More Population Genetics Practice Problems

 

1.         A) The selective coefficient for the AA genotype is 0.1. The selective

coefficient for the aa genotype is 0. There is complete dominance of the A

allele over the a allele. What are the fitnesses of the three genotypes?

 

 

B) If 40 out of a hundred individuals with the AA and Aa genotypes survive

to reproductive age and 80 out of 100 individuals with the aa genotype

survive to reproductive age what are the fitnesses of the three genotypes?

 

 

 

2.   A) Phenylketonuria (PKU) is an example of a genetic disease whose frequency may be due to an equilibrium between selection and mutation. If the mutation rate to PKU is 1x10-5 and the fitness of individuals with PKU is half the fitness of individuals without PKU what is the frequency of the PKU allele at equilibrium?

 

 

B) At equilibrium, what is the frequency of the individuals with PKU in the population?

 

 

 

C) PKU has become much less severe with modern medical treatment. If the fitness of individuals with PKU increases to 0.8 what will be the new equilibrium frequency of the allele?

 

 

 

D) What will the new equilibrium frequency of individuals with PKU ?

 

 

 

3.  Ectrodactyly, also known as Òlobster clawÓ is an autosomal recessive condition in humans in which the fingers and toes are fused.  Otherwise, individuals with this condition are healthy.  Suppose the frequency of ectrodactyly among newborns is approximately 1/10,000 (when the parents are unrelated).

 

(a) What is the risk of a child with ectrodactyly if the parents are siblings?

 

 

 

(b) What is the risk of a child with PKU if the parents are second cousins?

F for second cousins is 1/64, so following the same calculations as above:

 

 

 

4. In a large, randomly mating population of giraffes with no movement of individuals in and out of the population and no mutation, the two alleles at one gene, A and a, do not affect survival or reproduction of the giraffes.  The two alleles at the other gene, S and B, do affect survival to adulthood by affecting the degree to which giraffes are subject to parasitism by ticks and biting flies.  BB individuals have bitter blood, which repels parasites, and survive best.  SB individuals have neutral tasting blood and survive 80% as well as do BB individuals.  SS individuals have sweet blood and attract parasites; they survive only 4% as well as do BB individuals.

 

a)     In a population of ADULT giraffes, the frequency of individuals with the AA genotype is 0.04.  Calculate the frequency of individuals with the Aa genotype.

 

 

 

b)    In a population of gametes at the start of a generation, the frequency of the B allele is 0.14.  Calculate the frequency of zygotes with the SB genotype

 

 

 

c)     Continuing from part (b), calculate the frequency of the adults that survive from the zygotes that have the SB genotype.

 

 

 

d)    Continuing from part (c), calculate the frequency of the B allele in the gametes that will produce the next generation

 

 

 

5. Consider two genes in a large, randomly mating population of turtles with no movement of individuals in and out of the population and no mutation.  The two alleles at one gene, L and M, do not affect fitness.  The two alleles at the other gene, T and t, do affect fitness -- they affect the thickness of turtle shells, and the degree to which they are protected from predation.  TT individuals have thick shells, which repel predators, and survive best.  Tt individuals have medium shell thickness and survive 88% as well as do TT individuals.  tt individuals have thin shells and are easy for predators to eat; they survive only 14% as well as do TT individuals.

 

a)     In a population of ADULT turtles, the frequency of individuals with the MM genotype is 0.06.  Calculate the frequency of individuals with the LM genotype.

 

 

b)    In a population of gametes at the start of a generation, the frequency of the t allele is 0.23.  Calculate the frequency of zygotes with the Tt genotype.

 

c)     Continuing from part (b), calculate the frequency of the adults that survive from the zygotes that have the Tt genotype.

 

 

d)    Continuing from part (c), calculate the frequency of the t allele in the gametes that will produce the next generation

 

 

  1. A population of 80 squirrels resides on campus, and the frequency of the Est1 allele among these squirrels is 0.70.  Another population of squirrels is found in a nearby woods, and there the frequency of the Est1 allele is 0.50.  During a severe winter, 20 of the squirrels from the woods population migrate to campus in search of food and join the campus population.  What will be the frequency of the Est1 allele in the campus population in the spring?

 

 

 

  1. Calculate the effective population size for a breeding population of 60 adult males and 40 adult females.

 

 

  1. In a population, the Dˆd mutation rate is 4x10-6.  DD, Dd, and dd genotypes have equal fitness. If p=0.8 today, what will p be after 50,000 generations?

 

 

  1. As discussed in class, the gene for sickle-cell anemia exhibits heterozygote advantage in environments with a high prevalence of malaria.  An individual who is an HAHS heterozygote has increased resistance to malaria and has higher fitness than the HAHA homozygote who is susceptible to malaria, and the HSHS homozygote who has sickle-cell anemia.  Suppose the fitness values for the genotypes in a population are as follows:

HAHA = 0.91   HAHS = 1.0      HSHS = 0.04

            Give the expected equilibrium frequencies of the two alleles in this population.

 

 

  1. Determine the ultimate fate of the A allele with random mating when the relative fitnesses of AA, Aa, and aa are:

a)     1.00, 0.98, 0.96

 

b)    1.00, 1.02, 1.02

 

c)     1.00, 1.02, 0.98

 

d)    1.00, 1.01, 1.02

 

 

  1. The fitnesses of 3 genotypes are: wAA = 0.9, wAa = 1.0, waa = 0.7.

a)     If the population starts at the allelic frequency of p = 0.5, what is the value of p in the next generation?

 

 

b)    What is the predicted equilibrium frequency?