## Chapter 5: Activity## Case Studies: The Evolution of Human Resistance to Malaria |

*The Evolution of Human Resistance to Malaria*

by Juliette Winterer, Franklin and Marshall College

__Introduction__

In this case study, you will evaluate data that reveal the relationship between
frequencies of a rare hemoglobin allele in human populations, and resistance
to malaria, a disease that today is the third most deadly infectious disease
in the world. Several mechanisms of evolution come into play in this story:
mutation, migration, and natural selection. All of these
mechanisms shed light on the intricate interrelationship between humans and
this disease. You will be given several datasets and several analytical techniques,
and provided with the opportunity to evaluate the nature of the interaction
between humans and malaria. By answering a series of questions, you will discover
whether there is evidence for ongoing evolution in human populations.

__Human variation in hemoglobin ^{}__

Hemoglobin, the molecule that carries oxygen in the red blood cells of human children and adults, is a protein made of two alpha subunits and two beta subunits. The genes that encode the alpha and beta subunits are both known to have several alleles. Many of these alleles derive from point-mutations in the DNA sequence that lead to single amino-acid substitutions in the protein. Most of the mutant alleles are very rare, because they reduce the efficiency of oxygen transport by red blood cells.

In sub-Saharan Africa, there is a surprisingly high frequency of an allele
that produces an abnormal form of the ß-subunit of the hemoglobin molecule.^{2} The allele is the result of a single point mutation in the
coding region of the ß-subunit gene. This mutation results in a substitution
of valine for glutamic acid in position six of the ß-subunit. This substitution
alters the shape of the hemoglobin molecule. Hemoglobin molecules containing
altered ß-subunits will crystallize under conditions of low oxygen tension.
When this happens, the red blood cells which carry the hemoglobin molecules
change shape drastically. Instead of their normal platelet shape, the red blood
cells become sickle-shaped (see figure 4.1 on page 105 in your textbook).

We will use the symbol *A* to represent
the allele for the normal form of the ß-subunit, and the symbol *S*
to represent the mutant form responsible for cell sickling. The three possible
genotypes in a population containing both alleles are *AA,**AS,* and *SS.*
People with the genotype *AA* make normal
hemoglobin and have a normal phenotype. People with genotype *SS*
produce hemoglobin that is highly prone to sickling, and as a result suffer
from anemia caused by poor oxygen delivery by the sickle-shaped cells in the
blood. Furthermore, periodic and painful crises can lead to serious organ damage.
This condition, known as sickle-cell anemia, is often fatal. Many *SS* homozygotes die before the age of reproduction.^{3} People with the genotype *AS*
produce a mixture of normal and abnormal hemoglobin. For the most part, the
production of normal hemoglobin compensates for the production of mutant hemoglobin,
and the heterozygotes do not suffer from sickle cell anemia (although they are,
of course, carriers of the sickle-cell trait). In other words, allele *S* is recessive to *A.*

**Question: What is the expected frequency of alleles ****A**** and ****S**** in a population containing both?**

We said above that in sub-Saharan Africa the frequency of allele *S,*
which is greater than 0.12 in some areas, is surprisingly high. The basis for
this claim is a calculation of what the frequencies of *S* and *A*
ought to be, given the information we have just reported about the phenotypes
associated with each of the three possible genotypes. We can perform this calculation
using tools developed in section 5.3 of the textbook.

We will use the variable p to represent the frequency of allele *A,*
and q to represent the frequency of *S.*
Box 5.3 in your textbook (page 131) derives the following expression for , the change from one generation to the next in the frequency
of allele *A:*

where w_{AA} is the fitness of *AA*
individuals, w_{AS} is the fitness of *AS*
individuals, and is the average fitness for the whole population, equal to p^{2}w_{AA} + 2pqw_{AS}+ q^{2}w_{SS}. The fitness of individuals with a particular genotype is their
average lifetime reproductive success, which is a function of the probability
that they will survive to adulthood and the number of offspring they will have
if they do survive.

Based on the information provided above, we can assign fitness to the three hemoglobin genotypes as follows:

Individuals with genotypes *AA* and *AS*
have high and essentially equal fitness, whereas *SS*
individuals have fitness that is lower by some increment s, mostly due the to
their reduced probability of surviving to adulthood.

