Lecture 6: Inbreeding

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Lecture 6 Inbreeding
September 8, 2008
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Schedule Changes

• Moved Inbreeding lecture up to today
• Prerequisite for Lab 4 (LD)
• Also switching Lab 5 (Selection) and Lab 6
  (Inbreeding)
• Theyre interchangeable
• Keep lab topics closely linked to lecture topics
• Deleted Advanced Selection lecture
• Added a lecture Applications in Forensics
• See website for updated schedule

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Last Time

• Measures of genetic variation
• Hardy-Weinberg departures revisited
• Multiple loci and independent segregation
• Estimating linkage disequilibrium

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Today

• Introduction to nonrandom mating
• Effects of inbreeding on heterozygosity and
  genetic diversity
• Estimating inbreeding coefficients from pedigrees
• Estimating inbreeding from molecular marker data

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Inbreeding

• Nonrandom mating within populations resulting in
  greater than expected mating between relatives
• Assumptions (for this lecture) No selection,
  gene flow, mutation, or genetic drift
• Inbreeding very common in plants and some insects
• Pathological results of inbreeding in animal
  populations
• Recessive human diseases
• Endangered species

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Important Points about Inbreeding

• Inbreeding affects ALL LOCI in genome
• Inbreeding results in a REDUCTION OF
  HETEROZYGOSITY in the population
• Inbreeding BY ITSELF changes only genotype
  frequencies, NOT ALLELE FREQUENCIES and therefore
  has NO EFFECT on overall genetic diversity within
  populations
• Inbreeding equilibrium occurs when there is a
  balance between the creation (through
  outcrossing) and loss of heterozygotes in each
  generation

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Inbreeding can be quantified by probability (f)
an individual contains two alleles that are
Identical by Descent
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Effect of Inbreeding on Genotype Frequencies

• fp is probability of getting two A1 alleles IBD
  in an individual
• p2(1-f) is probability of getting two A1 alleles
  IBS in an individual
• Inbreeding increases homozygosity and decreases
  heterozygosity by equal amounts each generation
• Complete inbreeding eliminates heterozygotes
  entirely

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Fixation Index

• The difference between observed and expected
  heterozygosity is a convenient measure of
  departures from Hardy-Weinberg Equilibrium

Where HO is observed heterozygosity and HE is
expected heterozygosity (2pq under Hardy-Weinberg
Equilibrium)
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• Inbred fraction (f) and noninbred fraction (1-f)

• If departures from Hardy Weinberg are entirely
  due to inbreeding, f can be estimated from
  Fixation Index, F

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Example Pitcairn Island

• In 1789, 25 sailors on the HMS Bounty mutinied
  and put Captain Bligh and his loyalists off the
  ship
• Nine of these sailors landed on uninhabited
  Pitcairn Island with 18 Tahitians and started a
  new colony
• Today about 50 people live on Pitcairn, and most
  are direct descendants of the mutineers
• What would you predict about genetic diversity on
  Pitcairn today?
• How is it likely to have changed since the
  founding of the settlement?

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Effects of Inbreeding on Allele Frequencies

• Allele frequencies do not change with inbreeding
• Loss of heterozygotes exactly balanced by gain of
  homozygotes

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Extreme Inbreeding Self Fertilization

• Common mode of reproduction in plants mate only
  with self
• Assume selfing newly established in a population
• ½ of heterozygotes become homozygotes each
  generation
• Homozygotes are NEVER converted to heterozygotes

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Decline of Heterozygosity with Self Fertilization

• Steady and rapid decline of heterozygosity to zero

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Partial Self Fertilization

• Mixed mating system some progeny produced by
  selfing, others by outcrossing (assumed random)
• Rate of outcrossing T
• Rate of selfing S
• TS1
• Heterozygosity declines to equilibrium point

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Inbreeding Equilibrium

• Production of heterozygotes by outcrossing
  balances loss of heterozygotes by selfing
• For any value of p and S, there is a
  characteristic equilibrium point, regardless of
  starting genotype frequencies
• Inbreeding coefficient also reaches equilibrium
  point, purely a function of selfing rate

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Estimating Selfing in Populations

• If inbreeding is principal cause of deviation,
  Ff
• Therefore, assuming equilibrium

• What are the assumptions of this calculation?

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Estimating Inbreeding from Pedigrees

• Most accurate estimate of f derived from direct
  assessment of relationships among ancestors

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Estimating Inbreeding from Pedigrees

• Probability P contains two A1 alleles IBD
• from D
• (1/2)(1/2)(1/2) 1/8
• from E
• (1/2)(1/2)(1/2) 1/8
• Pr(A1A1(1/8)(1/8) 1/64
• Probability P contains two A2 alleles is same
• Probability P contains any alleles IBD is
  therefore
• 1/641/64 1/32

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Chain Counting

• Count links to Common Ancestor starting with one
  parent of inbred individual and continuing down
  to other parent
• D-B-CA-C-E
• N5 links

For multiple common ancestors, m
If common ancestors are inbred as well
Where fCAi is inbreeding coefficient of common
ancestor i
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Calculate the inbreeding coefficient for P
Two Generations of Full-Sib Mating
CA2
CA1
B
D
P
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Estimating Inbreeding from Progeny Sets

• Analyze genotypes of progeny arrays and mothers
• Estimate outcrossing rate based on nonmaternal
  alleles