Manipulating the diversity

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Chapter 5

• Manipulating the diversity

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Models of populations vs molecules

• Allele frequencies change over time- by chance
  (drift) by choice (selection).
• These changes can be investigated using models
  that approximate the reality.
• Understand the forces at play which explain these
  changes

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Models to derive equations

• These equations allow us to estimate parameters
  of interest from the data
• Population growth rate
• Migration rate between two populations
• Age of an allele

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Think of alleles as populations

• Think of alleles as populations- since this is
  what evolution acts upon.
• How is population defined
• Individuals grouped together for the sake of
  analysis
• Idealized group adhering to a certain
  mathematical model (I.e. random mating)
• Pratical population or theoretical population?

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Dominant (A) vs Recessive (a) Alleles

• Do dominant alleles become more frequent over
  time?
• No inherent tendency for dominant alleles to
  become more frequent or recessive ones to become
  less frequent
• Given certain assumptions, genotype and allele
  frequencies will remain constant from one
  generation to next
• Hardy-Weinberg Equilibrium

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Hardy-Weinberg Equilibrium Model

• Mathematical statement relating allele
  frequencies to expected genotype frequencies in
  the next generation
• 1 p2 2pq q2
• Where
• p frequency of the A allele
• q frequency of the a allele
• ? Model predicts that at equilibrium there is no
  change in allele frequency in a population over
  time

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Observed Changes ? Predictions

• ? one or more of the assumption of the model must
  be incorrect.
• ASSUMPTIONS
• Random mating
• No mutation
• No selection
• No gene flow
• No genetic drift

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Not in Equilibrium? Why?

• Observed vs expected genotype frequencies differ
  b/c of effects of evolutionary forces and/or
  nonrandom mating
• Four evolutionary forces are the only mechanisms
  that can cause frequency of an allele to change
  over time
• Nonrandom mating can cause genotype change
  without changing allele frequencies
• - inbreeding (biologically related individuals)
• - assortative mating (based on phenotype)

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In more depth.What changes allele frequencies

• Mutation pressure- random changes, polymorphisms
  could change frequencies by making new alleles.
• Even after 1000 generations a wild type gene
  would change from a frequency of 1.0 to 0.998.so
  not very much

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Models for mutational processes

• Infinite alleles model- each mutation generates a
  new allele not previously found in the
  population-
• Stepwise mutation model - for microsatellites

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Complex models of sequence evolution

• More realistic- as multiple mutations will happen
  at the same time across the genome. The question
  than becomes what is the probability that an A
  will change into a G or a C into a T and so on.

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Complex models neglect..

• Indels
• CpG hotspots
• Hotspots of mutation generally
• Sequence context

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Recombination

• Sexual reproduction- Provides advantageous
  alleles for populations to adapt to their
  environment.
• Asexual reproduction- accumulation of deleterious
  mutations leads to mullers ratchet- good example
  of this the Y chromosomes non-recombining region.

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Mullers ratchet
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Linkage Disequilibrium (LD)

• Non-random association between alleles in a
  population due to their tendency to be
  coinherited because of reduced recombination
  between them.
• The greater the distance between two alleles less
  likely they will remain associated with each
  other.
• LD occurs when alleles are found together more
  often than would be expected if alleles were
  segregating at random.
• LD is high when association is high
• LD is low when association breaks down
• Diversity is low within blocks and high between
  blocks

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Recombination in populations

• Consider A and B allele (a, b) with no
  association.
• Only factor determining whether we find them on
  the same haplotype is their relative frequencies.
  
• Frequency of AB A B
• If yes than the two loci are in Linkage
  equilibrium.
• The difference between the observed and expected
  frequencies of AB D.
• D 0 than Linkage equilibrium
• D gt 0 than Linkage disequilibrium

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Recombination and LD

• As time increases, D tends towards 0- less and
  less association of alleles.
• In infinitely large populations LD would continue
  to decay over time due to high frequency of
  recombination.
• Does this occur in most populations??? We will
  revist this later.

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Models of Recombination
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Eliminating diversityGenetic Drift

• No population is infinitely large as assumed in
  HW equilibrium. Each generation is a finite
  sample from the previous one. There is stochastic
  variation from one generation to the next
• Genetic drift the random change in allele
  frequency from one generation to the next because
  of basic probability.
• Allele frequencies may increase, decrease or stay
  the same all because of chance events.

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Simulations of drift

• Random process!
• Occurring in the population
• Hence allele frequencies will change from one
  generation to the next
• 100 generations, initial allele frequency of 0.5
  and 50 (25F 25M) individuals.

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50 individuals
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50 individuals
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50 individuals
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Wright-Fisher Model

• Simple idealized population model that helps
  describe the amount of drift populations of
  different sizes will have.
• Assumptions
• Population has constant size
• Equal sex ratios
• Non-overlapping generations
• Random mating
• Each individual has same probability of
  contributing to the next generation

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Effective Population Size (Ne)

• Effective population size- a quotient prepared
  by Sewall Wright to compare genetic drift
  experienced in different populations as they
  contrast with census population size.
• Wrights concept of Ne allows us to compare the
  amount of drift experienced by different
  population sizes.
• Difficult to relate Ne to Nc (Census size)

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What about genetic drift and population size

• Given enough time all alleles will tend to go
  towards fixation or extinction.
• Some will drift more, and others less
• 1 of the most important factors is POPULATION
  SIZE
• The smaller the population the greater the effect
  of drift.

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1000 Individuals
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1000 Individuals
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1000 Individuals
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Fixation or elimination of alleles

• t 4Ne
• t time to fixation
• Smaller Ne the quicker it will go to fixation or
  elimination.
• Lower mutation rate- the time to fixation is the
  same but the time between fixation of new alleles
  is greater

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Impact of Pop size on Ne

• Few populations are constant in size-The long
  term population size is harmonic mean of the
  pop size over time.
• Ne is disproportionately affected by smaller
  population sizes
• Recent human populations which have been
  expanding, Ne is determined by our small
  ancestral populations sizes (come back later to
  this)

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Expression
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Genetic Drift

• Genetic drift Change in the gene pool of a small
  population due to chance. Two examples
• Bottleneck effect
• Genetic drift (reduction of alleles in a
  population) resulting from a disaster that
  drastically reduces population size.
• Founder effect
• Genetic drift resulting from the colonization of
  a new location by a small number of individuals.
• Results in random change of the gene pool.

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Expression