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Related Concept Videos

Types of Selection01:46

Types of Selection

Natural selection influences the frequencies of particular alleles and phenotypes within populations in several different ways. Primarily, natural selection can be directional, stabilizing, or disruptive. Directional selection favors one extreme trait and shifts the population towards that phenotype while selecting against individuals displaying alternate traits. Stabilizing selection favors an intermediate trait with a narrow range of variation. Deviation from the optimal phenotype towards an...
Frequency-dependent Selection01:21

Frequency-dependent Selection

When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.Positive Frequency-Dependent SelectionIn positive...
Mutation, Gene Flow, and Genetic Drift01:09

Mutation, Gene Flow, and Genetic Drift

In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions of Hardy-Weinberg equilibrium can alter the genetic variation of a given population. Conditions that change the genetic variability of a population include mutations, natural selection, non-random mating, gene flow, and genetic drift (small population size).Mechanisms of Genetic VariationThe original sources of genetic variation are mutations,...
Genetics of Speciation02:16

Genetics of Speciation

Speciation is the evolutionary process resulting in the formation of new, distinct species—groups of reproductively isolated populations.The genetics of speciation involves the different traits or isolating mechanisms preventing gene exchange, leading to reproductive isolation. Reproductive isolation can be due to reproductive barriers that have effects either before or after the formation of a zygote. Pre-zygotic mechanisms prevent fertilization from occurring, and post-zygotic mechanisms...
Genetic Drift03:33

Genetic Drift

Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.Life is not fair. A deer grazing contentedly in a field can have her meal cut tragically short by a bolt of lightning. If the doomed doe is one of only three in the population, 1/3 of the population’s gene pool is lost. Random events like this can...
Speciation Rates01:07

Speciation Rates

Speciation can proceed at markedly different rates, and evolutionary biologists commonly describe these differences through the models of gradualism and punctuated equilibrium. Both patterns explain how new species arise, but they differ in the tempo and continuity of evolutionary change. In both cases, evolutionary change arises from heritable variation within populations, with natural selection often shaping traits that improve survival and reproduction under specific environmental conditions.

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Duality, ancestral and diffusion processes in models with selection.

Shuhei Mano1

  • 1Department of Statistics, University of Oxford, OX1 3TG, United Kingdom. mano@nsc.nagoya-cu.ac.jp

Theoretical Population Biology
|April 24, 2009
PubMed
Summary
This summary is machine-generated.

The ancestral selection graph models gene evolution with selection. This study derives its particle number distribution, linking allele fixation to the ancestral process reaching stability.

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Area of Science:

  • Population Genetics
  • Theoretical Biology
  • Mathematical Biology

Background:

  • The ancestral selection graph (ASG) models gene evolution under selection, analogous to the neutral coalescent.
  • The ASG's particle count follows a birth-death process with specific rates.

Purpose of the Study:

  • Derive an explicit probability distribution for the number of particles in the ASG.
  • Connect the ASG's behavior to allele frequency dynamics in diffusion models.
  • Analyze allele fixation times within the ASG framework.

Main Methods:

  • Utilized the allele frequency density from Kimura's diffusion model.
  • Applied mathematical analysis to the birth-death process of the ASG.
  • Investigated the convergence of the ancestral process to its stationary distribution.

Main Results:

  • Obtained an explicit probability distribution for the ASG particle number.
  • Demonstrated that allele fixation in diffusion models corresponds to the ASG reaching its stationary measure.
  • Characterized the conditional time to allele fixation using the ASG.

Conclusions:

  • The ASG provides a framework for understanding selection's impact on genetic genealogy.
  • The derived distribution offers insights into the stochastic behavior of selected genes.
  • This work links diffusion approximations to the ancestral process for analyzing fixation dynamics.