Given these fitnesses, we are interested in whether the frequency of allele
*A* will rise or fall from one generation
to the next. Notice that the value of ,
as calculated by equation 1, will be positive whenever

is greater than zero. Substituting the full expression for and the values
for w_{AA'}, w_{AS'}, and w_{SS'} from the table above gives:

This last quantity, q^{2}s, will be greater than zero anytime q is greater than zero
(and s is greater than zero). Our calculation shows that whenever allele *S*
is present in the population, the frequency of allele *A* should rise--until the frequency of allele *S*
is zero, and the frequency of allele *A*
is one. Another way to reach this conclusion is to set the expression for equal to 0, and solve for p. This gives the equilibrium value of
p, also known as . Note that , as calculated
in equation 1, is equal to zero whenever p is equal to zero or
is equal to zero. As an exercise, readers may want to solve the expression

for p, to show that = 1.

Thus, we expect the frequency of the *A*
allele to be one, and the frequency of the *S*
allele to be zero, regardless of s, the strength of selection against *SS*
homozygotes.

Because the frequency of the *S* allele
in sub-Saharan Africa is much greater than zero, there must be some process
competing with natural selection against the *S*
allele that maintains the *S* allele in
the population.

**Question: Is that process mutation?**

The rate of mutations converting allele *A*
to allele *S* would have to be 10^{-4}or higher to suggest that a balance between selection and mutation
is maintaining the *S* allele at a frequency
of just 0.03 in a population (see textbook pages 145-147, and Hartl and Clark
1997^{4}).
This mutation rate is extraordinarily high, and the frequency of the *S* allele is considerably higher than 3% in many
parts of Africa.

**Question: Why is ****S**** in
high frequency in African populations when there is clear natural selection
against ****SS**** individuals?**

__The biology of malaria ^{}__

Malaria, a disease which can cause debilitating anemia and potentially fatal brain blood clots in people, is caused by four species of protozoa in the genus

__The Relationship between ____S____
and malaria__

In 1949, J. B. S. Haldane^{6} suggested that the reason that the deleterious *S*
allele occurs in high frequency in some human populations is because individuals
who are heterozygous for the allele (genotype *AS*)
do not suffer from the severe anemia due to cell sickling, but also enjoy some
resistance to malaria. He based this proposition solely on the observation of
higher than expected frequencies of allele *S*
in regions where malaria is endemic.

We saw above that some evolutionary force must counteract natural selection
against the deleterious recessive *S* allele. We also concluded that that force was
not likely to be mutation balancing against selection. Haldane suggested that
that force was natural selection for resistance to malaria. If individuals with
genotype *AA* are less resistant to malaria,
their fitness will be lowered by some fraction, t, relative to individuals with
the genotype *AS*. Of course, individuals
with genotype *SS* still suffer from sickle-cell
anemia, so their fitness is still lowered by some fraction, s. Thus we can represent
the fitnesses of the three genotypes in a population as follows:

With these fitness values, is there now an equilibrium value for p (and for q) somewhere between zero and one? Looking back at equation 1, we know that = 0 when

or

Substituting the full expression for and the new fitnesses for w_{AA'},
w_{AS'},
and w_{SS'} gives

Simplifying this equation reduces it to

Rearranging terms and substituting (1-p) for q gives

Factoring (pt) out of the left hand side gives

or

This equation can be solved for p, which gives

Finally, we can substitute (1 - q) for p to get

In other words, the equilibrium frequency of *S* in the population is a function of the competing
strengths of the two opposing forces of natural selection: selection against
*SS* individuals because of sickle-cell
anemia, and selection against *AA* individuals because of susceptibility to malaria.
Through this process, wherein the heterozygote has a fitness advantage over
either homozygote, the frequency of *S*
may remain at levels seen in sub-Saharan Africa, even if the fitness of *SS* homozygotes is extremely low.

**Question: What does the selective advantage of having genotype ****AS****
have to be in order to see the observed frequency of ****S**** (as high as 0.15) in sub-Saharan
African populations?** (How high does t have to be if s = 1, and the frequency
of *S* is 0.15 in a population?)

__Exercise:__

Assume that s = 1 (that is, that all *SS*
individuals die before reproducing). Use equation 2 to calculate the predicted
value of t, the strength of selection for resistance to malaria, in a population
in which the frequency of *S* is 0.15.

