Population Genetics

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Population Genetics
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Topics

• Neutral variation
• Mutation
• Hardy-Weinberg and Wahlund effect
• Allele frequency change over time
• Effects of population size and structure
• Isolation and Fst
• Migration
• Recombination

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Topics

• Selection
• Types of selection
• Rate of change
• Interplay with other forces
• Special focus
• Linkage disequilibrium

Kent Holsingers lecture notes http//darwin.eeb.u
conn.edu/eeb348/lecture-notes/notes.html
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Questions to answer

• How are alleles distributed over genotypes?
• How long before a new mutation has reached
  fixation?
• How old are markers and disease mutations
• How do populations diverge?
• with or without selection
• Why does selection not remove deleterious
  alleles?
• How does LD arise and break down?

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Hardy-Weinberg law
Godfrey Hardy(1877-1947)

• Under certain conditions
• Allele frequencies are constant
• Genotype freqs are constant
• Genotypes follow standard distribution

Wilhelm Weinberg(1862-1937)
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H-W conditions

• mutation is not occurring
• natural selection is not occurring
• the population is infinitely large
• all mating is totally random
• there is no migration in or out of the population

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How it works
male genotypes
female genotypes
eggs
sperm
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(No Transcript)
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Do the next step yourself

• assume 5050 sex ratio

set p(a)male and p(a)female
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Results
male genotypes
female genotypes
p p(a)male p(a)female q1-p
After disturbance, HWE re-establishes in one
generation Under HWE conditions, genotype
distributions are identical across generations If
HWE is not found, a condition is violated
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No equilibrium

• Genotyping errors!
• Including CNVs
• Sampling errors
• Selection
• Non-random mating

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If aa mates with aa and AA with AA No aA
appears heterozygote deficit
If two sub-populations differ in allele freq. And
mate only among themselves Heterozygote deficit
occurs Wahlund effect Used to detect structure
aa
AA
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Allele frequency changeby random genetic drift
Each parent produces many gametes Gametes are
identical copies from parent 2N gametes at random
form next generation

Allele frequencies change from one generation to
next Fixation is inevitable Probability that a
specific allele gets fixed current
frequency There is no memory
Holsinger notes
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a word about time p new 1/2N tavg4Ne Ne(human)
?10,000 Generation time 20 years Origin of allele
that gets fixed 200 Kya Before origin of modern
human
2N20
2N100
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Population divergence by random genetic drift
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Figure 2 Genome-wide distribution of FST
Genome-wide distribution of FST. Solid bars show
the observed distribution of FST for
25,549 autosomal SNPs. The X chromosome was not
included in this analysis because it has a
different effective population size compared with
that of autosomal markers. Lightly shaded bars
represent the simulated distribution of FST. The
inset figure shows the observed and simulated
distributions of FST for values 0.5. Joshua M.
Akey et al. Genome Res. 2002 12 1805-1814
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Rate of neutral substitution
Neutral Per site mutation rate µ Nr of sites in
diploid population 2N Probability of fixation
p0 1/2N Per population fixation rate µ 2N
1/(2N) µ Every generation the same On average
(!) each neutral site will have changed after 1/
µ generations µ 10-8
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Summary neutral evolution

• Effects of mutation are slow
• between-species comparisons
• Effects of drift are rather slow
• Except in small populations

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Conservation

• Everything changes
• If not, mutations are probably deleterious, so
  carriers do not reproduce
• Similarity across species conservation

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UCSC browser Homo sapiens alpha one globin
(HBA1) Some parts of the protein seem more
important than other parts
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Directional Selection
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Modes of selection
More examples?
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Allele frequency change
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Finite populations
Probability of beneficial mutation to get fixed
In humans, weakly beneficial mutations are
invisible to selection
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Finite populations
Fixation prob. of deleterious mutation (p0.001)
Probability of deleterious mutation to get
fixed (s lt 0)
In humans, weakly deleterious mutations are
invisible to selection. Especially in small
isolated populations
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Effective population size

• Size of an ideal population which acts the same
  as the real population in question
• Ideal
• 11 sex ratio among breeders
• no selection
• constant population size
• Random distribution of offspring numbers
• Random mating
• Small size in the past reduces current Ne almost
  like geometric mean
• Human Ne estimated as 10,000
• Except for isolates

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Population size

• Some processes depend on
• Census size (6 billion)
• Some processes depend on
• Effective size (10,000 or locally smaller)

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Population genetics

• Behaviour of allele frequencies can be described
  by equations
• We can write out expectations for certain
  situations
• Deviations from expectations means deviation from
  assumptions