Download EEB 2245 Evolutionary Biology Spring 2015 Problem Set 2

EEB 2245 Evolutionary Biology Spring 2015 Problem Set 2 1. Consider a population of frogs in which the relative fitness of the AA genotype is 1.0, the AB genotypes is 0.6, and the BB genotype is 0.9. Draw a line graph for the scenarios in parts a and b with the frequency of the A allele on the y-­‐axis and the number of generations on the x-­‐axis. (a) Draw a graph of allele frequency over time where the initial frequency of the A allele is 0.7. (b) Draw a graph of allele frequency over time where the initial frequency of the A allele is 0.1. (c) Draw a graph of mean fitness versus the frequency of the A allele. (d) Given the information above, which of the following types of selection is occurring in this population? (Circle one). Directional Selection Stabilizing Selection Disruptive Selection (e) Would you expect this type of selection to decrease or maintain genetic diversity? Why? 2. Which of the following are necessary for evolution by natural selection? (Circle all that apply). (a) Environmental change (b) Variation among individuals (c) The best possible variant exists in the population (d) Variation among individuals is heritable (e) Different variants leave different numbers of offspring (f) What is best for the species and what is best for the individual must be the same 3. Calculate the degree of relatedness, r, between an aunt/uncle and a niece/nephew. Show your work! 4. Many vertebrates living in groups emit alarm calls to warn other individuals of approaching predators. However, the alarm call also attracts the predator’s attention, making the individual producing the alarm call more likely to be targeted. For the following 2 questions, assume the individual producing the alarm call has a 50% change of being eaten and individuals, once alerted, are sure to escape the predator. (a) According to Hamilton’s rule, would a ground squirrel be increasing its inclusive fitness by emitting an alarm call to warn 2 siblings that otherwise would be eaten by an approaching predator? Show your work/justify your answer. (b) Would the alarm-­‐caller be increasing its inclusive fitness by emitting an alarm call to warn 3 cousins that would otherwise be eaten? Show your work/justify your answer. 5. Consider a population under directional selection. Would you expect an advantageous dominant allele or an advantageous recessive allele to become fixed in a population more quickly? Explain your answer. In both cases, assume the advantageous allele is already relatively common. Hint: For the advantageous dominant allele scenario, assume the AA and Aa genotype have a relative fitness of 1, and the aa genotype has a lower relative fitness. For the advantageous recessive allele scenario, assume the aa genotype has a relative fitness of 1 and the Aa and AA genotypes have a lower relative fitness. 6. The genotypes of a population of 100 guppies are given below. AA AB BB 30 40 30 (a) Calculate the genotype frequencies (b) The relative fitness of the AA genotype is 0.9, the AB genotype is 1, and the BB genotype is 0.8. Calculate the mean fitness of this population. (c) What genotype and allele frequencies would you expect in the next generation assuming random mating? (d) Given the information above, which of the following types of selection would you expect to occur in this population? (Circle one). Directional Selection Stabilizing Selection Disruptive Selection (e) Over time, would you expect either allele to be lost from this population? Why or why not? 7. In the blank space, provide the letter (A-­‐C) of the fitness landscape that corresponds with each scenario. Some fitness landscapes will be used more than once. A B ! ω
