Lecture 9: Introduction to Genetic Drift

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Lecture 9 Introduction to Genetic Drift
September 25, 2015
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Last Time

• Overdominance and Underdominance
• Overview of advanced topics in selection
• Introduction to Genetic Drift

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Today

• First in-class simulation of population genetics
  processes drift
• Fisher-Wright model of genetic drift

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What Controls Genetic Diversity Within
Populations?
4 major evolutionary forces
Diversity
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Genetic Drift

• Relaxing another assumption infinite populations
• Genetic drift is a consequence of having small
  populations
• Definition chance changes in allele frequency
  that result from the sampling of gametes from
  generation to generation in a finite population
• Assume (for now) Hardy-Weinberg conditions
• Random mating
• No selection, mutation, or gene flow

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Drift Simulation

• Pick 1 red and 3 other mms so that all 4 have
  different colors
• Form two diploid genotypes as you wish
• Flip a coin to make 2 offspring
• Draw allele from Parent 1 if heads get
  another mm with the same color as the left
  allele, if tails get one with the color of
  the right allele
• Draw allele from Parent 2 in the same way
• Mate offspring and repeat for 3 more
  generations
• Report frequency of red allele in last
  generation

Parent 1
Parent 2
m
m
m
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Genetic Drift

• A sampling problem some alleles lost by random
  chance due to sampling "error" during reproduction

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Simple Model of Genetic Drift

• Many independent subpopulations
• Subpopulations are of constant size
• Random mating within subpopulations

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Key Points about Genetic Drift

• Effects within subpopulations vs effects in
  overall population (combining subpopulations)
• Average outcome of drift within subpopulations
  depends on initial allele frequencies
• Drift affects the efficiency of selection
• Drift is one of the primary driving forces in
  evolution

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Effects of Drift

• Simulation of 4 subpopulations with 20
  individuals, 2 alleles

• Random changes through time
• Fixation or loss of alleles
• Little change in mean frequency
• Increased variance among subpopulations

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How Does Drift Affect the Variance of Allele
Frequencies Within Subpopulations?
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Drift Strongest in Small Populations
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Effects of Drift
http//www.cas.vanderbilt.edu/bsci111b/drosophila/
flies-eyes-phenotypes.jpg

• Buri (1956) followed change in eye color allele
  (bw75)
• Codominant, neutral
• 107 populations
• 16 flies per subpopulation
• Followed for 19 generations

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Modeling Drift as a Markov Chain

• Like the m m simulation, but analytical rather
  than empirical
• Simulate large number of populations with two
  diploid individuals, p0.5
• Simulate transition to next generation based on
  binomial sampling probability (see text and lab
  manual)

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Modeled versus Observed Drift in Buris Flies
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Effects of Drift Across Subpopulations

• Frequency of eye color allele did not change much
• Variance among subpopulations increased markedly

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Fixation or Loss of Alleles

• Once an allele is lost or fixed, the population
  does not change (what are the assumptions?)
• This is called an absorbing state
• Long-term consequences for genetic diversity

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Probability of Fixation of an allele within a
subpopulation Depends upon Initial Allele
Frequency
where u(q) is probability of a subpopulation to
be fixed for allele A2
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Effects of Drift on Heterozygosity

• Can think of genetic drift as random selection of
  alleles from a group of FINITE populations
• Example One locus and two alleles in a forest of
  20 trees determines color of fruit
• Probability of homozygotes for alleles IBD in
  next generation?

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Drift and Heterozygosity

• Expressing previous equation in terms of
  heterozygosity

p and q are stable through time across
subpopulations, so 2pq is the same on both sides
of equation cancels

• Heterozygosity declines over time in
  subpopulations
• Change is inversely proportional to population
  size

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Diffusion Approximation

• Greatly simplifies the problem of simulating
  drift
• Readily extended to incorporate other factors

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Time for an Allele to Become Fixed

• Using the Diffusion Approximation to model drift
• Assume random walk of allele frequencies
  behaves like directional diffusion heat through
  a metal rod
• Yields simple and intuitive equation for
  predicting time to fixation

• Time to fixation is linear function of population
  size and inversely associated with allele
  frequency

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Time for a New Mutant to Become Fixed

• Assume new mutant occurs at frequency of 1/2N
• ln(1-p) -p for small p
• 1-p 1 for small p

• Expected time to fixation for a new mutant is 4
  times the population size!

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Effects of Drift

• Within subpopulations
• Changes allele frequencies
• Degrades diversity
• Reduces variance of allele frequencies (makes
  frequencies more unequal)
• Does not cause deviations from HWE
• Among subpopulations (if there are many)
• Does NOT change allele frequencies
• Does NOT degrade diversity
• Increases variance in allele frequencies
• Causes a deficiency of heterozygotes compared to
  Hardy-Weinberg expectations (if the existence of
  subpopulations is ignored Wahlund Effect)