Related papers: Population processes sampled at random times
We examine what happens in a population when it experiences an abrupt change in surrounding conditions. Several cases of such "abrupt transitions" for both physical and living social systems are analyzed from which it can be seen that all…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
We consider continuous space-time decay-surge population models which are semi- stochastic processes for which deterministically declining populations, bound to fade away, are rein- vigorated at random times by bursts or surges of random…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…
Consider a supercritical birth and death process where the children acquire mutations. We study the mutation rates along the ancestral lineages in a sample of size $n$ from the population at time $T$. The mutation rate is time-inhomogenous…
Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
We investigate the scaling properties of products of the exponential of birth--death processes with certain given marginal discrete distributions and covariance structures. The conditions on the mean, variance and covariance functions of…
Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival…
Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
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…
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…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…