Biology 14
“Spring”, 2011
Problem Set 1 , Due Feb 17 at 11:30 AM (not 12:50 PM)
Feb. 8, 2011
Use the handouts given out in lecture (by the same titles) to help solve these problems. If you have any difficulties see me about
them. Please show your work clearly so I can see that you understood what you were doing. This also enables me to see where
minor calculation errors, if any, were made. Please place your answer on the left margin of your document and show your work
to the right. It is not necessary to type it if your writing is clear and not crossed out (so use a pencil and erase if necessary).
Mendelian Genetics
1. Human eye color is determined by several autosomal genes (genes on non-sex chromosomes), with major and minor effects.
Some genes code for enzymes in the synthetic pathway for pigments, so mutations in them may block the synthesis of the
pigment or lessen the amount that is made. Other genes regulate where and how much pigment is deposited during the
development of the iris (thus giving variations in lighter colored eyes from blue to green). One gene that codes for an enzyme
required for pigment synthesis has two alleles; call them “B” and “b” to denote that B is dominant over b. So BB and Bb
individuals have brown eyes and bb individuals have blue eyes. Show by a diagram the possible genotypes and phenotypes in
offspring produced by crosses between the following people. Note that you are given phenotypes below, and there may be more
than one genotype for the same phenotype. Draw on the class handouts and the G&Z text to answer these problems. Note that
someone who is brown eyed in phenotype might be BB or Bb, whereas someone blue eyed in phenotype can only be bb.
a. A brown eyed male and a blue eyed female.
b. A brown eyed female and a brown eyed male.
c. A brown eyed male, whose father was brown eyed and mother blue eyed, with a blue eyed female.
Mendelian genetics and continuous variation
2. Darkness of coat color in a breed of dogs is controlled by 2 genes, each with 2 alleles (for the amount of the pigment, melanin,
deposited in the fur during development). The darkest dogs are XXYY, the lightest are xxyy, and the scale for darkness of coat is
based upon measuring the fraction of light absorbed by the coat. (The more light that is absorbed, the less is reflected and the
darker the dog is). Say that in XXYY individuals 72 percent of the light is absorbed by the pigments, and the contribution of the
X and Y alleles to this are the same, that is 18 percent absorption for each. So an XXYY coat would be 18+18+18+18= 72
percent of the light is absorbed. Assume that in xxyy individuals 12 percent of the light is absorbed, with each x and y allele
contributing 3 percent absorption (thus, xxyy is 3+3+3+3= 12 percent absorption). In humans, by the way, there are about 10
“polygenes” controlling melanin synthesis and deposition in the skin, so crosses between dark skinned and light skinned people
give a range of intermediates.
(a) As in the handout on Mendelian genetics and continuous variation, diagram a cross of an XXYY male with an xxyy female
and state what the genotypes and coat color values (in terms of % of light absorbed) of the heterozygous F1 offspring should be.
(b) Diagram the expected genotypes and phenotypes (in terms of % light absorbed= darkness) of a cross between one dog that is
XxYy and one that is xxYy.
Hardy Weinberg Law (handout on Understanding and Using the HW Law)
3. The following numbers of individuals of known genotypes for a gene with two alleles, X and x, were found in a
population of 670 individuals. 250 XX, 350 Xx, 70 xx
(a) Calculate the allele frequencies (p for X, q for x), the expected genotype frequencies (XX, Xx, xx) and the expected
genotype numbers. Is the population at HW equilibrium for these two alleles? (Use the allele frequencies to calculate the
expected genotype numbers and compare them to the actual numbers. Use handout on Hardy Weinberg Law.
(b) Do the same calculations for two generations (the next generation and the one after that) on the assumption that the xx
individuals are unable to breed each generation (delete them) and the population increases to 800 individuals and stays
the same over subsequent generations. So, from the data in (a) you have the frequency of X and x (p and q respectively), and
from those you calculate the expected numbers of each genotype (p2, 2pq and q2 , each times 800). Then remove all xx
individuals, recalculate p and q, then use p and q again to find expected genotype frequencies (p2 , 2pq and q2), and multiply
these frequencies again times 800 to get the expected numbers).
4. Migration. 320 Aa individuals emigrate to a population of 250AA, 150Aa and 220aa individuals.
a) What are the frequencies of the A and a alleles in the original population of 250AA, 150Aa and 220aa? (use handout on
HW Law)
b) What will the new frequencies of the two alleles be after the new immigrants arrive?
c) What will the expected frequencies and numbers of the genotypes be in the next generation, assuming HW equilibrium?
(Use gene frequencies calculated from b to determine genotype frequencies, and from them calculate the expected numbers
of each genotype, assuming that population size remains the same, namely, the sum of the immigrants, 320, plus the sum of
the population into which they immigrated (250+150+220).
