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Topic: 10.3 Hardy-Weinberg Principle
Essential Question: Is the Hardy-Weinberg principle a realistic model to use to study evolution?
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10.3 Hardy-Weinberg Principle
Is the Hardy-Weinberg principle a realistic model to use to study evolution?
Key Vocabulary:
Hardy-Weinberg Principle

2. Hardy-Weinberg Equation
P.40
Hardy-Weinberg Practice Problems

3. Objective
SWU: how the Hardy-Weinberg Equation is useful to calculate frequencies of genotypes in a population SW: calculate the frequencies of genotypes in practice problems

4. Understandings:
A gene pool consists of all the genes and their different alleles, present in an inbreeding population
Evolution requires that allele frequencies change with time in populations

5. Interbreeding Populations
Gene pool: all the genetic information present in the reproducing members of a population at a given time
Large gene pool= populations show much variation
Small gene pool= populations members show little variation (many times in cases of inbreeding)
Gene pools stay generally stable over time…
BUT, new alleles can be introduced as a result of mutation
Old alleles can go extinct

6. Natural Selection
In natural selection, individuals with characteristics that best adapt them to their environment have the most reproductive success
Some alleles prove to be advantageous and tend to be more frequent
Some are disadvantageous, and are not passed on to as many offspring
In addition:
Populations mix through immigrations and emigrations and so the gene pool is modified (allows for evolution)
NO CHANGE IN ALLELE FREQUENCIES= NO EVOLUTION

7. Genetic Drift
Genetic Drift: is a change in the gene pool of a population due to RANDOM CHANCE
The smaller the population, the more impact it is likely to have
Gene pool may not be an accurate representation in the next generation
An allele may be lost from a population
Over time, tends to reduce genetic variation through losses of alleles
Bottleneck Effect- event that drastically reduces population #s (Fire, flood,EQ…)
Founder Effect- Colonization of a new location by a small # of individuals

8. Genetic Drift and Endangered Species
Loss of genetic variation as a result of “bottlenecking” events may reduce the ability of a population to adapt to environmental change
Endangered species typically have low genetic variability
As their populations decline, their gene pool also declines
Ex: African Cheetah
1st bottleneck: 10,000 y.a. during ice age— environment, disease?, hunting?, and droughts
2nd bottleneck: 19th century when hunted to near extinction
Studies show the cheetah populations show VERY LITTLE genetic variability

9. Genetic Flow
Gene Flow: A population may gain or lose alleles when fertile individuals move into or out of a population or when gametes are transferred between populations
Tends to reduce differences between populations
Due to Immigration and Emigration

10. The Hardy-Weinberg Principle
Hardy-Weinberg Principle: is used to calculate the frequencies of alleles, genotypes, or phenotypes within a population
Useful for determining how fast a population is changing, or predicting the outcomes of matings or crosses
This principle is important because it gives biologists a standard from which to measure changes in allele frequency in a population.

11. The Hardy-Weinberg Equation
The Hardy-Weinberg equation is based on Mendelian genetics. It is derived from a simple Punnett square in which p is the frequency of the dominant allele (B) and q is the frequency of the recessive allele (b).

12. The Hardy-Weinberg Equilibrium
HWP: States that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences (5 must be met—next slides)
Values predicted by the equation are those that would be present if the population is in equilibrium or is NOT EVOLVING
What evolutionary influences MUST BE avoided for a population’s gene pool to STAY EXACTLY THE SAME????

13. The Hardy-Weinberg Principle
The gene pool will stay the same assuming these five conditions are met:
Very large population: no genetic drift.
In each generation, some individuals may, just by chance, leave behind a few more descendants (and genes, of course!) than other individuals. The genes of the next generation will be the genes of the “lucky” individuals, not necessarily the healthier, “better”, or “fit” individuals.
2. No emigration or immigration: no gene flow. No organisms coming or going into the population.

14. The Hardy-Weinberg Principle
3. No mutations: No new alleles added to gene pool.
4. Random mating: No sexual selection. They will mate with any female/male.
5. No NATURAL SELECTION: All traits aid equally in survival. No traits are better than others.

