Download Biology 32: Evolutionary Biology Problem set 2, 2010 Please write

Biology 32: Evolutionary Biology
Problem set 2, 2010
Please write legibly, show all work, & indicate unambiguously the answer to the question (or sub-question).
Due date: my office (LSB 224), 5pm, Friday,19 February.
1. Calculate the relative fitness values and selection coefficients for the three buzzard genotypes in the table
below. Assuming that the relative number of fledglings determines the frequencies of the three genotypes,
estimate population mean fitness.
Genotype
DD
Dd
dd
Absolute fitness
(no. of fledglings)
2.0
4.4
2.4
2. Consider a large, randomly mating population of wombats with no movement of individuals in and out of
the population and no mutation. Two alleles at a locus, T and t, affect survival to adulthood by determining
the degree to which wombats are subject to parasitism by ticks and biting flies.
Individuals with the tt genotype have bitter-tasting blood, which repels parasites; these survive best. Tt
individuals have neutral tasting blood and survive 85% as well as do tt individuals. TT individuals have
sweet-tasting blood and attract parasites; they survive only 5% as well as do tt individuals.
(a) In a population of gametes at the start of a generation, the frequency of the t allele is 0.14. Assuming
random mating, calculate the frequency of each genotype that survives from being a zygote to
reproduce in the next generation.
(b) Continuing from above, calculate the frequency of the t allele in the gametes that will be produced in
the next generation. Is selection strong or weak? Explain.
(c) In this example, is allele t recessive, dominant, overdominant, or partially dominant?
3. In a randomly mating population of 25,000 newts (large enough to be considered infinite for the purposes of
the assumptions of the models; assume this population size remains constant throughout the generations
described in this question), a locus affects the structure of the skin of developing newt larvae as follows:
QQ and Qq individuals have skin that resists drying out, while qq individuals have skin that tends to dry
out. Further, Qq and qq individuals have skin that is not harmed by ultraviolet light, whereas QQ
individuals have skin that is damaged by ultraviolet light.
(a) Given both dry conditions and ultraviolet radiation, which genotype has the highest fitness? More
generally, what is this phenomenon called?
The selection coefficients are 0.25 and 0.67 against QQ individuals and qq individuals, respectively. The
allele frequency of q at the start of a generation is 0.98.
(b) What will the genotype frequencies be after selection (i.e., those that contribute to the next
generation)?
(c) What are the allele frequencies among these genotypes at the start of the next generation?
Consider the same newt population with similar conditions except that the allele frequency of q at the start
of a generation is 0.02.
(d) What will the allele frequency of q be at the start of the next generation?
(e) Given your calculations above, what do you think will happen to the frequencies of Q and q in these
newt populations over time (i.e., will either allele become fixed in the population)? If so, which allele
and why do you believe this? If not, why not, and what would the equilibrial allele frequencies be?
4. If the egg-to-adult survival rates of genotypes A1A1, A1A2, and A2A2 are 90, 85, and 75 percent, respectively,
and their fecundity values are 50, 60, and 65 eggs per female, what are the approximate absolute and relative
fitness values for these genotypes?
(a) What are the allele frequencies at equilibrium?
(b) Suppose the species has two generations per year, that the genotypes do not differ in survival, and that
the fecundity values are 50, 55, and 70 in the spring and 70, 65, and 55 in the fall. Will polymorphism
persist or will one allele become fixed?
(c) What if the fecundity values are 55, 65, and 75 in the spring and 75, 65, and 55 in the fall? Will
polymorphism persist or will one allele become fixed?
5. The relative fitnesses in a rat population for a gene conferring warfarin resistance have been estimated to be
0.37, 1.0, and 0.68 for genotypes RR, RS, and SS, respectively. What is the equilibrium frequency of the R
allele for populations beginning with a frequency of R equal to 0.3, 0.7, and 1.0?
6. If a recessive, lethal allele has a frequency of 0.05 in newly formed zygotes in one generation, and the locus
is in Hardy-Weinberg equilibrium, (a) what will the allele and genotype frequencies be at this locus at the
beginning of the next generation? (b) If the lethal allele arises by mutation at a rate of 10-6 per gamete, what
will be its frequency at equilibrium?
7. The rate of mutation to and selection coefficient against a deleterious allele (A2) are 10-6 and 0.2,
respectively. The relative fitness of a heterozygous genotype is also reduced, but only 10% of that of the
A1A1 genotype. What is the dominance coefficient? What is the equilibrium frequency of the A2 allele?
8. Albinism (i.e., chlorophyll mutants) in a line of pea plant is caused by an autosomal recessive mutation. As
you might imagine, the fitness of such plants is severely affected and generally afflicted plants do not
survive to reproduction. In the greenhouse, approximately 1 in every 10,000 seedlings is affected.
(a) Assuming Hardy-Weinberg equilibrium, what is the expected frequency of heterozygous carriers?
(b) If albinism is at the equilibrium of mutation-selection balance, then the equilibrium frequency is given
µ
by qˆ =
. Assuming a mutation rate of 2×10-6, what is the selection pressure against afflicted
s
individuals? What is the relative fitness of those individuals with the disease compared to normal
individuals? Do your calculations make sense – why or why not?
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