Transcript Document

Estimating nucleotide mutation rate in human
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The approach by Nachman and Crowell to measuring the human
mutation rate takes advantage of the well-known result that for
neutral mutations, the mutation rate is equal to the rate of mutation
substitution
Knowing divergence time and generation length of two species
allowed them to estimate of the rate and pattern of mutation in
stretches of DNA without function
They sequenced 18 pseudogenes in humans and chimpanzees,
including 12 on autosomes and 6 on the X chromosome. In this way,
they
1. estimated the average mutation rate per nucleotide site
2. compared mutation rates for different sites and for different classes of
mutation to evaluate heterogeneity of mutation rate
3. compared rates of divergence on the X chromosome and on autosomes
to evaluate the hypothesis that the X chromosome has a lower mutation
rate than the autosomes
4. provided an approximation of the genomic deleterious mutation rate by
considering the total mutation rate and the fraction of the genome that is
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subject to constraint
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Nachman and Crowell main results
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Nachman and Crowell results (1)
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Nachman and Crowell results (2)
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Nachman and Crowell results (3)
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Nachman and Crowell results (4)
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Mutation rates per gene in humans
A list of traits specified by dominant mutant alleles whose mutation rates
have been estimated is given below
Mutation rates may be estimated
by a direct method (counting
affected individuals born from
normal parents among a large
number of births) or by an
indirect method (using the
frequency of affected
individuals in a population and
estimating their average
selective disadvantage)
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Summary of mutation rates in human
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Mutation rates per generation
• Per base pair ~10-8
• Per gene ~10-6 - 10-5
• Per genome
 All
point mutations: ~100 per gamete
 Deleterious mutations: 1 ~ 2 per gamete
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Selection
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Changes in a species in response to a changing environment occur because the
different genotypes produced by mutation and recombination have different abilities
to survive and reproduce.
The differential rates of survival and reproduction are what is meant by
selection, and the process of selection results in changes in the frequencies of the
various genotypes in the population.
Darwin called the process of differential survival and reproduction of different types
natural selection by analogy with the artificial selection carried out by animal and
plant breeders when they deliberately select some individuals of a preferred type.
The relative probability of survival and rate of reproduction of a phenotype or
genotype is now called its Darwinian fitness.
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Although geneticists sometimes speak loosely of the fitness of an individual, the concept
of fitness really applies to the average survival and reproduction of individuals in a
phenotypic or genotypic class. Because of chance events in the life histories of
individuals, even two organisms with identical genotypes and identical environments will
differ in their survival and reproduction rates. It is the fitness of a genotype on average
over all its possessors that matters
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How selection works
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The simplest way to see the effect of selection is to consider an allele,
a, that is completely lethal before reproductive age in homozygous
condition.
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Suppose that, in some generation, the allele frequency of this gene is 0.10. Then,
in a random mating population, the proportions of the three genotypes after
fertilization are.
How are these genotype frequencies connected to the allele frequency
of 0.1?
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The answer is provided by the law of Hardy-Weinberg, which is the way an
elementary statistical principle is named in population genetics
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Hardy-Weinberg Equilibrium
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If the frequency of allele A is p in both the sperm and the eggs and the frequency of
allele a is q = 1-p, then the consequences of random unions of sperm and eggs may
be worked out in a Punnett square.
The Hardy-Weinberg equilibrium frequencies that result from
random mating. The frequencies of A and a among both eggs
and sperm are p and q ( = 1-p), respectively. The total
frequencies of the zygote genotypes are p2 for A/A, 2pq for A/a,
and q2 for a/a. The frequency of the allele A in the zygotes is the
frequency of A/A plus half the frequency of A/a, or p2 + pq =
p(p + q) = p.
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The probability that both the sperm and the egg will carry A is p × p = p2, so p2 will
be the frequency of A/A homozygotes in the next generation. In like manner, the
chance of heterozygotes A/a will be (p × q) + (q × p) = 2pq, and the chance of
homozygotes a/a will be q × q = q2. The three genotypes, after a generation of
random mating, will be in the frequencies p2:2pq:q2.
In the next generation, the frequencies of the three genotypes will again be
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p2:2pq:q2, and so forth, forever.
