Hardy Weinberg Theorem

1
Hardy Weinberg Theorem

• Purpose To calculate allele frequency over time
  to compare Changes microevolution!
• If allele frequencies ARE NOT Under Selection (5
  conditions of HW) then frequencies should NOT
  change!
• If frequencies change evolution!

2
Hardy-Weinberg Genetics ProblemsUses 2 equations

• EQUATION 1
• p q 1
• p dominant allele
• q recessive allele

• EQUATION 2
• p2 2pq q2 1
• What is p2?
• Homozygous dominant
• p x p
• What is 2pq?
• Heterozygous
• p x q (two combinations)
• What is q2?
• Homozygous recessive

3
Calculating Allele Frequencies

• The Hardy-Weinberg Principle
• (pg 424 Math Connection)
• Calculating ALLELES
• How many of each allele is in the population?
• p q 1
• p frequency of dominant allele
• q frequency of recessive allele
• If you know one of these, you can solve for the
  other

4
So for example

• If the recessive allele is in a population 40 of
  the time (.4) q
• Then the dominant allele will be present (p)
• 60 (.6) of the time
• WHY?
• p q 1

5
Calculating Frequencies

• Problem
• Tongue rolling is a dominant trait
• Ex If 6 out of 20 are non-tongue rollers (tt)
• WHAT IS THE FREQUENCY OF THE RECESSIVE GENE?
• Lets work this problem together

6
Calculating Frequencies

• Problem
• Tongue rolling is a dominant trait
• Ex If 6 out of 20 are non-tongue rollers (tt)
• WHAT IS THE FREQUENCY OF THE RECESSIVE GENE?
• SOLVE
• q2 30 ( .3) (6 ? 20)
• Why q2?
• b/c each of the 6 non-rollers has 2 alleles q X
  q
• So what is q
• q ?.3 .55
• 55 of the alleles in the population are t

7
Calculating Frequencies

• So how many alleles are T
• Solving for p 1 - .55 .45
• WHY PERCENTAGES?
• The population must 100
• SUMMARY
• Use q2 to solve for q and then for p
• Start with q2 b/c you DEFINITELY know these
  theyre recessive!
• REMEMBER q2 homozygous recessive
• p2 homozygous dominant

8
Calculating Gene Frequencies

• The Hardy-Weinberg Principle
• (pg 424 Math Connection)
• Calculating GENENOTYPES
• p2 2pq q2 1
• This equation can be use to determine the
  phenotypic amounts of TT, Tt and tt

9
Calculating Gene Frequencies

• The Hardy-Weinberg Principle
• (pg 424 Math Connection)
• Back to our Tongue-rolling example
• REMEMBER p .45 and q .55
• p2 2pq q2 1
• (.20) (.50) (.30) 1
• (TT) (Tt) (tt) 1
• SO
• 20 of the population are TT
• 50 of the population are Tt
• 30 of the population are tt

10
ANOTHER EXAMPLEYour Turn

• 1 in 1700 US Caucasian newborns have cystic
  fibrous. C for normal is dominant over c for
  cystic fibrous
• What percent of the above population have cystic
  fibrous (cc or q2)?
• 1/1700 .000588
• What is the frequency of q?
• q2 .000588
• q .0242

11
ANOTHER EXAMPLEYour Turn

• Now that we know q, we can find p
• p q 1
• p 1 q
• p 1 - .0242
• p .9758

12
ANOTHER EXAMPLEYour Turn

• Now that you know that p .9758 and q .0242,
  The following genotypes can be found
• CC- Normal homozygous dominate p2 ?
• .97582 .9522 95.22 CC
• Cc -carriers of cystic fibrous 2pq ?
• 2 ? .9758 ? .0242 .0472 4.72 Cc

13
ANOTHER EXAMPLEYour Turn

• FINALLY How many PEOPLE have each phenotype?
• How many of the 1700 of the population are
  homozygous Normal?
• .9522 ? 1700 1618.74
• How many of the 1700 in the population are
  heterozygous (carrier)?
• .0472 ? 1700 80.24

14
SUMMARYHow to solve a Hardy-Weinberg problem

• Use homozygous recessive (q2) to solve for q
• Use q to solve for p
• How? p q 1
• Now that you have p q you can solve for
• p2, 2pq and q2 (homozygous dominant, heterozygous
  and homozygous recessive)
• Use those amounts to find how many ACTUAL
  ORGANISMS in the population are in each category

15
Hardy-Weinberg YOUR TURN

• You try some practice problems

16
PTC Tasting Practice Problem

• a. 18 ? 50 .36 q2
• So, q .6
• b. p q 1
• So, p .4
• c. p2 .16
• d. 2pq .48
• e. 16 TT, 48 Tt, 36 tt
• f. 8 are TT and 24 are Tt

17
Hardy-Weinberg Conditions

• A genetic equilibrium of allele frequencies will
  remain in each succeeding generation of sexually
  reproducing individuals if the following five
  conditions must be met
• No mutations
• No gene flow (i.e. no immigration or emigration)
• Random mating must occur (i.e. pairing by chance)
  
• The population must be large so that no genetic
  drift (random chance) can cause a change.
• No natural selection can occur (i.e. certain
  alleles are selected for, or against)

Hardy-Weinberg Animation
18
Importance of Alleles/Variation Evolution

• Evolution Example
• In 1900 11 out of 100 squirrels in Iceland had
  the recessive phenotype of green fur.
• Work the H-W to determine the genotypic and
  allele frequencies in 1900.
• In 2000 24 out of 100 squirrels in Iceland had
  the recessive phenotype of green fur.
• Work the H-W to determine the genotypic and
  allelic frequencies.
• Using the 5 conditions of the H-W think of one
  possible cause of this change in allelic
  frequency.