PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “branching process”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

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

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↗
PubMed1978

[Mathematical model of epidemiology of an anthropozoonose: brucellosis (author's transl)].

We are trying to make a model of the epidemiology of Brucellosis by using a two-type branching process. In this text, we are studying the probability of extinction. A complete study on the theory of process with a finite number of types was made by SEVAST'YANOV (1951) [6]. The study of the behaviour of such a process is made with the help of the generating function of the number of infected animals by a single animal. To express this generating function, we start with the same hypothesis as BARTOSZYNSKI [2] (1965) when he makes an interhuman epidemic model by a simple branching process of GALTON-WATSON. However these hypothesis will be modified in order to adapt them to the types of Brucellosis contamination.

Animals↗
PubMed1979

Fission models of population variability.

Most models in population genetics are models of allele frequency, making implicit or explicit assumptions of equilibrium or constant population size. In recent papers, we have attempted to develop more appropriate models for the analysis of rare variant data in South American Indian tribes; these are branching process models for the total number of replicates of a variant allele. The spatial distribution of a variant may convey information about its history and characteristics, and this paper extends previous models to take this factor into consideration. A model of fission into subdivisions is superimposed on the previous branching process, and variation between subdivisions is considered. The case where fission is nonrandom and the locations of like alleles are initially positively associated, as would happen were a tribal cluster or village to split on familial lines, is also analyzed. The statistics developed are applied to Yanomama Indian data on rare genetic variants. Due to insufficient time depth, no definitive new inferences can be drawn, but the analysis shows that this model provides results consistent with previous conclusions, and demonstrates the general type of question that may be answered by the approach taken here. In particular, striking confirmation of a higher-than-average growth rate, and hence smaller-than-previously-estimated age, is obtained for the Yan2 serum albumen variant.

Biological Evolution↗
PubMed1979

Morphology of dissociated hippocampal cultures from fetal mice.

Dissociated hippocampal cultures from fetal mice (13--18 days gestational age) can be maintained for up to two months in culture. Cells grow as either isolated neurons or in small neuronal aggregates. Neurons remain small with a soma diameter of 15--20 micrometer even in mature cultures and develop extensively branched processes during the first two weeks in culture. After this time, processes become more difficult to visualize with phase-contrast optics because of a tendency to grow within the underlying non-neuronal cells. However, the presence of processes has been proved by silver-staining which demonstrates an organizational complexity ranging from a loosely reticulated neuropil to fascicles containing many fibers. More detailed study of individual neuronal morphology was carried out in cells filled with the fluorescent dye, Lucifer Yellow CH, in conjunction with the intracellular recording of synaptic and action potentials from dye-containing micropipettes. Dye-filled cells show a well-developed branching morphology. Process specializations include spines, beading, and basket-like endings. Processes tend to emanate from one side of the soma, either originating at the cell body or from a single trunk. Commonly there are 2--4 orders of branching, but up to 6 orders can occur (counted centrifugally from the soma). Electron microscopy revealed synapses distributed predominantly on dendrites with a smaller number on somata. Dendritic spines are present and are contacted principally by asymmetric synaptic junctions. Symmetric synapses are relatively more common on somata and proximal dendrites.

Action Potentials↗
PubMed2025

Estimation of demography and mutation rates from one million haploid genomes.

As genetic sequencing costs have plummeted, datasets with sizes previously unthinkable have begun to appear. Such datasets present opportunities to learn about evolutionary history, particularly via rare alleles that record the very recent past. However, beyond the computational challenges inherent in the analysis of many large-scale datasets, large population-genetic datasets present theoretical problems. In particular, the majority of population-genetic tools require the assumption that each mutant allele in the sample is the result of a single mutation (the "infinite-sites" assumption), which is violated in large samples. Here, we present DR EVIL, a method for estimating mutation rates and recent demographic history from very large samples. DR EVIL avoids the infinite-sites assumption by using a diffusion approximation to a branching-process model with recurrent mutation. This approach results in tractable likelihoods that are accurate for rare alleles. We show that DR EVIL performs well in simulations and apply it to rare-variant data from one million haploid samples. We identify mutation-rate heterogeneity even after accounting for trinucleotide context and methylation status. We also predict that at modern sample sizes, the alleles at most polymorphic sites with high mutation rates represent the descendants of multiple mutation events.

Haploidy↗
PubMed1978

Genetic and evolutionary fitness.

