A discrete-time, multi-type generational inheritance branching process model of cell proliferation

1996 ◽  
Vol 137 (1) ◽  
pp. 25-50 ◽  
Author(s):  
David N. Stivers ◽  
Marek Kimmel ◽  
David E. Axelrod
Keyword(s):  
Cell Proliferation ◽  
Discrete Time ◽  
Process Model ◽  
Branching Process

scholarly journals A Branching Process Model of Evolutionary Rescue

2021 ◽  
Author(s):  
Peter Olofsson ◽  
Ricardo B. R. Azevedo
Keyword(s):  
Population Growth ◽  
Mutation Rate ◽  
Discrete Time ◽  
Growth Curve ◽  
Process Model ◽  
Branching Process ◽  
Selective Advantage ◽  
Population Declines ◽  
Beneficial Mutations ◽  
Evolutionary Rescue

Evolutionary rescue is the process whereby a declining population may start growing again, thus avoiding extinction, via an increase in the frequency of beneficial genotypes. These genotypes may either already be present in the population in small numbers, or arise by mutation as the population declines. We present a simple two-type discrete-time branching process model and use it to obtain results such as the probability of rescue, the shape of the population growth curve of a rescued population, and the time until the first rescuing mutation occurs. Comparisons are made to existing results in the literature in cases where both the mutation rate and the selective advantage of the beneficial mutations are small.

scholarly journals The Probability of Fixation in Populations of Changing Size

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 723-733 ◽  
Author(s):  
Sarah P Otto ◽  
Michael C Whitlock
Keyword(s):  
Diffusion Equation ◽  
Adaptive Evolution ◽  
Process Model ◽  
Branching Process ◽  
Approximate Solutions ◽  
Logistic Growth ◽  
Beneficial Mutations ◽  
Demographic Models ◽  
Deleterious Alleles ◽  
Probability Of Fixation

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

scholarly journals A branching process model for the analysis of abortive colony size distributions in carbon ion-irradiated normal human fibroblasts

2014 ◽  
Vol 55 (3) ◽  
pp. 423-431 ◽  
Author(s):  
T. Sakashita ◽  
N. Hamada ◽  
I. Kawaguchi ◽  
T. Hara ◽  
Y. Kobayashi ◽  
...  
Keyword(s):  
Colony Size ◽  
Process Model ◽  
Branching Process ◽  
Human Fibroblasts ◽  
Size Distributions ◽  
Carbon Ion ◽  
Normal Human

scholarly journals Simulating the impact of vaccination rates on the initial stages of a COVID-19 outbreak in New Zealand (Aotearoa) with a stochastic model

2021 ◽  
Author(s):  
Leighton M Watson
Keyword(s):  
New Zealand ◽  
Stochastic Model ◽  
Process Model ◽  
Branching Process ◽  
Total Population ◽  
Median Number ◽  
Vaccination Rate ◽  
Vaccination Rates ◽  
The Impact ◽  
Different Levels

Aim: The August 2021 COVID-19 outbreak in Auckland has caused the New Zealand government to transition from an elimination strategy to suppression, which relies heavily on high vaccination rates in the population. As restrictions are eased and as COVID-19 leaks through the Auckland boundary, there is a need to understand how different levels of vaccination will impact the initial stages of COVID-19 outbreaks that are seeded around the country. Method: A stochastic branching process model is used to simulate the initial spread of a COVID-19 outbreak for different vaccination rates. Results: High vaccination rates are effective at minimizing the number of infections and hospitalizations. Increasing vaccination rates from 20% (approximate value at the start of the August 2021 outbreak) to 80% (approximate proposed target) of the total population can reduce the median number of infections that occur within the first four weeks of an outbreak from 1011 to 14 (25th and 75th quantiles of 545-1602 and 2-32 for V=20% and V=80%, respectively). As the vaccination rate increases, the number of breakthrough infections (infections in fully vaccinated individuals) and hospitalizations of vaccinated individuals increases. Unvaccinated individuals, however, are 3.3x more likely to be infected with COVID-19 and 25x more likely to be hospitalized. Conclusion: This work demonstrates the importance of vaccination in protecting individuals from COVID-19, preventing high caseloads, and minimizing the number of hospitalizations and hence limiting the pressure on the healthcare system.

Multitype processes with reproduction-dependent immigration

1998 ◽  
Vol 35 (02) ◽  
pp. 281-292
Author(s):  
Ibrahim Rahimov
Keyword(s):  
Limit Theorem ◽  
Discrete Time ◽  
Branching Process ◽  
Martingale Approach ◽  
Offspring Distribution ◽  
Second Moments ◽  
Branching Process With Immigration

The multitype discrete time indecomposable branching process with immigration is considered. Using a martingale approach a limit theorem is proved for such processes when the totality of immigrating individuals at a given time depends on evolution of the processes generating by previously immigrated individuals. Corollaries of the limit theorem are obtained for the cases of finite and infinite second moments of offspring distribution in critical processes.

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