15. The Hardy-Weinberg Principle
Because all of these disruptive forces commonly occur in nature, the Hardy- Weinberg equilibrium rarely applies in reality.
Describes an idealized state, and genetic variations in nature can be measured as changes from this equilibrium state.
Real populations rarely meet all five conditions!!!

16. Crash Course: Population Dynamics 6m40s

17. The Hardy-Weinberg Equation
When looked at individually, the frequencies of the alleles on chromosomes MUST ADD UP to 1
p+q=1
If p=.3 or (30%)
then q=???
q= .7 (70%)

18. The Hardy-Weinberg Equation
What complicates things is the fact that we usually want to consider diploid organisms that carry TWO copies of any particular gene:
As a result, the equation becomes (p+q)²=1
OR expanded to
p² + 2pq + q²=1
= 1

19. Copy on top ½ of p. 40 p + q = 1 The Hardy-Weinberg Equation
Expanded form due to having 2 alleles for each gene (p+q)2 =1
BB Bb bb
p= frequency of the dominant allele (B)
q= frequency of the recessive allele (b)
p²= frequency of dominant genotype (BB)
2pq= frequency of heterozygous genotype (Bb)
q²= frequency of recessive genotype (bb)
Copy on top ½ of p. 40

20. Hardy-Weinberg: Clarification + Connection
GG= ¼ .25 (p ²- freq of Homo Dom) Gg= ½ .50 (2pq- freq of Hetero) gg= ¼ .25 (q ²- freq of homo recessive) = 1

21. The Hardy-Weinberg Example: Genotypic freq
Find:
p (B)=
q (b)=
p² (BB)=
2pq (Bb)=
q² (bb)=

22. The Hardy-Weinberg Example: Genotypic freq
Find:
p (B)=
q (b)=
p² (BB)= .36 or 36%
2pq (Bb)= .48 or 48%
q² (bb)= .16 or 16%

23. How can I find p if I know p²? Use the square root! √ of p² = p
How to find allele frequencies: p and q
p + q = 1
p= dominant allele frequency
q= recessive allele frequency
How can I find p if I know p²?
Use the square root!
√ of p² = p
How else can I find p?
p²+ ½ 2pq= p

24. The Hardy-Weinberg Example: Allelic freq
Find:
p (B)= .6 or 60%
q (b)= .4 or 40%
p² (BB)= .36 or 36%
2pq (Bb)= .48 or 48%
q² (bb)= .16 or 16%
p= √.36=
q=√.16= .6 .4

25. The Hardy-Weinberg Example: Allelic freq
p²+ ½ 2pq= p
Find:
p (B)= .6 or 60%
q (b)= .4 or 40%
p² (BB)= .36 or 36%
2pq (Bb)= .48 or 48%
q² (bb)= .16 or 16% = = .6 .4

26. The Hardy-Weinberg Principle Practice
1. You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:
a. The frequency of the "aa" genotype.
b. The frequency of the "a" allele.
c. The frequency of the "A" allele.
d. The frequencies of the genotypes "AA" and "Aa."
e. The frequencies of the two possible phenotypes if "A" is completely dominant over "a.“
Hint for e: “How many of my cats will be black?”
Basically, Find:
p (A)=
q (a)=
p² (AA)=
2pq (Aa)=
q² (aa)=
Bottom of P. 40

27. The Hardy-Weinberg Principle Practice
1. You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:
Find:
p (A)= .4 or 40%
q (a)= .6 or 60%
p² (AA)=
2pq (Aa)=
q² (aa)= .36 or 36%
aa= 36… q²= .36
Sq. Root of .36=
q = .6
p + q = 1
_____ + .6= 1
p= .4

28. The Hardy-Weinberg Principle Practice
You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:
Find:
p (A)=.4 or 40%
q (a)=.6 or 60%
p² (AA)= .16 or 16 %
2pq (Aa)= .48 0r 48%
q² (aa)= .36 or 36%
p² + 2pq + q² = 1
p²: (.4)²=
p²= .16
2pq 2(pxq)=
2(.4x.6)= .48

