Genetics- Extra Credit
Question 1: (2 points)
If 1 percent of individuals in a population at Hardy-Weinberg equilibrium express a recessive trait, we
might like to know what is the probability that the offspring of any two individuals who do not express
the trait will express it. This asks you to use the probability thinking from both population genetics
(where expectations come from HWE) and Mendelian genetic crosses (where expectations are
made about the outcomes of a specific mating).
The logic: We know that two carriers (individuals not expressing the trait, but being able to pass the
recessive alleles to offpsring) have a 25% chance of producing a child that inherits recessive alleles
from both parents (1/2 x 1/2 = 0.25). But, now we need to know how likely it is that individuals in the
population are carriers, so that we can predict the probability that any two people not expressing the
trait will have a child that does express the trait.
To estimate this from the information that we know -- 1% of individuals express the recessive trait -we need to recognize what this frequency represents. Let the frequency of the rare recessive allele
be represented by 'q'.
a) Assuming the population is in HWE, the frequency of individuals in the population expressing the
disease, in this case 1% or 0.01, would then be represented by
(a) p2
(b) 2pq
(c) q2
b) Given this, the frequency of the disease allele in the population (q) is: ____________
c) Carriers are heterozygotes, so we can estimate their frequency in the population using the HWE
expectation of 2pq. Using this equation, what is the frequency of carriers of the recessive allele in
the population? ____________
d) What is the probability that the offspring of two individuals who themselves do not express the
disease will express it? Here we need to first calculate the probability that two individuals who are
carriers mate, which is the product of the probabilities of each being a carrier. And then we need to
multiply that by the probability that two heterozygotes have an offspring that inherits two copies of
the recessive allele. Enter that combined probability here: ____________
** Note: Some of you may have realized that, to be precise, we should incorporate the information
that the two individuals do not express the disease, meaning that we should only be considering the
99% of individuals that do not express the trait when we do this calculation. This ends up modifying
the probability only slightly and both answers are scored correct.
Enter numeric answers to 4 decimal places, if rounding is necessary (e.g., 0.66666… should be
entered as 0.6667).
Scientific Calculator
Question 2: (2 points)
In the graph below, note the y-axis and think about what this change in allele frequency over time
means for the population. If there are two alleles at this locus, A and a, that affect fitness in a
population, use the graph to describe what is happening over time to each allele.
a) The A allele will __________
The a allele will __________
b)
Which of the trajectories above represents relatively strong selection? __________
Which of the trajectories above represent relatively weak selection? __________
c) Match the following patterns of relative fitness values to the trajectories in the graph below.
wAA = 1.0, wAa = 0.998, waa = 0.996 is most likely to cause allele frequency change similar
to __________
wAA = 0.8, wAa = 0.9 , waa = 1.0 is most likely to cause allele frequency change similar
to __________
d) Which of the migration scenarios below could also generate a trajectory like the blue (right-most)
line above? Recall that the equation for how migration can change allele frequencies is p1’ = p1(1-m)
+ p2(m), where m is the proportion of individuals in focal population 1 that are migrants. In other
words, what process below would lead to a deterministic decrease in the frequency of a alleles in the
population over time?
(a) Migration is occurring from a population with a higher frequency of heterozygous Aa individuals.
(b) Migration cannot change allele frequencies in a directional way like natural selection can.
(c) Migration is occurring from a population with a higher frequency of a alleles.
(d) Migration is occurring from a population with a higher frequency of A alleles.