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Results for “branching process”

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At least 19 recordsLinked to original sources
PubMed1977

Estimation for discrete time branching processes with application to epidemics.

Certain estimators for the mean of the offspring distribution of a Galton-Watson process are considered. The asymptotic behaviour of each of these estimators is studied when the true underlying model is in fact a multitype branching process or a branching process with a random environment. It is revealed which of the estimators remain consistent indicators of whether or not the process is subcritical, under these alternative underlying models. It is then indicated how this "robustness" result might influence the choice of an estimator by considering the problem of estimating the level of immunity required in a community in order to prevent major epidemics. The application is illustrated with references to smallpox using data from an outbreak in São Paulo, Brazil.

Disease Outbreaks↗
PubMed1976

A condition for the extinction of a branching process with an absorbing lower barrier.

A branching process with an absorbing lower barrier is considered. This is a Galton-Watson process with the condition that at any generation the number of individuals is greater than a lower barrier or it is equal to zero (i.e. all individuals in populations which are too small die and have no offspring). A necessary and sufficient condition is given for the process to become extinct with probability one. At the end of the paper there are three illustrating examples.

Models, Biological↗
PubMed1992

Survival probabilities for some multitype branching processes in genetics.

Consider a positively regular, slightly supercritical branching process with K types. An approximation to the probability of survival of a line descended from a single individual of type i has recently been derived by Hoppe. If K is large, however, this approximation may not be easy to compute. A further approximation that is easily computable is given. The result is used to estimate probabilities of survival of an allele A that is originally present in one male or one female in a large, random mating, age-structured population. Both autosomal and sex-linked loci are considered. Another application of the approximation is also discussed.

Alleles↗
PubMed1985

Branching process results in terms of moments of the generation-time distribution.

A number of simple formulae concerning the growth rate, doubling time, and age distribution of cell populations are in common usage. Many of these are invalid unless the generation times have no variation, a situation which occurs rarely. The correct formulae, which are available from the theory of age-dependent branching processes, are often ignored in the biological literature, perhaps due to their complexity. In this paper the major formulae from the theory of age-dependent branching processes are reorganised in terms of the mean, coefficient of variation, and skewness of the generation times. This leads to a greater insight into the theory and some simple formulae which account for the variability.

Analysis of Variance↗
PubMed1988

A branching process model for the evolution of transposable elements.

A discrete-time multitype branching process model is presented for the evolution of transposable elements in haploid populations. An individual is classified as type i if it possesses i copies of the TE, i greater than or equal to 0. The general model incorporates copy-dependent selection and transposition, and recursion relations are derived for the distribution of the number of individuals of the various types. The asymptotic relative proportions of individuals of the different types is studied in the neutral case. The behavior of this equilibrium distribution is examined for various patterns of regulated transposition and deletion.

Biological Evolution↗
PubMed1990

A biological and computational model of megakaryocyte development as a stochastic branching process.

The purpose of this paper is to describe a model of megakaryocytopoiesis as a branching process with stochastic processes regulating critical control points of differentiation along the stem cell megakaryocyte platelet axis. Progress of cells through these critical control points are regulated by transitional probabilities, which in turn are regulated by influences such as growth factors. The critical control points include transition of resting megakaryocytic stem cells (CFU-meg) into proliferating stem cells, the cessation of cytokinesis, and the cessation of DNA synthesis. A computerized computational method has been developed for directly fitting the stochastic branching model to colony growth data. The computational model has allowed transitional probabilities to be derived from colony size data. The model provides a unifying explanation for much of the heterogeneity of stages of maturation within populations of megakaryocytes and is fully compatible with historical data supporting the stochastic nature of hematopoietic stem cell regulation and with modern molecular concepts about control of the cell cycle.

Cell Differentiation↗
PubMed1986

On a stochastic integral of a branching process.

This paper is concerned with the properties of a stochastic integral which arises in the study of a modified Markov branching process. Explicit expressions are found for the mean and the limit distribution of the integral.

Animals↗
PubMed1992

Branching process with emigration--a genetic model.

Solution of a genetic improvement problem under the model of assortative mating is proposed. This has been achieved through the technique applied to a branching process incorporating a generation-dependent emigration component. The model explains a population subject to culling against genes governing undesirable characters and this work has been tried for a diploid population with two alleles at a single locus, which may be extended to the multilocus case.

Animals↗
PubMed1991

The dynamics of gene amplification described as a multitype compartmental model and as a branching process.