**Question: Do the data support Haldane's prediction that individuals with
the ****S**** allele have
greater resistance to malaria than ****AA**** individuals?**

It wasn't until the 1960's that data that could address this prediction became
available. Below you will find the original data^{7} that were used to test Haldane's hypothesis. They are a compilation
of 10 independent studies on the incidence of severe plasmodium infection among
children with or without the sickle-cell allele.

__Exercise:__

Examine the data, and show whether the evidence supports or rejects the hypothesis
that the *S* allele confers resistance to
infection by the plasmodium that causes malaria. (Most of the individuals in
the category 'with *S* allele' were heterozygotes, but a few were *SS*
homozygotes.)

__Method for Analysis:__

For each of the ten populations, calculate the frequency of infection among
people with the *S* allele, and among people
without. If Haldane's hypothesis is correct, then there should be higher rates
of infection among *AA* individuals than among *AS* or *SS*
individuals. Does this appear to be true?

Could we have gotten this result by chance, even if the *S* allele has no effect on resistance to malaria?
Answering this question requires a statistical test. Following the strategy
outlined in Box 8.1 (page 260-261 of your textbook), we can conduct a test as
follows:

1) Specify a null hypothesis. In this case, our null hypothesis is that there is no association between genotype and resistance to malaria.

2) Calculate a test statistic. We will take as our test statistic the number
of populations in our set of ten for which the rate of infection is higher among
*AA* individuals than among *AS*
or *SS* individuals.

3) Determine the probability that chance alone could have made the test statistic
as high as it is. Under the null hypothesis that genotype does not affect resistance
to malaria, determining whether the frequency of infection is higher in individuals
with or without the *S* allele is like tossing
a coin. The true frequency of infection should be the same in both groups, with
the group that appears to have the higher frequency in any given study determined
by chance. If we toss a coin ten times and count the number of heads, we could
get a number anywhere from 0 to 10. The graph below shows the probability of
each possible result. The table shows the total probability of getting 6 or
more heads, 7 or more heads, and so on.

4) Decide whether the outcome is statistically significant. If the value of
the test statistic is 9 or 10, then we can we can consider our result to be
significant. In other words, we can conclude that the data demonstrate that
having at least one copy of the *S* allele
makes a person more resistant to malaria.

**Question: What kind of data would show evidence that tolerance to malaria
is the mechanism by which natural selection maintains high frequency of the
****S**** allele
in human populations?**

Now that we have compelling evidence that the sickle cell allele protects individuals from infection by the plasmodium that causes malaria, we can test the hypothesis that it is the process of natural selection that explains high frequencies of this allele in human populations from regions where malaria is endemic.

__Approaches and Data:__

Approach 1: Examine historical data showing an increase in the frequency of
the allele with the appearance of endemic malaria.

We have no historical record of human hemoglobin allele frequencies prior to
the emergence of malaria as an endemic tropical disease. In fact, data suggest
that the plasmodium that causes malaria may have been around as long as the
genus *Homo* (Cavalli-Sforza et al 1994). However, current research is
in progress that may approach this question. In our DNA are the footprints of
natural selection. When balancing selection occurs, it leaves characteristic
traces in the variability of the DNA sequence surrounding the locus under selection
(See textbook chapter 18, pages 612-617; and chapter 13, pages 446-450.)
Michael Nachman at the University of Arizona and his colleagues are now analyzing
the sequence variation surrounding hemoglobin genes to look for evidence of
a history of balancing selection on the *S*
allele.

Approach 2: Examine correlative data showing an association of high frequencies of the allele in regions of endemic malaria.

We have maps of the distribution of the S allele in Africa, as well as maps
of the distribution of malaria prior to the 1950's, when global intervention
against the disease began. These maps^{8}
show that there is some correspondence between high frequency of *S* and endemic malaria. The maps, however, do not
correspond perfectly, and we can only conclude that these patterns are not inconsistent
with the hypothesis that malaria-resistance and the sickle cell trait are causally
related.

Approach 3: Evaluate experimental data^{9}
showing that when malaria is removed, the frequency of the *S*
allele declines.

Several hundred years ago, African populations were forcibly removed from Africa
and brought to the United States and sold into slavery. Some of these people
moved to the Caribbean, and their descendants have lived there ever since. Some
Caribbean regions have endemic malaria and some do not. Thus, the setting of
a "natural experiment" exists. We can evaluate the frequency of *S*
in populations that originated in Africa where malaria was endemic and ask whether
the frequency of *S* remains high when these
people were removed from Africa but relocated to malarial regions. We can also
ask whether the frequency of *S* has declined
among these Caribbean peoples living in regions without malaria.

