Anthropology 005
Problem Set # 3:
Winter 2023
Scientists have various methods for studying the world we live in; one of those is
building mathematical models of it. A mathematical model makes certain assumptions
and attempts to answer what would happen if those assumptions were true. A field
called population genetics focuses on mathematical models of evolution. Question 1 on
this problem set will introduce you to some basic population genetics. While the field
can be quite complex, this problem set isn’t, and won’t go past simple Algebra I. To
answer the various parts of question 1, you’ll need the equations and techniques
developed on pages 64-66 of your textbook. They rely on the binomial expansion;
remember that? It’s the key to the “proportional Punnett Square”. (If case you need
additional support on this question, I put a video called “Supplemental video explaining
the mathematics of population genetics” on the website, in the Week 3 module.)
1. Sickle-cell anemia is a disease that occurs when a person is homozygous for a
particular allele, s, and this condition is very often fatal. It might seem odd that
there would be an allele that causes a fatal disease. You probably wonder why
selection hasn’t gotten rid of this allele, and we’re going to help you figure that out.
Follow the stepping stones…
A. The Hardy-Weinberg Equilibrium is written as:
1 = (p2 + 2pq + q2)
Please define each of the four terms in the equation (1, p2, 2pq, q2); what does each
represent?
B. Now let’s see if population genetics can help us understand the fate of the sickle-
cell allele. Let’s assume that some homozygote ss individuals do survive and reproduce,
but on average they produce only 15% as many offspring as homozygote SS and
heterozygote Ss individuals; they are experiencing strong negative selection. Let’s
also assume that the SS and Ss types don’t differ from each other in their
reproductive success. Finally, let’s specify that the starting frequencies of the S and
s alleles (p and q) are 0.7 and 0.3, respectively. Given these values, please solve for p’
and q’ (the frequencies of S and s after one generation of selection). After one
generation, has anything changed? Does that answer make sense? Please show your
work!
C. If selection were to operate in this same way for many generations, what would be
the eventual frequency of the (recessive) s allele? Why?
D. Now let’s add an important real-world observation: Heterozygote individuals (who
have one copy of the s allele) have some resistance to malaria, an insect-transmitted
disease which can also be fatal (hundreds of thousands of people die of malaria every
year). In a particular area where malaria is common these heterozygotes (Ss) have
