Related papers: Population processes sampled at random times
We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
We consider a bivariate first hitting-time model in which durations are the crossing times of dependent compound Poisson processes with fixed thresholds. The identifiability of the model is discussed, and likelihood estimators of the model…
The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
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 consider a continuous time Markov process on $\mathbb{N}_0$ which can be interpreted as generalized alternating birth-death process in a non-autonomous random environment. Depending on the status of the environment the process either…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the…
Motivated by the study of a parasite infection in a cell line, we introduce a general class of Markov processes for the modelling of population dynamics. The population process evolves as a diffusion with positive jumps whose rate is 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…
The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\lambda$ and leaves can…
For birth-and-death processes, we show that every initial distribution is reproduced from the first hitting time distribution. The reproduction is done by applying to the distribution function a differential operator defined through the…
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered:…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…