability generating functions of the even…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We establish recurrence and transience criteria for critical branching processes in random environment with immigration. These results are then applied to discuss recurrence and transience of a recurrent random walk in a random environment…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…
Immigration can rescue local populations from extinction, helping to stabilise a metapopulation. Local population dynamics is important for determining the strength of this rescue effect, but the mechanistic link between local demographic…
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…
We study a dynamic model of ecosystems where immigration plays an essential role both in assembling the species community and in mantaining its biodiversity. This framework is particularly relevant for insular ecosystems. Population…
We study the escape behavior of a lamb to safe haven pursued by a hungry lion. Identifying the system with a pair of vicious Brownian walkers we evaluate the probability density function for the vicious pair and from there we estimate the…