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 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 Haldane's Sieve and Adaptation From the Standing Genetic Variation

Genetics ◽  
2001 ◽  
Vol 157 (2) ◽  
pp. 875-884 ◽  
Author(s):  
H Allen Orr ◽  
Andrea J Betancourt
Keyword(s):  
Population Genetics ◽  
Genetic Variation ◽  
Environmental Change ◽  
Adaptive Evolution ◽  
Sex Expression ◽  
Background Selection ◽  
Beneficial Mutations ◽  
Deleterious Alleles ◽  
Molecular Population Genetics ◽  
New Mutations

Abstract We consider populations that adapt to a sudden environmental change by fixing alleles found at mutation-selection balance. In particular, we calculate probabilities of fixation for previously deleterious alleles, ignoring the input of new mutations. We find that “Haldane's sieve”—the bias against the establishment of recessive beneficial mutations—does not hold under these conditions. Instead probabilities of fixation are generally independent of dominance. We show that this result is robust to patterns of sex expression for both X-linked and autosomal loci. We further show that adaptive evolution is invariably slower at X-linked than autosomal loci when evolution begins from mutation-selection balance. This result differs from that obtained when adaptation uses new mutations, a finding that may have some bearing on recent attempts to distinguish between hitchhiking and background selection by contrasting the molecular population genetics of X-linked vs. autosomal loci. Last, we suggest a test to determine whether adaptation used new mutations or previously deleterious alleles from the standing genetic variation.

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.

scholarly journals Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation

2019 ◽  
Vol 3 (2) ◽  
pp. 14 ◽  
Author(s):  
Ndolane Sene ◽  
Aliou Niang Fall
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Generalized Fractional Derivative

In this paper, the approximate solutions of the fractional diffusion equations described by the fractional derivative operator were investigated. The homotopy perturbation Laplace transform method of getting the approximate solution was proposed. The Caputo generalized fractional derivative was used. The effects of the orders α and ρ in the diffusion processes was addressed. The graphical representations of the approximate solutions of the fractional diffusion equation and the fractional diffusion-reaction equation both described by the Caputo generalized fractional derivative were provided.

scholarly journals Cancer recurrence times from a branching process model

2019 ◽  
Vol 15 (11) ◽  
pp. e1007423 ◽  
Author(s):  
Stefano Avanzini ◽  
Tibor Antal
Keyword(s):  
Process Model ◽  
Branching Process ◽  
Cancer Recurrence ◽  
Recurrence Times

scholarly journals Evolutionary stalling and a limit on the power of natural selection to improve a cellular module

2020 ◽  
Vol 117 (31) ◽  
pp. 18582-18590 ◽  
Author(s):  
Sandeep Venkataram ◽  
Ross Monasky ◽  
Shohreh H. Sikaroodi ◽  
Sergey Kryazhimskiy ◽  
Betul Kacar
Keyword(s):  
Escherichia Coli ◽  
Natural Selection ◽  
Adaptive Evolution ◽  
Genetic Load ◽  
Performance Theory ◽  
Biological Functions ◽  
Beneficial Mutations ◽  
Translation Machinery ◽  
Adaptive Mutations ◽  
Organismal Fitness

Cells consist of molecular modules which perform vital biological functions. Cellular modules are key units of adaptive evolution because organismal fitness depends on their performance. Theory shows that in rapidly evolving populations, such as those of many microbes, adaptation is driven primarily by common beneficial mutations with large effects, while other mutations behave as if they are effectively neutral. As a consequence, if a module can be improved only by rare and/or weak beneficial mutations, its adaptive evolution would stall. However, such evolutionary stalling has not been empirically demonstrated, and it is unclear to what extent stalling may limit the power of natural selection to improve modules. Here we empirically characterize how natural selection improves the translation machinery (TM), an essential cellular module. We experimentally evolved populations ofEscherichia coliwith genetically perturbed TMs for 1,000 generations. Populations with severe TM defects initially adapted via mutations in the TM, but TM adaptation stalled within about 300 generations. We estimate that the genetic load in our populations incurred by residual TM defects ranges from 0.5 to 19%. Finally, we found evidence that both epistasis and the depletion of the pool of beneficial mutations contributed to evolutionary stalling. Our results suggest that cellular modules may not be fully optimized by natural selection despite the availability of adaptive mutations.

Analytical approximate solutions of the time-domain diffusion equation in layered slabs

2002 ◽  
Vol 19 (1) ◽  
pp. 71 ◽  
Author(s):  
Fabrizio Martelli ◽  
Angelo Sassaroli ◽  
Yukio Yamada ◽  
Giovanni Zaccanti
Keyword(s):  
Diffusion Equation ◽  
Time Domain ◽  
Approximate Solutions ◽  
The Time Domain

scholarly journals Hitchhiking and epistasis give rise to cohort dynamics in adapting populations

2017 ◽  
Vol 114 (31) ◽  
pp. 8330-8335 ◽  
Author(s):  
Sean W. Buskirk ◽  
Ryan Emily Peace ◽  
Gregory I. Lang
Keyword(s):  
Adaptive Evolution ◽  
Driving Force ◽  
Parallel Evolution ◽  
Low Frequency ◽  
Target Size ◽  
Driver Mutations ◽  
Beneficial Mutations ◽  
Large Target ◽  
Asexual Populations ◽  
Comprehensive Study

Beneficial mutations are the driving force of adaptive evolution. In asexual populations, the identification of beneficial alleles is confounded by the presence of genetically linked hitchhiker mutations. Parallel evolution experiments enable the recognition of common targets of selection; yet these targets are inherently enriched for genes of large target size and mutations of large effect. A comprehensive study of individual mutations is necessary to create a realistic picture of the evolutionarily significant spectrum of beneficial mutations. Here we use a bulk-segregant approach to identify the beneficial mutations across 11 lineages of experimentally evolved yeast populations. We report that nearly 80% of detected mutations have no discernible effects on fitness and less than 1% are deleterious. We determine the distribution of driver and hitchhiker mutations in 31 mutational cohorts, groups of mutations that arise synchronously from low frequency and track tightly with one another. Surprisingly, we find that one-third of cohorts lack identifiable driver mutations. In addition, we identify intracohort synergistic epistasis between alleles of hsl7 and kel1, which arose together in a low-frequency lineage.

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