Hardy weinberg equilibrium the mystery unraveled
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Hardy-Weinberg Equilibrium The 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!. The Equations (For Monogenetic Traits). p + q = 1

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Hardy weinberg equilibrium the mystery unraveled

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!


The equations for monogenetic traits
The Equations (For Monogenetic Traits)

p + q = 1

p = Dominant Allele Frequency

p = #Dominant Alleles/Total Alleles

q = Recessive Allele Frequency

q = #Recessive Alleles/Total Alleles


The equations for monogenetic traits1
The Equations (For Monogenetic Traits)

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


How to work it out
How to Work it Out

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!


How to work it out1
How to Work it Out

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


How to work it out2
How to Work it Out

  • 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.


How to work it out3
How to Work it Out

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


How to work it out4
How to Work it Out

  • 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


How to work it out5
How to Work it Out

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


How to work it out6
How to Work it Out

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


How to work it out7
How to Work it Out

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


How to work it out8
How to Work it Out

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


Conclusion
Conclusion

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.


Extra problems answers can be found in the last slide
Extra Problems – Answers can be found in the last slide

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


Extra problems answers can be found in the last slide1
Extra Problems – Answers can be found in the last slide

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


Extra problems answers
Extra Problems – Answers

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


Hwe not so difficult
HWE – Not so Difficult!

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…


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