29. The Hardy-Weinberg Principle Practice
Using the information you have gathered answer the following questions:
a. Calculate the frequency of the "aa" genotype.
36%
Find:
p (A)=.4 or 40%
q (a)=.6 or 60%
p² (AA)= .16 or 16 %
2pq (Aa)= .48 0r 48%
q² (aa)= .36 or 36%

30. The Hardy-Weinberg Principle Practice
Using the information you have gathered answer the following questions:
b. Calculate the frequency of the "a" allele.
.6 or 60%
Find:
p (A)=.4 or 40%
q (a)=.6 or 60%
p² (AA)= .16 or 16 %
2pq (Aa)= .48 0r 48%
q² (aa)= .36 or 36%

31. The Hardy-Weinberg Principle Practice
Using the information you have gathered answer the following questions:
c. Calculate the frequency of the "A" allele.
.4 or 40%
Find:
p (A)=.4 or 40%
q (a)=.6 or 60%
p² (AA)= .16 or 16 %
2pq (Aa)= .48 0r 48%
q² (aa)= .36 or 36%

32. The Hardy-Weinberg Principle Practice
Using the information you have gathered answer the following questions:
d. Calculate the frequencies of the genotypes "AA" and "Aa”.
AA= 16%
Aa= 48%
Find:
p (A)=.4 or 40%
q (a)=.6 or 60%
p² (AA)= .16 or 16 %
2pq (Aa)= .48 0r 48%
q² (aa)= .36 or 36%

33. The Hardy-Weinberg Principle Practice
Using the information you have gathered answer the following questions:
e. Calculate the frequencies of the two possible phenotypes if "A" is completely dominant over "a.“
= 64% of the population will show the trait.
Find:
p (A)=.4 or 40%
q (a)=.6 or 60%
p² (AA)= .16 or 16 %
2pq (Aa)= .48 0r 48%
q² (aa)= .36 or 36%

34. The Hardy-Weinberg Principle Practice
2. Albinism  is a rare genetically inherited trait that is only expressed in the phenotype of homozygous recessive individuals (aa).  The most characteristic symptom is a marked deficiency in the skin and hair pigment melanin.  This condition can occur among any human group as well as among other animal species.  The average human frequency of albinism in North America is only about 1 in 20,000.
Referring back to the Hardy-Weinberg equation (p² + 2pq + q² = 1), the frequency of homozygous recessive individuals (aa) in a population is q². 
Therefore, in North America the following must be true for albinism: q² = 1/20,000 =
Find:
p (A)=
q (a)=
p² (AA)=
2pq (Aa)=
q² (aa)=

35. Find: p (A)= q (a)= p² (AA)= 2pq (Aa)= q² (aa)= .00005
Referring back to the Hardy-Weinberg equation (p² + 2pq + q² = 1), the frequency of homozygous recessive individuals (aa) in a population is q². 
Therefore, in North America the following must be true for albinism: q² = 1/20,000 =
Figure out the predicted frequency of homozygous individuals, heterozygous individuals, and homozygous recessive individuals.
Find:
p (A)=
q (a)=
p² (AA)=
2pq (Aa)=
q² (aa)=

36. Find: p (A)= .99293 or 99.3% q (a)= .00707 or .71 %
Referring back to the Hardy-Weinberg equation (p² + 2pq + q² = 1), the frequency of homozygous recessive individuals (aa) in a population is q². 
Therefore, in North America the following must be true for albinism: q² = 1/20,000 =
Figure out the predicted frequency of homozygous individuals, heterozygous individuals, and homozygous recessive individuals.
Find:
p (A)= or 99.3%
q (a)= or .71 %
p² (AA)= or 98.6 %
2pq (Aa)= or 1.4 %
q² (aa)= or .005%

37. p²= predicted freq. of homozygous dominant individuals= .986….98.6%
2pq= predicted freq. of heterozygous individuals=
.014…..1.4 %
q²= predicted freq. of homozygous recessive individuals=
.00005…..005%
With a frequency of .005% (about 1 in 20,000), albinos are extremely rare. 
However, heterozygous carriers for this trait, with a predicted frequency of 1.4% (about 1 in 72), are far more common than most people imagine. 
There are roughly 278 times more carriers than albinos. 
Clearly, though, the vast majority of humans (98.6%) probably are homozygous dominant and do not have the albinism allele.

