in Nature: Demonstrating Qualitative Agreement with equation for gene
frequency change (Continued from last lecture).
C. Sickle-Cell anemia and malarial resistance
1. Natural history.
a. Sickle cell anemia affects primarily people from Africa and is
caused by a mutant allele of the normal gene
that codes for the production of hemoglobin.
b. Normal hemoglobin is made up of two identical protein subunits, each subunit consisting of a pair of protein
chains. One of the protein chains, the a-chain, consists of 141 amino acids; the other protein, the b-chain,
contains 146 amino acids.
c. Each protein chain is produced by a separate gene. The sickle cell trait is produced by a mutation at
the gene that codes for the b-chain; at position 6, valine is substituted for glutamic acid.
d. Persons heterozygous have one normal chain and one mutant chain. They thus produce normal and altered
b-chains. The hemoglobin thus contains some molecules that are completely normal, some that are half
normal, and some that are completely altered. This condition produces a mild form of anemia, but it is
usually not very debilitating. It can be recognized by the capacity of red blood cells to be deformed from
their natural round shape to a sickle-shape under consitions of low oxygen in the blood.
e. Individuals homozygous for the altered chain produce no normal hemoglobin. This condition is extremely
debilitating and often is fatal.
2. Expected fitnesses.
a. From the natural history information alone, we might venture to
make some prediction about the equilibrium
gene frequencies of the sickle cell trait. If we call the normall allele A and the sickle-cell allele S, then
clearly individuals of genotype SS have much lower fitness than AA individuals, since often they don't live
long enough to reproduce. Moreover, we might expect that at best the AS individuals would have fitness
equal to that of AA individuals, and probably it would be somewhat lower, since they do suffer from some
mild symptoms of anemia.
b. Under these superficially reasonable assumptions,
WAA > WAS >> WSS
and we would predict that the S allele would be eliminated from the population.
c. We would be wrong, however. In some parts of Africa, the gene frequency of the S-allele is as high as 0.16.
With gene frequencies that high, close to 30% of individuals are AS. Moreover, natural selection certainly has
had sufficient time to eliminate the S allele, or to reduce it below the observed frequencies.
d. It would thus seem that our initial assumptions about relative fitnesses might be wrong and that this is a
3. Alternative hypothesis: the polymorphism is maintained by heterosis.
a. J.B.S. Haldane was first to suggest heterosis as an explanation.
b. He observed a fairly close correlation between the frequency of the S allele and the distribution of
malaria (see Map).
c. Frequency of sickle-cell trait is highest in Central Africa, Arabian peninsula, and parts of India.
d. These are precisely the areas in which the incidince of the highly debilitating falciparum malaria is highest.
e. On the basis of this similarity of distributions, Haldane suggested that heterozygous individuals, AS, may be
afforded some protection from malaria.
f. Hypothesis suggests that mortality among heterozygote individuals would be lower than among homozygote
4. Evidence supporting Haldane's hypothesis.
a. In one survey, in areas where malaria is prevalent, the mortality
rate among AS individula was only 85% that of
b. AS individuals are more resistant to malaria than are AA individuals
--in one study by Allison, 15 AA and 15 AS volunteers were infected with malaria.
--Malarial parasites were subsequently found in the blood of 14 of the AA volunteers, but in only 2 of the
&nb AS volunteers
c. AS individuals have reduced mortality rates
--In a study of 100 children who had died of malaria, only one was AS.
--The remaining 99 were all AA individuals.
--From the population gene freq. of 0.07 for S allele, 13 of the children should have been AS if malarial
mortality was the same for both genotypes.
--There were thus many fewer AS individuals than would be expected if there were no difference between
the two genotypes in mortality due to malaria.
d. AS individuals also appear to have a higher fertility than AA individuals.
--The advantage in various studies ranges up to 45%.
--Possible explanation: malarial infection of placenta, which can lead to death of the fetus, is lower in
heterozygotes. Consequently, their rate of natural abortion is lower than the rate for AA.
a. It appears that AS individuals have a higher fitness than AA individuals,
due to both lower mortality
(l) and higher fertility (m).
b. Both of these advantages seem to be conferred by the resistance of AS individuals to falciparum malaria.
c. The true fitness rankings are thus WAA < WAS >> WSS
d. The maintenance of the sickle-cell polymorphism in these human populations thus appears to be an example
of heterozygote superiority
f. Existence of a stable polymorphism consistent with the qualitative predictions of the predictive equation for
gene frequency change.