______ Stabilizing Selection ______ AA ω = 1, AB ω = 0.8 BB ω = 0.3 ______ Heterozygote is most fit ______ Disruptive Selection ______ _____ AA ω = 1, AB ω = 0.3 BB ω = 0.8 ______ Directional Selection ______ Freq. A allele C 8. A botanist is growing pea plants. The mean height of the parent plants before selection (x̄ p) is 95cm, but after allowing only the shortest plants to breed, the mean height of the offspring plants (x̄ o) is 80cm. Calculate the response to selection, R. (b) Given that narrow sense heritability for height in peas (h2) is 0.8, calculate the selection differential, S. 9. The botanist knows height in pea plants is a quantitative trait. Assume that height in these plants is controlled by only 3 loci (A1/A2, B1/B2, C1/C2), which contribute equally to the phenotype (e.g., A1/B1/C1 all have the same effect on the phenotype, and A2/B2/C2 all have the same effect). (a) Across these 3 loci, how many different genotypes are possible? (b) How many different phenotypes are possible? (c) After crossing pea plants for many generations, the botanist has 2 completely inbred lines: one that is very short (60cm) and one that is very tall (120cm). Assume that the short line is homozygous for the “1” allele (A1, B1, C1) at all loci, and that the tall line is homozygous for the “2” allele (A2, B2, C2) at all loci. How much of a difference does the replacement of a “1” allele with a “2” allele cause in the height of a pea plant? (d) Given the information in part (c), how tall will a plant be that has 4 “2” alleles (A2/B2/C2) across those 3 loci? (e) If the botanist were to cross her 2 inbred strains (very short and very tall), how tall would their offspring be? 10. Eggs of this species of fly differ in how cryptic they are. Eggs with an AB genotype are the best camouflaged, followed by the AA genotype, and the BB genotype has the lowest relative fitness. Use the data in the chart to answer the following questions. AA AB BB Eggs 30 50 20 Survivorship 0.6 0.9 0.5 Adults (a) Given the starting number of eggs with each genotype, and their survivorship, fill in the rest of the chart by calculating the number of individuals you would expect to survive from egg to adulthood. (b) What are the expected genotype frequencies of the adults? (c) What are the expected allele frequencies of the adults? (d) Assuming these different genotypes have no difference in reproductive output, only survivorship, calculate the mean fitness of the population before selection acts and after selection acts. (e) How does this related to Fisher’s fundamental theorem? 11. A classic example of balancing selection is sickle-­‐cell anemia in regions where malaria commonly occurs. The sickle cell allele (S) gives protection against malaria in heterozygotes, but in homozygotes it causes severe deformities of the red blood cells. The relative fitnesses of the different genotypes are estimated below. AA AS SS 0.9 1 0.2 (a) Calculate the mean fitness of a population with Hardy-­‐Weinberg proportions of each genotype for the following frequencies of S: 0, 0.1, 0.15, 0.25, 0.5, 1. (b) Use these data to draw a graph of mean fitness of a population versus the frequency of the S allele. (c) From your graph, estimate the frequency of the S and A alleles expected at equilibrium. 12. You find a recessive lethal allele (L) occurring at a frequency of 0.01.
(a) In a population of 100,000 individuals, how many individuals do you expect
of each of the following genotypes BEFORE selection?
VV
VL
LL
(b) What will the frequency of L be AFTER selection? (Use enough decimal
places that you can see a change.)
(c) Suppose the probability of survival of the VL genotype was 99% that of the
VV genotype. In this scenario, what would the frequency of L be after selection?
(d) What effect does being recessive have on the rate at which the L allele is lost?
Explain.
13. Consider the following evolutionary argument: Darwin’s finches have been selected
to lay fewer eggs during times of drought because smaller populations have a higher
probability of surviving a drought.
(a) Explain, in a few sentences, why this is a bad argument.
(b) Assuming that it’s true that smaller populations have a higher probability of
surviving a drought, explain what alternative scenario would provide a better explanation
for the reduction in egg laying during the drought.
(c) What would you measure in the population to determine whether your
alternative explanation is supported?
14. An undergraduate research assistant at Rocky Mountain Bio Labs spent last summer
measuring aspects of the phenotype of columbines, an alpine flower. The phenotypic
data are summarized below.
Leaf size
Average # of
seeds
< 2.5 cm
27
2.5-5 cm
50
5-7.5 cm
45
7.5-10 cm
30
>10 cm
42
(a) Graph the relationship between leaf size and fitness.
(b) What form of selection is the population experiencing? Explain your answer.