38. The Hardy-Weinberg Principle Practice
Please complete the Hardy-Weinberg practice problems (both sides)

39. Objective
SWU: how the Hardy-Weinberg Equation is useful to calculate frequencies of genotypes in a population SW: participate in the Hardy-Har-Har Weinberg lab

40. The Hardy-Weinberg Principle Practice
Get out HW and pass to one person at table for signature

41. The Hardy-Weinberg Principle Pre-Lab
Solve.
Fill out table
Genotype
# of Pirates in population with allele
Gene frequency (Freq. #/Total)
Homozygous Dominant LL p²
Heterozygous Ll
2pq
Homozygous Recessive ll q²
Total
Find:
q²= q= p=
p²=
2pq=

42. The Hardy Har Har-Weinberg Principle Activity
Read your Hardy-Weinberg Principle notes for background
Write hypothesis. What do you think is going to happen to the allele frequencies as we move from generation to generation?

43. P 1 (Parental Generation)
p²+ ½ 2pq= p
q²+ ½ 2pq= q
*Round to 4th decimal
Homozygous Dominant (LL)
Heterozygous
(Ll)
Homozygous Recessive (ll) p²
2pq q²
Freq of L
Freq. of l p q
*DON’T USE √ !!!
Instead use
p2 +½ pq or
q2 + ½ pq

44. F 1 (Parental Generation)
p²+ ½ 2pq= p
q²+ ½ 2pq= q
*Round to 4th decimal
Homozygous Dominant (LL)
Heterozygous
(Ll)
Homozygous Recessive (ll) p²
2pq q²
Freq of L
Freq. of l p q
*DON’T USE √ !!!
Instead use
p2 +½ pq or
q2 + ½ pq

45. F 2 (Parental Generation)
p²+ ½ 2pq= p
q²+ ½ 2pq= q
*Round to 4th decimal
Homozygous Dominant (LL)
Heterozygous
(Ll)
Homozygous Recessive (ll) p²
2pq q²
Freq of L
Freq. of l p q
*DON’T USE √ !!!
Instead use
p2 +½ pq or
q2 + ½ pq

46. F 3 (Parental Generation)
p²+ ½ 2pq= p
q²+ ½ 2pq= q
*Round to 4th decimal
Homozygous Dominant (LL)
Heterozygous
(Ll)
Homozygous Recessive (ll) p²
2pq q²
Freq of L
Freq. of l p q
*DON’T USE √ !!!
Instead use
p2 +½ pq or
q2 + ½ pq

47. F 4 (Parental Generation)
p²+ ½ 2pq= p
q²+ ½ 2pq= q
*Round to 4th decimal
Homozygous Dominant (LL)
Heterozygous
(Ll)
Homozygous Recessive (ll) p²
2pq q²
Freq of L
Freq. of l p q
*DON’T USE √ !!!
Instead use
p2 +½ pq or
q2 + ½ pq

48. F 5 (Parental Generation)
p²+ ½ 2pq= p
q²+ ½ 2pq= q
*Round to 4th decimal
Homozygous Dominant (LL)
Heterozygous
(Ll)
Homozygous Recessive (ll) p²
2pq q²
Freq of L
Freq. of l p q
*DON’T USE √ !!!
Instead use
p2 +½ pq or
q2 + ½ pq

49. F 6 (Parental Generation)
p²+ ½ 2pq= p
q²+ ½ 2pq= q
*Round to 4th decimal
Homozygous Dominant (LL)
Heterozygous
(Ll)
Homozygous Recessive (ll) p²
2pq q²
Freq of L
Freq. of l p q
*DON’T USE √ !!!
Instead use
p2 +½ pq or
q2 + ½ pq

50. The Hardy Har Har-Weinberg Principle Lab
Please answer the 6 analysis questions
Tape in on P. 40