Drift leads to fixation at all loci

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Drift leads to fixation at all loci

• If genetic drift is the only force operating
  within a population, all loci will eventually
  become fixed for a single allele. This means
  there is no genetic variation left within such a
  population.

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Consequences of Drift
In a population, size N, a new mutation has a
frequency 1/2N probability of that it will
eventually become fixed. So, a new mutation has
a higher probability of fixation in a small
population. If the same mutation arises in many
populations of size N, it will become fixed in
1/2N of them. Of all the new mutations that ari
se in a single generation, 1/2N of them will
become fixed. Over time, all genes will become
fixed for one allele. Therefore, both
heterozygosity and polymorphism go to zero,
although Within a generation, genotypes are i
n approximate Hardy-Weinberg proportions.
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Drift usually occurs faster than in simulations
because simulations assume

• Equal numbers males
• and females
• If there are 200 females, but only 50 males that
  contribute to the next generation as in fig
  wasps, then the population has a census size of
  250, but it will undergo drift as if it had a
  census size of Ne4NfNm/NfNm 160.

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Drift actually occurs faster than in simulations
because simulations assume

• Constant population size
• If the population size varies across generations,
  then a population that has a census size of Ni,
  over n generations, will undergo drift as if it
  had a census size of

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Example

• N1 100,000
• N2 100
• N3 100,000

Ne much closer to the smallest Ni
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Drift actually occurs faster than in simulations
because simulations assume

• No selection
• If there is greater than random variation in
  reproductive success, then

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Red Deer (Cervus elaphus)

• 35 females, Vf9
• 33 males, Vm42
• Ne?

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Effective size of a population is typically much
less than the census size
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In small populations, both genetic drift and
inbreeding contribute to loss of genetic
variation

• All individuals will be related if small size
  persists for many generations.
  
• There will be loss of alleles and loss of
  heterozygosity.

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Florida panther, Felis concolor coryi
By the 1980s only 30-50 adults remained in the
population. Congenital heart defects, poor sper
m quality, and high incidence of cryptorchidism,
and kinked tail, are possible consequences of
inbreeding (Roelke 1991 Dunbar 1993).
Isolated from other subspecies of cougar for at
least 100 years.
Range contraction.
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Drift removes genetic variation
Factors slowing loss of variation by drift

• Large population size
• Migration between subpopulations
• Mutation
• Balancing natural selection (frequency-dependent
  selection, heterozygote advantage, varying
  selection pressure.

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Population Differentiation
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Genetic drift causes populations to diverge
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Consider this a metapopulation

• What are the allele frequencies at Gen. 19?
• What are the genotype frequencies?
• Would you observe deviations from H-W genotypic
  proportions?

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Changes in Heterozygosity caused by Drift

• If a metapopulation is divided into
  subpopulations, subpopulations will undergo drift
  and alleles tend to become fixed
  
• HE2pq, as p or q -- 0, HE--0
• Across the whole metapopulation, there are fewer
  heterozygotes thatn there would be in a single,
  panmictic (all interbreeding) population of the
  same size.

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Measures of population differentiation

• Sewall Wright one of the founders of population
  genetics, born in Illinois, got a Masters degree
  at Univ. Illinois, and spent most of his career
  as a professor at the University of Chicago.
• Invented F Statistics to understand the genetic
  effects of population structure.
  
• Note These are not the same as the F ratio
  used in the statistical procedure called Analysis
  of Variance.

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Measures of heterozygosity needed for F statistics

• HI observed heterozygosity (proportion
  heterozygotes) within a subpopulation.
  
• HS expected heterozygosity within a
  subpopulation. If there are i different alleles
  at a locus in a subpopulation, pi is the
  frequency of the ith allele
• HT expected heterozygosity if there was random
  mating across the entire metapopulation.
  
• average frequency of the ith allele
  across all subpopulations

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F statistics

• FST is the statistic that tells us how
  differentiated the subpopulations are. Formally,
  FST tells us if there is a deficit of
  heterozygosity in the metapopulation, due to
  differentiation among subpopulations
• Bars mean that the values are the averages over
  all the subpopulations that we are considering.

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F statistics

• FIS tells us if there is inbreeding within
  subpopulations by comparing HI and HS
  
• Bars mean that the values are the averages over
  all the subpopulations that we are considering.
  
  
• So FIS measures whether there is, on average, a
  deficit of heterozygotes within subpopulations.

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F statistics

• FIT tells us how much population structure has
  affected the average heterozygosity of
  individuals within the population
  
• Also (1-FIS) (1-FST) (1-FIT).

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Two Structured Populations
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Intuitive meaning of FST

• The proportion of total genetic variation that is
  distributed among subpopulations, rather than
  within subpopulations.

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Metapopulation structure Drift within
populations, migration between populations
p0.7 N15
m.07
m.02
p0.4 N70
p0.6 N50
m.01
p0.3 N10
p0.5 N150
p1.0 N20
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Drift and migration have opposite effects

• Drift makes subpopulations differerent
• Migration homogenizes subpopulations

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Population differentiation under migration and
drift

• If Ne and m are small, FST is large
• If Nem
• FST 0.2
• If there is 1 migrant per generation,
  populations do not diverge much.

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Useful for estimating gene flow

• If you know FST and Ne, you can calculate m