__Exercise:__

Analyze these data and draw your own conclusions. One method for analyzing the
data is as follows:

First, calculate the frequency of the *S*
allele in each of the 11 populations. For this calculation, assume that *SS*
individuals are rare, and that to a first approximation all individuals in the
category "*SS* or *AS*" are heterozygotes. Does it appear to
be the case that the frequency of the *S* allele has fallen where malaria is absent?

Now perform a statistical test as follows (this test is Wilcoxon's rank sum test, described in many basic statistics books):

1) Take as the null hypothesis the claim that the frequency of the *S*
allele is the same in regions where malaria is present as in regions were malaria
is absent.

2) Calculate a test statistic as follows. Arrange all 11 populations in a list,
in order of their frequency of the *S* allele. The population with the lowest frequency
should be first; the population with the highest frequency should be last. The
position of each population in the list is its rank. Take the sum of the ranks
of the four populations from areas without malaria. For example (not the actual
result), if Curaçao is first, St. Vincent seventh, Dominique fourth, and Barbados
ninth, then the sum of their ranks is 21.

3) Under the null hypothesis, our procedure for calculating the test statistic is just like picking at random four numbers between 1 and 11 (such that no number is picked twice), then adding them up. The answer could be anything from 1 + 2 + 3 + 4 = 10 to 8 + 9 + 10 + 11 = 38. The graph below shows the probability of each possible result. The table shows the total probability of getting a sum of 16 or smaller, 15 or smaller, and so on.

4) If the value of the rank sum we calculate from the actual data is 14 or
smaller, we can consider our result to be statistically significant. In other
words, we can conclude that the frequency of the *S*
allele is lower in African-Caribbean populations living in areas without malaria
than it is in similar populations living in areas with malaria.

__Footnotes__:

Cavalli-Sforza, L. L. and W. F. Bodmer. 1971.

The Genetics of Human Populations.W. H. Freeman and Company, San Francisco, CA.Collins, F. H. and S. M. Paskewitz. 1995. Malaria: Current and future prospects for control. Annu. Rev. Entomol. 40: 195-219.

DNA Learning Center, Cold Spring Harbor Laboratory, One Bungtown Road, Cold Spring Harbor, New York 11724. http://www.dnalc.org/

**2.** See figure 2.14.1.D from: Cavalli-Sforza, L. L., P.
Menozzi, and A. Piazza. 1994. *The History and Geography of Human Genes.*
Princeton University Press, Princeton, NJ. for a map of the distribution of
the allele from sub-saharan Africa.

**3.** Medical researchers recently discovered that treatment
with hydroxyurea dramatically decreases the frequency of crises. See Charache,
S., et al. 1995. Effect of hydroxyurea on the frequency of painful crises in
sickle cell anemia. New England Journal of Medicine 332: 1317-1322.

**4.** Hartl, D. L., and A. G. Clark 1997. *Principles
of Population Genetics.* 3rd edition. Sinauer Associates, Inc. Sunderland,
MA.

Collins, F. H. and S. M. Paskewitz. 1995. Malaria: Current and future prospects for control. Annu. Rev. Entomol. 40: 195-219.

World Health Organization, Division of Control of Tropical Diseases. http://www.who.ch/programmmes/ctd/diseases/mala/malamain.htm

**6.** Haldane, J. B. S. 1949. Disease and evolution. Ricerca
Sci. 19:(Suppl. 1):3-10.

**7.** Data from: Allison, A. C. 1965. Polymorphism and natural
selection in human populations. Cold Spring Harbor Symposium in Quantitative
Biology. 29:137-149.

**8.** See figures 4.8 and 4.9 on p. 149 from: Cavalli-Sforza,
L. L. and W. F. Bodmer. 1971. *The Genetics of Human Populations.* W.
H. Freeman and Company, San Francisco, CA. for maps of the distribution of Hbs
in Africa, and of the distribution of malaria prior to 1950.

**9.** Data from: Allison, A. C. 1965. Polymorphism and natural
selection in human populations. Cold Spring Harbor Symposium in Quantitative
Biology. 29:137-149 (table 4) .

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