Bio4250 midterm questions.
1) I may change the numbers to be used in any of the numerical calculations given below. I may require an answer to one question in particular, with a choice of any two others.
2) Your answers should be no shorter than 2/3rds &no longer than one 8.5 page.
3) You may bring one-half of an 8.5 x 11 sheet of paper with notes; please don't try to cram all of the answer in the smallest handwriting possible. Hand in these sheets with your answers.
BIOL4250 - Midterm Questions for exam on Thursday,
2024 October 17
Prepare answers to ALL of
the HOMEWORK questions below. For the exam, I will choose
FOUR: you must answer any THREE in the exam Period. Show
your work.
[I
suggest that you not use calculators]
1.
Prior
to the advent of molecular data in the 1960s, it was assumed
that the large organismal differences between humans
relative to other apes (including chimpanzees
and gorillas)
were due to a large amount of genetic change along the human
lineage. (a) Test
this hypothesis by counting the
number of SNP changes between the three pairwise
combination of primate species A, B,
& C as instructed. Report these
numbers. (b) Do the data support or reject the hypothesis?
Explain.
2.
William J
Spillman was an
American agronomist who in 1901 observed experimentally what
would later be called Mendelian ratios. Answer the HOMEWORK question here
on his crosses. Write your answer as a teaching exercise for a
Biol2250 student trying to understand Mendelian
ratios.
3.
With a sample
size of n = 100, is a
ratio of 58:42 sufficient to demonstrate a
significant deviation from an expected 50% : 50% ratio
at p = 0.05? Explain,
with numbers. (2) With n=100,
what is the minimum deviation from
expectation that could be detected as statistically
significant at p=0.01? From the
formula for Chi-Square, show algebraically what
the minimum deviation is. A table of Chi-square values
will be provided.
4.
(a) Calculate
Hexp for a locus
with 100 alleles at equal
frequency: show your work. (b) How many genotypes
are there at such a locus? (c) Calculate Hexp for a locus
with one allele at q = 0.5,
and 50, at equal
frequencies. Show your work. [Hint: use
appropriate shortcuts. Don't use a calculator].
5.
Re-write the
derivation of the Hardy-Weinberg Theorem in
terms of 
p = (p' -
p).
6.
The
course notes state: "The dominance relationships
of the two alleles with respect to fitness are fixed
genetically, according to whether the A1A2
heterozygote is more similar to the A1A1
or A2A2 homozygotes. It is not
determined by the phenotypic values themselves."
Explain the idea of genetic dominance, & in
doing so explain the difference between genetic
dominance and phenotypic value.
7. For a graph of the fate of a
rare allele under positive selection, the
same notes state "The
information in the graph also shows the fate of a common
allele under negative directional selection, IF the
Y-axis values were inverted top to bottom (1 
0)
and labelled f(A1) = p.
That is, the behavior of the two alleles at a locus are complementary for any
particular dominance model." For
a locus with two alleles, A & B, show that
the graph for A dominant to B is in fact
complementary to the graph of B dominant to A.
For a numerical argument, assume the fitness of the dominant
phenotype is twice that of the recessive phenotype.
8.
For each of
the graphs of q = f(B), identify which
mode of selection is acting to produce change in q. Identify
and explain the features of the curve of q over
time that allow you to recognize the mode of selection. The
particular graphs to be used are a
work in progress.
9.
For a
phenotype due to semi-dominant alleles with Additive or
Genic selection, for an
initial f(B) < 0.01 and s < 0.5, use the GSM
worksheet in Excel to run the (1) Additive and (2) Genic selection schemes in
the table provided. At what values do the curves deviate and
(or) converge on each other? Why?
10. Professor Blue's midterm will
have three questions, hardest (A), hard (B),
and easy (C). She will ask any two of them.
Student Red decides they can study for any
two, but not all three. The student
will get 10 points for a prepared answer, but only
3, 5, & 7 for unprepared
answers to A, B, & C
respectively. For the two 2x2 games in italics
[upper left] or bold [lower right] below, calculate
the optimal mixed strategies for Blue and Red, where
matrix values are payoffs (test scores) to Red. Calculate
the Value of the game to Red.
BONUS: the matrix implicitly
includes six other
2x2 games: what
are they? Based on basic
principles of game theory, why do
none require mixed strategy solutions?