The advantages and disadvantages of evolutionary fitness (probability that a single mutant line will not become extinct) and genetic fitness (mean fecundity) are compared. For deterministic processes the two are equivalent, but for stochastic branching processes they may be totally unrelated except that an absolute genetic fitness of unity or less implies an evolutionary fitness of zero. To know the variance as well as the mean family size does not in general uniquely determine the evolutionary fitness. Except where genetic fitness is close to unity, the impact of selection is shown to be rapid for the binomial, Poisson, negative binomial, and truncated negative binomial distributions. Evolutionary fitness, though somewhat cumbersome, has greater relevance to evolution, genetic counseling, and voluntary population control; but genetic fitness which is much easier to handle is the more appropriate measure where a large number of mutants is involved. Some empirical data on the transmission of various types of characters from parent to child are analyzed to allow comparison of genetic fitness, Crow's index, and a Malthusian parameter, with evolutionary fitness. There is a fair, but far from perfect, agreement among them. Multiple correlation of evolutionary fitness with mean and variance of family size taken jointly suggests a much more satisfactory approximation. It thus appears that, at the least, the population geneticist cannot afford to ignore the variance (which is not adequately represented in Crow's index). These relationships, based on two sets of data only may be accidental and should be invoked with caution. It seems more than likely that other aspects of the distribution of family size (eg, even higher moments) may contain relevant information in certain cases.

Biological Evolution↗
PubMed1978

A numerical method to model excitable cells.

We have extended a fast, stable, and accurate method for the numerical solution of cable equations to include changes in geometry and membrane properties in order to model a single excitable cell realistically. In addition, by including the provision that the radius may be a function of distance along an axis, we have achieved a general and powerful method for simulating a cell with any number of branched processes, any or all of which may be nonuniform in diameter, and with no restriction on the branching pattern.

Action Potentials↗
PubMed1976

Fine structure of the epidermis of the optic tentacle in a slug, Limax flavus L.

The epidermis at the tip of the optic tentacle in Limax flavus is constructed of columnar epithelial cells, distal processes of nerve cells, and scattered processes of the collar cells. The epithelial cells extend stout microvilli called plasmatic processes by Wright perpendicularly from the free surface. Each plasmic process branches into a few terminal twigs embedded in a fuzzy filamentous substance. Most nerve cells have their nuclei under the basal lamina. The distal processes of these nerve cells reach the free surface and send long microvilli to form the spongy layer under a filamentous covering. At the side surface of the tentacle the epithelial cells are cuboidal or squamous and the neural elements are fewer. Here, no spongy layer is formed; and the collar cell processes are replaced by the lateral cell processes. Peculiar secretion granules are contained in the lateral and collar cell processes as well as in their cell bodies situated beneath the basal lamina.

Animals↗
PubMed1976

The pig synovium. I. The intact synovium in vivo and in organ culture.

1. The normal synovium of the metacarpophalangeal joints of young pigs was examined by light and electron microscopy with special reference to the superficial layer (intima). 2. Cells of the macrophage-like or A-type (Barland et al. 1962) constituted only a small proportion of the intimal synoviocytes; the majority were of the intermediate and B-types. 3. Synovial villi were explanted on Millipore filters and maintained as organ cultures. The intimal cells in contact with the Millipore formed long branched processes which penetrated deeply into the substrate; these cells, which had a very well-developed endoplasmic reticulum, resembled those of the B-type. The synoviocytes at the upper (free) surface of the villus withdrew their long processes, acquired lamelliform pseudopodia, and their endoplasmic reticulum regressed; they were similar in appearance to the A-type. 4. In the organ cultures the highly branched cells (B-type) next to the Millipore were less phagocytic than the rounded cells (A-type) at the free surface of the villus.

Animals↗
PubMed1978

[Labeled mitosis curve in the presence of different states of cell proliferation kinetics. IV. Additional remarks on the method of a posteriori modeling].

Using the conditional probability density function of phase duration--h (a, t), defined for a cell just completing a given phase of the mitotic cycle at the moment t it is possible to construct a mathematical description of the fraction labeled mitoses curve. The function h (a, t) defined for any separate phase can be described by means of a certain mathematical expression which is applicable even in the presence of transient processes in cell kinetics and serves as an appropriate generalization of the same result from the theory of exponentially growing cell populations (the model of age-dependent branching process). When the sum of r successive phases with stochastically dependent durations is under consideration and the age of a cell is measured from the start of phase r, it is necessary to find out the expression for the function hr (ar, t). The derivation of such an expression is given.

Cytological Techniques↗