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Hardy-Weinberg Equilibrium The Mystery Unraveled!

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Hardy-Weinberg EquilibriumThe Mystery Unraveled!

The Assumptions

- No Mutation
- No Gene Flow (Migration)
- No Genetic Drift
- No Natural Selection
- Random Mating
- The 5 main mechanisms of evolution are assumed to NOT be occurring!

p + q = 1

p = Dominant Allele Frequency

p = #Dominant Alleles/Total Alleles

q = Recessive Allele Frequency

q = #Recessive Alleles/Total Alleles

p2 + 2pq + q2 = 1

p2 = Homozygous Dominant Individual Frequency

p2 = #Homozygous Dominant Individuals/Total Population

2pq = Heterozygous Individual Frequency

2pq = #Heterozygous Individuals/Total Population

q2 = Homozygous Recessive Individual Frequency

q2 = #Homozygous Recessive Individuals/Total Population

Dark Gene (D) in Huskies

- Being dark colored is a dominant monogenetic trait
- So what is the genotype of the dark colored puppies?
- Either DD or Dd
- To find out for sure we’d have to know where the locus for color was located and we’d have to take a DNA sample
- Since we don’t want to poke the puppies,
we’ll estimate their genotypes using HWE!

1.Figure out which equation you’ll need.

Can we tell either ALLELE frequency for D or d (p and q)?

- No because we don’t know whether the two dark colored puppies are DD or Dd

- Therefore we cannot start with the p + q = 1 equation because that equation deals only with ALLELE frequencies

- So we have to start with the second equation because it deals with INDIVIDUAL frequencies and not ALLELE frequencies:
p2 + 2pq + q2 = 1

3.Which of the three terms can we figure out from what we know? Go back to slide 4 and review what each term represents while thinking about the puppies’ phenotypes.

4.Count the total number of puppies (population)

- There are 7 puppies (one is kinda hiding in the back)

5.Count which ones are dark colored and which ones are light colored

- 2 puppies are dark colored

- 5 puppies are light colored

- So of the two dark colored puppies, can we tell from their phenotype if they are homozygous dominant (DD) individuals or heterozygotes (Dd)?
- NO!

- Therefore we can only estimate q2 from the individuals that we know are homozygous recessive because their phenotype shows light colored fur.

- Remember that q2 = #Homozygous Recessive Individuals/Total Population so our q2 is 5 (light colored puppies [dd])/7 puppies total = 0.71

Now that we know q2, HWE becomes simple algebra:

- To find q we take the square root of q2.
√q2 = √.71 = q = 0.84

8.To find p we subtract q from 1.

1 – q = 1 – 0.84 = p = 0.16

9.To find p2 we square p:

p2 = 0.162 = 0.03

10.To find 2pq we multiply 2 by p by q.

2pq = 2 * 0.16 * 0.84 = 0.27

11.Now if we want to know the estimated number of homozygous dominant puppies we would multiply p2 by the total population because

p2 = #DD/Total Population so if we multiply both sides by the total population we get #DD

0.03 * 7 = 0.21 DD individuals

12.We perform similar algebra to estimate the number of heterozygous puppies by multiplying 2pq by the total population because

2pq = #Dd/Total Population so if we multiply both sides by the total population we get #Dd

0.27 * 7 = 1.89 Dd individuals

So in all probability, using HWE, both the dark colored puppies are probably heterozygotes based on our numbers, however, a DNA analysis would be required to verify whether or not this is correct.

Try a few examples on your own from the following slides.

Grey is the dominant coat color in these kittens and is a monogenetic trait so grey kittens will have either genotype GG or Gg

Find the allele frequencies p and q

Estimate the number of Homozygous Dominant (GG) Kittens and the number of Heterozygous (Gg) Kittens

White is the dominant coat color in these bunnies and is a monogenetic trait so white bunnies will have either genotype WW or Ww

Find the allele frequencies p and q

Estimate the number of Homozygous Dominant (WW) Bunnies and the number of Heterozygous (Ww) Bunnies

Kittens: p = 0.37, q = 0.63

#GG Kittens = 0.70

#Gg Kittens = 2.35

Bunnies: p = 0.59, q = 0.41

#WW Bunnies = 2.10

#Ww Bunnies = 2.88

When you start to think that HWE is difficult, just think back to the puppies, kittens, and bunnies.

Also, always remember, things could be much, much worse…