IV. Inferring Evolution by Natural Selection without measuring fitnesses
A. Distribution patterns.
1. Populations that differ genetically for a character offer an opportunity
to determine whether population
divergence has occured because of natural selection.
a. Alternative hypothesis is that divergence is due to genetic drift,
a process that will be discussed soon.
b. Because genetic drift is a random process, it can not generate correlations across populations or species
between environmental characters and genetic composition.
2. Consequently, evidence of non-random associations between gene
frequencies and environmental variables
are strong evidence for selection.
B. Example: variation in shell banding patterns in Cepea nemoralis.
C. Example: coordinate variation in gene frequencies
in two species of crickets.
Definition: An adaptation is any trait that has evolved due to natural
I. WHAT IS GENETIC DRIFT?
1. Genetic drift is a change in gene frequency due to statistical (chance) fluctuations in a finite population.
2. Drift is a specific example of a more general process: variation due to random sampling.
1. Suppose you have an urn filled with marbles, half of which are black and half of which are white.
2. Suppose further you choose a random sample of 10 marbles from the bag.
3. Two questions:
a. If you had to bet on how many of the marbles in your sample were black,
what number should you choose?
--answer: 5 . This is the most likely number of black marbles in your sample.
b. If you had to bet on whether exactly five marbles in the sample were black, should you bet yes or no?
--answer: no. Although 5 is the most likely number of black marbles, there is a reasonable probability
your sample will actually have some number other than 5
--in fact, the likelihood that the sample will contain some number of black marbles other than 5 is greater than
the likelihood it will contain exactly 5.
4. These questions illustrate the essence of the general phenomenon
of sampling variation: When one takes a
finite sample from some larger universe, we can not expect the sample to reflect the larger universe exactly.
5. Application to gene frequencies.
a. In a genetic context, the adults in every generation represent
a finite sample of genes taken from a much
larger gamete pool.
b. The gene frequency in the sample is thus not expected to reflect exactly the gene frequency in the gamete pool.
c. Similarly, the gamete pool represents a finite sample of genes available in the adults in the previous generation,
and thus the gene frequency in the gametes is not expected to reflect exactly the gene frequency in the adults
in the previous generation. (The variability introduced at this step is in most cases very small, however,
because while finite, the gamete pool is very large.)
d. These two expectations together mean that the gene frequency in adults of one generation is not expected to
equal exactly the gene frequency in adults of the previous generation.
e. But this simply means that from one generation to the next, a change in gene frequency has occurred, i.e.
evolution has occurred.
C. Long-term consequences of genetic drift.
1. Computer simulation of genetic drift --described in lecture
2. Gene frequency performs a "random walk", so that after many generations
gene frequency may be very different
from initial gene frequency.
D. Properties of genetic drift
1. The direction of change in gene frequency can not be predicted.
a. Increase or decrease in gene frequency due to drift may occur any
b. Whether increase or decrease occurs is not affected by the direction of change in any previous generations.
2. Magnitude of change in gene frequency can not be predicted with certainty
a. Change may be large or small.
b. Can place "reasonable" upper bounds on expected magnitude of change (see below)
3. One allele will eventually be fixed, the other eliminated: genetic drift tends to eliminate genetic variation.
4. Which allele eventually is fixed and which eliminated can not be predicted with certainty.
a. For each allele, there is a finite chance it will be fixed.
b. Chance of fixation is proportional to initial frequency
--implies that the fate of most neutral mutations is loss soon after they arise.
E. Quantitative properties of genetic drift (see Handout)
1. Bounds on expected change in gene frequency due to genetic drift
are related to the standard deviation of a
bionomial distribution, as described in the handout:
where p is the frequency of one allele, q is the frequency of the other allele, and N is the number of individuals
in the population.
a. Approximately 67% of the time |Dp| < s
b. Approximately 95% of the time |Dp| < 2s
c. Approximately 99% of the time |Dp| < 3s
2. In other words, a change in gene frequency greater that 2 due to genetic
drift is very improbable; is a change
of this magnitude is observed, we would expect some other process (e.g. Natural Selection) to be operating.
3. Because population size is in the denominator of the above expression,
the bounds on the magnitude of
gene frequency change are smaller in large populations than in smaller populations; i.e. genetic drift is a \
much more important evolutionary force in small populations.
4. However, genetic drift occurs in all finite populations.