5. Among the children born to Americans of Northern European descent, about one child in 2,500 has cystic fibrosis, a
homozygous recessive condition (cc) that leads to fluid accumulation in the lungs (the main effect); affected children
usually die from lung infections before age 20, but some live longer with constant medical treatment. The gene, of which
there are many mutant alleles, codes for a “pore” protein that resides in cell membranes and regulates chloride ion transport;
mutations at many sites in the gene result in proteins that allow chloride ion to leak through and accumulate on the other(
out) side of the membrane, with the result that water follows.
a) Use the HW Law to calculate the frequencies of the gene alleles (call them C and c) and of the genotypes. Hint: you were
given the frequency of affected individuals, q2, who are homozygous recessive, cc.
b) Use the HW Law to calculate the frequencies of possible marriages between homozygous normal individuals, CC, and
heterozygous carriers, Cc. Note: there are 3 possible combinations of marriages, and you find their frequencies by
multiplying the frequencies of the genotypes.
c) If two carriers (heterozygotes) of the disease marry and have children what proportion of them will have the disease?
Note that one of the major uses of in vitro fertilization and pre-implantation screening is to prevent partners with a history of
cystic fibrosis in their family from having an affected child. Multiple ovulation is hormonally stimulated in the female, in
vitro fertilization is carried out, single cells are removed from 6 to 8 cell embryos and screened for the presence/ absence of
the mutant allele. Embryos carrying the mutant allele are discarded, and the embryos carrying normal copies of the gene are
implanted.
Natural selection defined: fitness and selection coefficients. Use handout on calculating fitness, W, and selection coefficients, s.
6. Calculate the relative fitness and selection coefficients of the 3 genotypes in (a) and (b) below.
(a) Given below are the numbers of genotypes before and after selection in the same generation (e.g., number of individuals
surviving a drought, a famine, a plague, a storm, or an onslaught of predators)
before selection
after selection
AA Aa aa
554 442 222
310 298 104
(b) Below are the numbers of genotypes in the generation before selection and in the generation after selection (e.g. observed
numbers of individuals in a population of birds in the fall over two successive years---before and after they reproduced.) As in
the handout on quantifying natural selection, you will have to use the HW Law to calculate the EXPECTED frequencies and
numbers of genotypes in the generation after selection FROM the frequencies of the two alleles in the generation before
selection.
generation before selection
generation after selection
AA Aa aa
144 157 120
356 320 245
The Logic of Animal Conflict and Evolutionary Stable Strategies (frequency dependent selection)
7. In the handout with the above title, change the payoffs of the encounters in the following ways: winner of Hawk versus Hawk
encounter gains +60 looser loses –80, and Hawks win or lose half the time; in Dove versus Dove encounters winners gain +40,
looser loses –5, and Doves win or lose half the time In Hawk versus Dove encounters, Hawks always win (+60) because Doves
withdraw (thus losing nothing, 0). Set up the table of payoffs in the same way as in the handout and find the equilibrium
frequencies expected for Hawks and Doves with these new payoffs.
Calculation of Life History (Populations Demography) Parameters (use handout on this)
8. The data below are the numbers of the females in each age category of an organism (could be weeks, months, years,
decades) and the number of offspring or "fecundity", mx, for each age interval. Using the handout on population growth and
demography, calculate lx, gross reproductive rate (GRR the sum of all mx’s), the net replacement rate (R, the sum of all
lxmx’s), and vx, the reproductive value (age-specific expectation of future numbers of offspring for each age).
Age
0
1
2
3
4
5
N
955
522
300
181
40
8
lx
mx
lxma
vx
0
4.2
4.6
6.2
7.1
.1
Plot lx, mx, and vx on the same graph using ordinate scales for these parameters so that you
can see the differences across the lifespan; that is, for the ordinate scale for l x make the highest value 1.0, for the mx
ordinate scale make the highest value 7.1, and for the vx scale make the highest value whatever the highest value is
that you calculate. Suggest two ways in which selection might affect the evolution of timing of maturation (growth,
differentiation), reproduction and senescence. That is, imagine how natural selection might favor mutations that cause
an individual to allocate more energy and resources in early life to survivorship and growth, thus less to early
reproduction, so that its likelihood of surviving longer is increased. Or natural selection could favor mutations that
cause individuals to allocate more energy and resources to reproduction early in life, thus less to growth and survival
and more to producing baybees earlier. How would these two sorts of evolutionary changes in life history affect
senescence on the “adaptive demography theory of senescence”?
9. What was antigerasone made of? Hint: read Vonnegut’s “Tomorrow and Tomorrow and Tomorrow”, ER.
Would you take the stuff if it became available?