The present work is aimed at developing the mathematical tools by which the dynamics of gene amplification (GA) can be described in detail. Some discrete compartmental models of GA by disproportionate replication and a general model for other putative GA mechanisms are presented and analyzed. The dynamical distribution of gene copy number in the cell population is calculated with the loss of cells taken either as constant or as copy-number-dependent. Our analysis shows that for a one-copy GA process with constant loss of cells, the relative frequency of single-gene-copy cells (sensitive cells) converges to zero, with the rate of convergence depending on the amplification probability. In contrast, for a one-copy GA process with copy-number-dependent loss of cells, the relative frequency of single-copy cells is bounded, implying a bounded compartment of many-gene-copy cells. Using branching processes theory we calculate the dynamical distribution of the single-gene-copy compartment as well as its extinction probability. Our models are used for estimating treatment prognosis as affected by drug resistance due to GA, showing significant differences in prognosis resulting from small changes in drug dose.

Animals↗
PubMed1992

A branching process model of gene amplification following chromosome breakage.

We have devised a mathematical model of gene amplification utilizing recent experimental observations concerning dihydrofolate reductase (DHFR) gene amplification in CHO cells. The mathematical model, based on a biological model which proposes that acentric elements are the initial intermediates in gene amplification, includes the following features: (1) initiation of amplification by chromosomal breakage to produce an acentric structure; (2) replication of acentric DNA, once per cell cycle; (3) dissociation of replicated acentric DNA; (4) unequal segregation of acentric DNA fragments to daughter cells at mitosis; (5) subsequent reintegration of acentric fragments into chromosomes. These processes are assumed to be independent for each element present in a cell at a given time. Thus, processes of unequal segregation and integration may occur in parallel, not necessarily in a unique sequence, and may be reiterated in one or multiple cell cycles. These events are described mathematically as a Galton-Watson branching process with denumerable infinity of object types. This mathematical model qualitatively and quantitatively reproduces the major elements of the dynamical behavior of DHFR genes observed experimentally. The agreement between the mathematical model and the experimental data lends credence to the biological model proposed by Windle et al. (1991), including the importance of chromosome breakage and subsequent gene deletion resulting from resection of the broken chromosome ends as initial events in gene amplification.

Animals↗
PubMed2025

Bayesian inference of fitness landscapes via tree-structured branching processes.

MOTIVATION: The complex dynamics of cancer evolution, driven by mutation and selection, underlies the molecular heterogeneity observed in tumors. The evolutionary histories of tumors of different patients can be encoded as mutation trees and reconstructed in high resolution from single-cell sequencing data, offering crucial insights for studying fitness effects of and epistasis among mutations. Existing models, however, either fail to separate mutation and selection or neglect the evolutionary histories encoded by the tumor phylogenetic trees. RESULTS: We introduce FiTree, a tree-structured multi-type branching process model with epistatic fitness parameterization and a Bayesian inference scheme to learn fitness landscapes from single-cell tumor mutation trees. Through simulations, we demonstrate that FiTree outperforms state-of-the-art methods in inferring the fitness landscape underlying tumor evolution. Applying FiTree to a single-cell acute myeloid leukemia dataset, we identify epistatic fitness effects consistent with known biological findings and quantify uncertainty in predicting future mutational events. The new model unifies probabilistic graphical models of cancer progression with population genetics, offering a principled framework for understanding tumor evolution and informing therapeutic strategies. AVAILABILITY AND IMPLEMENTATION: The Python package FiTree and the analysis workflows are available at https://github.com/cbg-ethz/FiTree.

Bayes Theorem↗
PubMed1991

A branching-process model for the evolution of transposable elements incorporating selection.

We have formulated a very general mathematical model to analyze the evolution of transposable genetic elements in prokaryotic populations. Transposable genetic elements are DNA sequences able to replicate and insert copies of themselves at new locations in the genome. This work characterizes the equilibrium distribution of copy number under the influence of copy number-dependent selection, transposition and deletion. Our principal results concern the equilibrium distribution of copy number in response to various selective regimes. For particular transposition patterns (e.g., unregulated transposition or copy number-dependent transposition), equilibrium distributions are calculated numerically for a variety of specific selection patterns. Selection is quantified through specification of the expected number of offspring for individuals of each type, which is generally a non-increasing function of copy number, in accord with the usual evolutionary speculations.

Animals↗
PubMed1987

Inference for an age-dependent, multitype branching-process model of mast cells.

We consider an age-dependent, multitype model for the growth of mast cells in culture. After a colony of cells is established by an initiator type, the two possible types of cells are resting and proliferative. Using novel inferential procedures, we estimate the generation-time distribution and the offspring distribution of proliferative cells, and the waiting-time distribution of resting cells.

Animals↗