Evolution vs. Genetic Equilibrium

1
Evolution vs. Genetic Equilibrium

• The Hardy-Weinberg Equilibrium Principle

2

• Evolution Versus Genetic Equilibrium

• What is genetic equilibrium?
• Allele frequencies stay the same in a
  population.
• If allele frequencies dont change, the
  population is
• not evolving.
• Are there non-evolving populations in nature?
• What conditions are required to maintain genetic
  equilibrium?
• What the heck is Hardy-Weinberg, who are these
  people and why are they messing with stuff???

3
Evolution of populations

• Evolution change in allele frequencies in a
  population
• hypothetical what conditions would cause allele
  frequencies to not change?
• non-evolving population (fulfills H-W
  equilibrium)
• REMOVE all agents of evolutionary change
• very large population size (no genetic drift)
• no natural selection (everyone is equally fit)
• no mutation (no genetic change)
• random mating (no sexual selection)
• no migration (no gene flow in or out)

4
Hardy-Weinberg equilibrium

• Hypothetical, non-evolving population
• preserves allele frequencies
• Serves as a model (null hypothesis)
• natural populations rarely in H-W equilibrium
• useful model to measure if forces are acting on a
  population
• measuring evolutionary change

W. Weinberg physician
G.H. Hardy mathematician
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Hardy-Weinberg Principle

• Hardy-Weinberg - original proportions of
  genotypes in a population will remain constant
  from generation to generation.
• OrThe frequencies of alleles in a population
  stay the same from generation to generation
  unless acted upon by chance, natural selection,
  or other factors.
• Sexual shuffling of genes (meiosis and
  fertilization) alone will not change allelic
  (genotypic) proportions.

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Hardy-Weinberg theorem

• Counting Alleles
• assume 2 alleles B, b
• frequency of dominant allele (B) p
• frequency of recessive allele (b) q
• frequencies must add to 1 (100), so
• p q 1

bb
Bb
BB
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Hardy-Weinberg Principle

• Calculate genotype frequencies with a binomial
  expansion
• (pq)2 p2 2pq q2
• p2 individuals homozygous for first allele
• 2pq individuals heterozygous for alleles
• q2 individuals homozygous for second allele

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Hardy-Weinberg principle

• Counting Individuals
• frequency of homozygous dominant p x p p2
• frequency of homozygous recessive q x q q2
• frequency of heterozygotes (p x q) (q x p)
  2pq
• frequencies of all individuals must add to 1
  (100), so
• p2 2pq q2 1

bb
Bb
BB
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H-W formulas

• Alleles p q 1
• Individuals p2 2pq q2 1

bb
Bb
BB
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Using Hardy-Weinberg equation
population 100 cats 84 black, 16 white How many
of each genotype?
q2 (bb) 16/100 .16 q (b) v.16 0.4 p (B) 1
- 0.4 0.6
p2.36
2pq.48
q2.16
bb
Bb
BB
What are the genotype frequencies?
Must assume population is in H-W equilibrium!