Related papers: Time to MRCA for stationary CBI-processes
The study considers the model of an abstract organism, called Arbitrary Oscillator (ArbO), which is capable of making decisions at each timed step. These decisions are 'critical' since, randomly, their outcome can be 'fatal' for ArbO, thus…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent…
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…
We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We mainly rely on two concepts, namely, the killed ancestral selection graph and the pruned…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
We consider a general class of Markovian models describing the growth in a randomly fluctuating environment of a clonal biological population having several phenotypes related by stochastic switching. Phenotypes differ e.g. by the level of…
This paper presents how to use common random number (CRN) simulation to evaluate Markov chain Monte Carlo (MCMC) convergence to stationarity. We provide an upper bound on the Wasserstein distance of a Markov chain to its stationary…
To analyze and project age-specific mortality or morbidity rates age-period-cohort (APC) models are very popular. Bayesian approaches facilitate estimation and improve predictions by assigning smoothing priors to age, period and cohort…
The study begins by considering an abstract object (cellular automaton) able of moving -- by arbitrary decision -- between two given fixed positions. That is, at each clock step, it can change position or remain stationary in its current…
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic…
Monte Carlo algorithms simulate some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the…
Several demographic and health indicators, including the total fertility rate (TFR) and modern contraceptive use rate (mCPR), evolve similarly over time, characterized by a transition between stable states. Existing approaches for…
Consider the batch-arrival $GI^X/M/c/N$ model with $c$ servers, general inter-arrival batch times, finite buffer, and exponential service times. Inter-arrival batch times, batch sizes, and service times are $i.i.d.$ and independent of each…
Source-sink systems are metapopulations of habitat patches with different, and possibly temporally varying, habitat qualities, which are commonly used in ecology to study the fate of spatially extended natural populations. We propose new…
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 present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a…
We consider the problem of determining the arrival statistics of unbiased planar random walkers to complex target configurations. In contrast to problems posed in finite domains, simple moments of the distribution, such as the mean (MFPT)…