1. Friday’s Class 3 Extra Credit Questions
3 Questions, Multiple Choice
10 Minutes
12 Extra Points Possible
Not Required to Participate; if you are happy with your grade, come to class 10 minutes later at 9:15 on Friday.

2. Our Goal: To understand the “population consequences”
Of Mendel’s Laws.
Question 1: How do we describe a Mendelian population?

3. Genes in Populations With NO Natural Selection
Mating
System
Generation Begins
Zygotes
(fertilized eggs)
Gametes
(Sperm and eggs)
{GYY, GYy, Gyy}
NO Natural
Selection
Natural
Selection
Life cycle
Generation Ends
Reproducing Adults
Natural
Selection
Juveniles
{GYY, GYy, Gyy}

4. Answer: We describe a diploid Mendelian Population in
two ways:
1. List all the different genetic kinds of individuals,
i.e., all the genotypes.
Calculate the genotype frequencies.
2. List all the different kinds of genes,
i.e., all the alleles at all the genes.
Calculate the allele frequencies.

5. Can ALWAYS take individual genotypes apart into alleles
150 YY
300 Y Alleles = 2 x 150
400 Y Alleles = 1 x 400 Yy
400
400 y Alleles = 1 x 400 yy 90
180 y Alleles = 2 x 90
PY = {(2)(#YY) + (1)(#Yy)}/{(2)(Total # Genotypes)}
PY = {(2)(#YY)}/{2N} + {(1)(#Yy)}/{2N}
PY = (1){(#YY)}/{N} + (1/2){(#Yy)}/{N}
PY = GYY + (1/2)GYy

6. Can ALWAYS take individual genotypes apart into alleles
150 YY
300 Y Alleles = 2 x 150
400 Y Alleles = 1 x 400 Yy
400
400 y Alleles = 1 x 400 yy 90
180 y Alleles = 2 x 90
Py = {(2)(#yy) + (1)(#Yy)}/{(2)(Total # Genotypes)}
Py = {(2)(#yy)}/{2N} + {(1)(#Yy)}/{2N}
Py = (1){(#yy)}/{N} + (1/2){(#Yy)}/{N}
Py = Gyy + (1/2)GYy

7. There is More than One Way to package alleles into genotypes.
Unique
Genotypes
There is More than One Way to package alleles into
genotypes.
Knowing {PY, Py} CANNOT ALWAYS calculate the
One and only, unique genotype frequency distribution:
{GYY, GYy, Gyy}

8. The Two ways to genetically describe a Mendelian
Population are only partially interchangeable
Always Unpackage
Genotypes
Alleles
Alleles
Unique
Genotypes
Cannot
Always REpackage

9. Genes in Populations With NO Natural Selection
Generation Begins
Diploid Zygotes
(fertilized eggs)
Generation Ends
Reproducing Adults
{GYY, GYy, Gyy}
{GYY, GYy, Gyy} ??
Parents
Offspring
How are these Genotype Frequency
Distributions related to one another?

10. Under What Circumstances are the Two ways to
genetically describe a Mendelian Population
interchangeable ???
Always Unpackage
Genotypes
Alleles
Alleles
Unique
Genotypes
When CAN we
Repackage????
THE ANSWER: is something you need to know

11. Random Mating is a mating system in which the
frequency of a Mating Type or Family Type
equals the PRODUCT of the
Genotype Frequencies of the Parents.
Examples:
Family Type Family Type Frequency
Male x Female
Parents
YY x YY (GYY)(GYY) = (GYY)2
YY x Yy (GYY)(GYy)
yy x Yy (Gyy)(GYy)

12. YY Yy yy Female Parents in Population ½ YY, ½ Yy M a l e s ¼ YY
Gametes: 1 Y
Frequency: GYY Yy
Gametes: ½ Y, ½ y
Frequency: GYy yy
Gametes: 1 y
Frequency: Gyy
(GYY)2
½ YY, ½ Yy
(GYY)(GYy)
(GYY)(Gyy)
¼ YY
½ Yy
¼ yy
(GYy)2
½ Yy, ½ yy
(GYy)(Gyy)
(Gyy)2 M a l e s

13. YY Yy yy Female Parents in Population ½ YY, ½ Yy M a l e s ¼ YY
Adding up YY Offspring
Female Parents in Population YY
Gametes: 1 Y
Frequency: GYY Yy
Gametes: ½ Y, ½ y
Frequency: GYy yy
Gametes: 1 y
Frequency: Gyy
(GYY)2
½ YY, ½ Yy
(GYY)(GYy)
(GYY)(Gyy)
¼ YY
½ Yy
¼ yy
(GYy)2
½ Yy, ½ yy
(GYy)(Gyy)
(Gyy)2 M a l e s

14. Parental Genotype Frequencies: GYY , GYy, Gyy
Parental Allele Frequencies: pY = GYY + (½)Gyy
Offspring Genotype Frequencies: GYY , GYy, Gyy
GYY = (1)(GYY)2 + (½)(GYY)(GYy)
+ (½)(GYY)(GYy) + (¼) (GYy)2
= (GYY +[½][GYy])2 = (pY)2
Note: Genotype frequency in offspring, GYY, equals
square of the gene frequency, pY, in the parents.

