HardyWeinberg Theorem 2 alleles at 1 locus

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Hardy-Weinberg Theorem (2 alleles at 1 locus)

• Population gene and genotypic frequencies dont
  change over generations if is at or near
  equilibrium.
• Gene Frequencies can be used to estimate
  Genotypic Frequencies

2
Assumptions for equilibrium

• large population (no random drift)
• Random mating
• no selection
• no migration (closed population)
• no mutation

3
Hardy-Weinberg Theorem (2 alleles at 1 locus)

• Allele freq.
• f(A) p
• f(a) q
• p q 1
• Sum of all alleles 100

• Genotypic freq.
• f(AA) p2 Dominant homozygous
• f(Aa) 2 pq Heterozygous
• f(aa) q2 Recessive homozygous
• p2 2 pq q2 1
• Sum of all genotypes 100

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Hardy-Weinberg Theorem

• Allele freq.
• f(A) p
• f(a) q
• p q 1
• Sum of all alleles 100

• Genotypic freq.
• f(AA) p2 Dominant homozygous
• f(Aa) 2 pq Heterozgous
• f(aa) q2 Recessive homozygous
• p2 2 pq q2 1
• Sum of all genotypes 100

AA pp p2 Aa pq qp 2pq Aa
qq q2
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Hardy-Weinberg Theorem

• X2 test used to verify if population is in HWE.
• Analyze/Compare differences between the observed
• and expected values

• Ho Observed not different than expected values
• Or observed differences are due sampling error (
  not real differences)

• o observed value for a given category
• e expected value for that category
• ? Sum of the calculated value for each category
  in the ratio

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Hardy-Weinberg Theorem

• Reject Ho Observed Different Than observed
• Accept Ho Observed not Different Than observed

df degrees of freedom df categories - 1
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Example Herd of 100 Short-horn. 37 red, 47 roan
and 16 white.Co-dominance 3 categories

Parental Generation. Observed Values RR 37 Rr
47 Rr 16 Total 100 Observed Allele
freq. f(R) p 2(37)(47)/2x .6050 f(r) q
2(16)(47)/2x .3950

• Allele freq.
• f(R) p
• f(r) q
• p q 1

• Genotypic freq.
• f(RR) p2 Homozygous RR
• f(Rr) 2 pq Heterozgous Rr
• f(rr) q2 Homozygous rr
• p2 2 pq q2 1

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Example Herd of 100 Short-horn. 37 red, 47 roan
and 16 white.
Observed Allele freq. f(R) p .605 f(r) q
.395 Expected Genotypic freq. f(RR) p2 gt.605
x .605 .36603 f(Rr) 2 pq gt2 x.605 x
.395.47795 f(rr) q2 gt.395 x .395
.15602 Expected values RR p2 x n 36.603
Rr 2 pq x n 47.795 rr q2 x n 15.602

• Allele freq.
• f(A) p
• f(a) q
• p q 1

• Genotypic freq.
• f(AA) p2 Homozygous RR
• f(Aa) 2 pq Heterozygous
• f(aa) q2 Homozygous rr
• p2 2 pq q2 1

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Hardy-Weinberg Theorem
Obs. Values Expect. values RR 37 RR
36.603 Rr 47 Rr 47.795 rr 16 rr
15.602 Difference Difference2 Dif2/Exp .397
RR .15761 0.0043 -.795 Rr .63203 0.0132 .398
rr .15984 0.0102 X2 ? .0277

• o observed value for a given category
• e expected value for that category
• ? Sum of the calculated value for each category
  in the ratio

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Hardy-Weinberg Equilibrium
X2 ? .0277
df degrees of freedom 3 categories df 3 -1
2 P between .9 and 1 Accept Ho gt Population in
HWE
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Example 2 Population of 1000 Angus BB 605
Bb 313 bb 82. HWE?
Parental Generation. Observed Values BB 598 Bb
332 bb 70 Total 1000 Observed Allele
freq. f(B) p 2(598)(332)/2x1000 p 0.764
f(b) q 2(70)(332)/2x1000 q 0.236
Expected Genotypic freq. f(BB) p2
gt0.5837 f(Bb) 2 pq gt0.3606 f(bb) q2
gt0.0557 Expected values BB p2 x n
583.7 Bb 2 pq x n 360.6 bb q2 x n
55.7
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Hardy-Weinberg Equilibrium
Obs. Values Expect. values BB 598 BB
583.7 Bb 332 Bb 360.6 bb 70 bb
55.7 Difference Difference2 Dif2/Exp BB 14.3
204.49 .3503 Bb -28.6 817.96 2.268 bb 14.3 2
04.49 3.6713 X2 ? 6.29

• o observed value for a given category
• e expected value for that category
• ? Sum of the calculated value for each category
  in the ratio

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Hardy-Weinberg Equilibrium
X2 ? 6.29
df degrees of freedom 3 categories df 3 -1
2 P between .05 and .01 Reject Ho gt Population
not in HWE