Lecture 6: Population and Mathematical Genetics

Question 1

What are the 2 most important equations in hardy-weinburg equilibrium?

Answer 1

1. 1= p^2 + 2pq + q^2

2. 1= p +q

Question 2

How can the the frequency of offspring for each different allele group be determined?

Answer 2

By carrying out spectate genetic crosses for each allele cross.

Question 3

What is the frequency from an AA x AA cross?

Answer 3

P^4

Question 4

What is the frequency for an AA x Aa cross?

Answer 4

4p^3q

Question 5

What is the frequency for an Aa x Aa cross?

Answer 5

4p^2q^2

Question 6

What is the frequency for an AA x aa cross?

Answer 6

2p^2q^2

Question 7

What is the frequency for an Aa x aa cross?

Answer 7

4pq^3

Question 8

What is the frequency for an aa x aa cross?

Answer 8

q^4

Question 9

What is Hardy-Weinberg Equilibrium?

Answer 9

Hardy-Weinberg Equilibrium is a model that states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences such as random mating, natural selection, mutations, genetic drift, and gene flow. If a generation retains the same allele frequencies and genotypes as the generation before, the population is said to be in HW equilibrium.

Question 10

What is the rate of mutation denoted by?

Answer 10

U, mu

Question 11

Describe how a mutation that causes a dominant allele to appear recessive will affect the allele frequencies and genotype of the resulting population

Answer 11

The new model denotation for the dominant allele would be p-pu, because a percentage of the dominant alleles, determined by the mutation rate, will have become recessive.
The new model denotation for the recessive allele would be q+pu, because a percentage of the dominant allele, determined by the mutation rate, will have become recessive and will add to the existing recessive alleles.

Question 12

Of 100,000 children, 12 are born with the disorder. 10 caused by new mutations, 2 inherited from parents. 200,000 single alleles.

1. What is the mode of Inheritance?
2. What is the mutation rate?
3. What can be said about the fitness of the trait?

Answer 12

1. New mutation
2. 10/200,000 or 1/20,000
3. Mild/ moderate fitness as those affected are able to live long enough to produce; new mutation is not fatal.

Question 13

What is selection?

Answer 13

A process by which certain traits become more prevalent in a species than other traits.

Question 14

What is s?

Answer 14

S is the selection coefficient. Measure of fitness of aa relative to the fittest genotype, AA. An s value of 1 means the trait is lethal. The higher the s value, the more lethal the trait is, and the less likely that the offspring are to survive and reproduce.

Question 15

What is h?

Answer 15

H is the heterozygous effect. A measure of the relative fitness of the heterozygous allele relative to the selective difference of the 2 homozygotes. A h value of 1 means the Aa is like AA, where as a h value of 0 means the Aa is like aa. If h is 0.5, the Aa allele mutation is expressed as additive.

Question 16

What is the frequency of A and a alleles in the first generation of a population?

Answer 16

A= p^2 + pq/ p^2 + 2pq + q^2
a= q^2 + pq/ p^2 + 2pq + q^2

Question 17

What is the frequency of A and a alleles in the second generation of a population, affected by selection?

Answer 17

A(p’)= p^2 + pq(1-hs) / p^2 + 2pq(1-hs) + q^2(1-s)
a(q’)= 1-p’

Question 18

What is the fitness and frequency of AA?

Answer 18

Frequency: p^2
Fitness: 1

Question 19

What is the fitness and frequency of Aa?

Answer 19

Frequency: 2pq
Fitness: 1-hs

Question 20

What is the fitness and frequency of aa?

Answer 20

Frequency: q^2
Fitness: 1-s

Question 21

What is random genetic drift?

Answer 21

Genetic drift is the change in the frequency of an existing gene variant in a population due to random sampling of organisms. Genetic drift may cause gene variants to disappear completely and thereby reduce genetic variation, or cause initially rare alleles to become much more frequent and even fixed. Random genetic drift has a greater effect on small populations.

Question 22

What is the affect of random genetic drift on heterozygosity?

Answer 22

Allele frequencies change each generation due to genetic drift and heterozygosity is lost at a rate of 1/2N. The smaller the population (N), the greater the rate of loss of heterozygosity.

Question 23

What happens when s > 1/2N?

Answer 23

Natural selection will dominate the change in allele frequency whenever s> 1/2N.