15. YY Yy yy Female Parents in Population ½ YY, ½ Yy M a l e s ¼ YY
Adding up Yy Offspring
Female Parents in Population YY
Gametes: 1 Y
Frequency: GYY Yy
Gametes: ½ Y, ½ y
Frequency: GYy yy
Gametes: 1 y
Frequency: Gyy
(GYY)2
½ YY, ½ Yy
(GYY)(GYy)
(GYY)(Gyy)
¼ YY
½ Yy
¼ yy
(GYy)2
½ Yy, ½ yy
(GYy)(Gyy)
(Gyy)2 M a l e s

16. Parental Genotype Frequencies: GYY , GYy, Gyy
Parental Allele Frequencies: pY = GYY + (½)Gyy
Offspring Genotype Frequencies: GYY , GYy, Gyy
GYy = (½)(GYY)(GYy) + (½)(GYY)(GYy) + (½)(GYy)2
+ (½)(GYy)(Gyy) + (½)(GYy)(Gyy) + (2)(GYY)(Gyy)
= (2)(GYY +[½][GYy])(Gyy +[½][GYy])
GYy = (2)(pY)(py)
Note: Genotype frequency in offspring, GYY, equals
product of gene frequencies, pY and pY in the parents.

17. Hardy – Weinberg Equilibrium
Describes a population that is NOT evolving, because there is NO Natural Selection or any other Evolutionary Force acting on the population.
Allele frequencies do not change from parents to offspring under Hardy-Weinberg conditions!
Genotype frequencies {GYY, GYy, Gyy} in the offspring population at fertilization are a simple function of the allele frequencies {p, q} in the parent generation.
{GYY, GYy, Gyy}
= { PY 2 , 2PY Py, Py2 }
Freq. of A allele
Freq. of a allele
and parents PY = offspring PY

18. NECESSARY ASSUMPTIONS for H-W
The Hardy – Weinberg Equilibrium is one of the Population consequences of Mendel’s Laws
NECESSARY ASSUMPTIONS for H-W
Large Mendelian population
Random mating
No mutation
No migration
No natural selection
Under these assumptions there is no change in allele frequency from one generation to the next (i.e. no evolution)!
parents PY = offspring PY

19. (1) Mating is not random in the population; Or
The Hardy – Weinberg Equilibrium is one of the Population consequences of Mendel’s Laws
It is an Equilibrium that is achieved in one generation of random mating.
When a population deviates away from the Hardy-Weinberg Equilibrium it means EITHER:
(1) Mating is not random in the population; Or
(2) Some Evolutionary Force is acting in the population!

20. Mutation as an Evolutionary Force
It occurs when errors are made in duplicating alleles in producing the gametes.
It is one of the weaker evolutionary forces, because errors are relatively rare. The error rate or mutation rate, m, in copying an allele of a nuclear gene is ~ 1 x 10-6 to 1 x 10-9.
It changes allele frequencies in a population and this change in the genetic composition of a population from parents to offspring is what we mean by evolution.

21. No Mutation
AA Parents produce only ‘A’ bearing gametes.
Aa Parents produce ½ ‘A’ and ½ ‘a’ bearing gametes
aa Parents produce only all ‘a’ bearing gametes.
With Mutation
AA Parents produce some ‘a’ bearing mutant gametes.
Aa Parents produce ½ ‘A’ and ½ ‘a’ gametes
aa Parent produce some ‘A’ bearing mutant gametes.

22. Parent population Offspring population
= A alleles
= a alleles
Parent
population
Reproduction
With Mutation
Offspring
population

23. How strong is mutation as an evolutionary force?
Calculate how much the frequency of an allele changes in the population as a result of mutation. μ
Mechanism of
Mutation a A
Mutant Allele in the
Gamete and then
In the Offspring
Allele in the
Parent u a A
Mutant Allele in the
Gamete and then
In the Offspring
Allele in the
Parent

24. a A Change in allele frequency, DPa, as a result of mutation μ u
Mechanism of
Mutation a A u
Reproduction
With Mutation
Offspring Frequencies:
{PA’, Pa’}
Parent Frequencies:
{PA, Pa}
How similar are PA’ and PA?

25. ΔPa = Pa’– Pa = μ – (u + m)Pa
The change in allele frequency, DPa, caused by mutation
Reproduction
With Mutation
Parent Frequencies:
{PA, Pa}
Offspring Frequencies:
{PA’, Pa’}
Freq of a allele in offspring after mutation
Mutation rate from A to a times the Freq of A before mutation
Non-Mutation rate times the Freq of a before mutation
Pa’ = (1- v) Pa μPA
ΔPa = Pa’– Pa = μ – (u + m)Pa

26. ΔPa = Pa’– Pa = μ – (u + m)Pa
Change in allele frequency, DPa, as a result of mutation
Reproduction
With Mutation
Parent Frequencies:
{PA, Pa}
Offspring Frequencies:
{PA’, Pa’}
ΔPa = Pa’– Pa = μ – (u + m)Pa
At the Mutation Equilibrium, ΔPa = 0.
0 = μ – (u + m)P*a
P*a = μ/(u + m) =
The Equilibrium Allele Frequency =
Rate at which A is wrongly copied as a,
Relative to all errors at that gene.