Evolution Lecture 8 : Population Genetics: HardyWeinberg Equilibrium

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Evolution Lecture 8 Population Genetics
Hardy-Weinberg Equilibrium
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Population Genetics

• Integrates evolution by natural selection with
  Mendelian genetics
• Changes in relative abundance of traits is tied
  to the relative abundance of alleles that
  influence them
• Evolution here is the change in allele
  frequencies across generations

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The Null Model in Population Genetics

• We first need to see how allele frequencies
  operate without selection, migration etc..
• This is a null model...a benchmark at which we
  can compare changes in real populations due to
  other factors
• What is a population? A group of interbreeding
  individuals and their offspring

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How do we determine allele frequencies

• Example Examine a population of 43 individuals
  for the Delta 32 gene
• We have a total of 86 alleles
• If we have 16 heterozygotes and one homozygote
  for the - allele, then we get a frequency of this
  gene at 162/860.209
• The other ( allele) is 5216/860.791
• The frequency of both alleles must 1.0
• We could also do this by homo 26/430.605,
  het 16/430.372, homo - 1/430.023. Therefore
  the - allele freq. is 0.023 x 1/2 (0.372)0.209

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Generic Life-Cyclefrom haploid to diploid.
Alleles taken from haploid stage as individual
genes are combined into the diploid stage
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The allele frequency is 0.4 a and 0.6 A
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By randomly plucking gametes and making zygotes,
we see that our frequencies change over time
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Numerical Calculation

• If 60 of Eggs Contain A allele, and 60 Sperm
  Contain A allele, then we can make predictions
  about the probability of Zygotes
• AA0.6x0.60.36
• Aa2(0.6x0.4)0.48
• aa0.4x0.40.16
• These must equal one
• If the population is in equilibrium, the
  frequencies remained the same form generation to
  generation

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Hardy-Weinberg Equilibrium

• Yule thought that equilibrium meant that the
  allele freq. must be 0.50 and 0.50
• Hardy demonstrated that they dont have to be
  0.50/0.50, but simply must remain the same
  between generations
• if allele freq. are given by p and q, then the
  genotypes can be calculated by p22pqq21
• Also,pq1

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In Order for Equilibrium to be Maintained We
Assume

• No Selection
• No Mutation
• No Migration
• No chance events
• Random mating
• So, if allele freq. change from generation to
  generation, and genotype freq. cannot be
  calculated by multiplying allele freq., then one
  of these assumptions is occurring...Evolution