ESTIpop: a computational tool to simulate and estimate parameters for continuous-time Markov branching processes

Summary ESTIpop is an R package designed to simulate and estimate parameters for continuous-time Markov branching processes with constant or time-dependent rates, a common model for asexually reproducing cell populations. Analytical approaches to parameter estimation quickly become intractable in complex branching processes. In ESTIpop, parameter estimation is based on a likelihood function with respect to a time series of cell counts, approximated by the Central Limit Theorem for multitype branching processes. Additionally, simulation in ESTIpop via approximation can be performed many times faster than exact simulation methods with similar results. Availability and implementation ESTIpop is available as an R package on Github (https://github.com/michorlab/estipop). Supplementary information Supplementary data are available at Bioinformatics online.

An Algorithmic Approach to Modelling the Co-Evolution of Parasites and Their Hosts

This paper is a reformulation of the paper, Mode 1958 Evolution 12:158 - 165, which was written in terms of a deterministic paradigm, using di erential equations In this paper, however, the working paradigm will be stochastic, and from the mathematical point of view, it will be a stochastic process that may be viewed as a branching process within a branching process. In particular, it will be assumed that the population of host plants will evolve as a multitype branching process, and the pathogen, which grows on the leaves of the host in every generation of the host, will also be assumed to evolve as a multitype branching processes during each generation of the host. The contents of this paper, were motivated by problems in Agriculture in which Plant Pathologists and Plant Breeders work together to control the damage inflicted by a pathogen on a growing crop of a cultivar such as flax, wheat. and many other cultivars. The focus of attention in this paper is the development of algorithms that will guide the development of software to run Monte Carol simulation experiments taking into account mutations in the host and pathogen. The writing of software to implement the algorithms developed in this paper would require a major e ort, and is, therefore, beyond the scope of this paper

Multitype branching processes with inhomogeneous Poisson immigration

In this paper we introduce multitype branching processes with inhomogeneous Poisson immigration, and consider in detail the critical Markov case when the local intensity r(t) of the Poisson random measure is a regularly varying function. Various multitype limit distributions (conditional and unconditional) are obtained depending on the rate at which r(t) changes with time. The asymptotic behaviour of the first and second moments, and the probability of nonextinction are investigated.

Self-normalized large deviation for supercritical branching processes

We consider a supercritical branching process (Zn, n ≥ 0) with offspring distribution (pk, k ≥ 0) satisfying p0 = 0 and p1 > 0. By applying the self-normalized large deviation of Shao (1997) for independent and identically distributed random variables, we obtain the self-normalized large deviation for supercritical branching processes, which is the self-normalized version of the result obtained by Athreya (1994). The self-normalized large deviation can also be generalized to supercritical multitype branching processes.