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How selection works
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Going back to our example of a recessive letal gene with frequency of 0.1, we have
the genotype frequencies among newborns of
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At reproductive age, however, the homozygotes a/a will have already died, leaving
the genotypes at this stage as
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But these proportions add up to only 0.99 because only 99 percent of the population
is still surviving. Among the actual surviving reproducing population, the
proportions must be recalculated by dividing by 0.99 so that the total proportions
add up to 1.00. After this readjustment, we have
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The frequency of the lethal a allele among the gametes produced by these survivors
is then
and the change in allelic frequency in one generation, expressed as the new value
minus the old one, has been 0.091- 0.100 = 0.019. We can repeat this calculation in
each successive generation to obtain the predicted frequencies of the lethal and
normal alleles in a succession of future generations
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Fitness and selection
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We may take the phenotype with highest absolute fitness, whose
overall expectation of progeny that reach reproductive age is
maximum),Wmax, as the standard phenotype, with which the fitnesses
Wj of other phenotypes can be compared.
Thus, the relative fitness wj of phenotype j is wj = Wj/Wmax and it can
assume any value included between 0 and 1.
We define the selection coefficient or selective disadvantage of
phenotype j to be sj = 1 – wj. Sometimes it is easier to reason in terms
of fitness (w), sometimes it is easier in terms of selection coefficient
(s).
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A letal phenotype has fitness 0 and the selection coefficient against it is 1.
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Change of allele frequency in one generation
• We can now consider the example of a deleterious recessive gene in general terms.
Multiplying the initial frequency by the fitness of each genotype we obtain the
contribution of each genotype to the gametes that will form the next generation:
Genotypes
Frequency before selection
Fitness
Frequency after selection
AA
p2
1
p2
Aa
aa
Total
2
2pq
q
1,00
1
1-s
2pq q2 (1-s) 1-sq2
• To find the frequency of a genes in the progeny, we can apply the calculation already
seen, from which we arrive at the following general formula for the change of the
allele frequency in one generation :
sq2(1-q)
Dq = 1 – sq2
• We will use this equation to obtain the number of generations of selection needed to
reach a specific change of gene frequency. An aswer to this question is sometimes
required in connexion with breeding programmes or proposed eugenic measures. We
will consider, for simplicity, the special case of s = 1 (complete selection against aa).
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Number of generations required
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By working with the recursive equation for Dq, we may easily arrive at the result
qt = q0/(1+tq0), from which we obtain t = 1/qt – 1/q0.
Consider albinism as an example, and ask the question: how long it take to reduce
its frequency to half its present value if albinos are prevented from reproduction ?
The present frequency is about 1/20,000, and this makes q0 = 1/141 (q2 = 1/20,000,
so q = q2, from the Hardy-Weinberg law). The objective is q2 = 1/40,000, which
makes qt = 1/200. So, from the above equation t = 200 – 141 = 59 generations. With
25 years to a generation it would take nearly 1,500 years to achieve this modest
result.
A general conclusion from the above example is that it is extremely difficult to
significantly reduce the frequency of an allele that is already rare in a population.
Thus, eugenic programs designed to eliminate deleterious recessive genes from
human populations by preventing the reproduction of affected persons do not work.
Of course, if all heterozygotes could be prevented from reproducing, the gene could
be eliminated (except for new mutations) in a single generation. Because every
human being is heterozygous for a number of different deleterious genes, however,
no one would be allowed to reproduce.
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Selection in complex situations
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A case that illustrates a more complex relation of fitness to
environment is sickle-cell anemia. An allelic substitution at the
structural-gene locus for the b chain of hemoglobin results in
substitution of valine for the normal glutamic acid at chain position 6.
The abnormal hemoglobin crystallizes at low oxygen pressure, and the
red cells deform and hemolyze.
Homozygotes HbS/HbS have a severe anemia, and survivorship is low.
Heterozygotes have a mild anemia and under ordinary circumstances
exhibit the same or only slightly lower fitness than normal
homozygotes HbA/HbA.
However, in regions of Africa with a high incidence of malaria
(Plasmodium falciparum), heterozygotes (HbA/HbS) have a higher
fitness than normal homozygotes because the presence of some
sickling hemoglobin apparently protects them from the malaria.
Where malaria is absent, the fitness advantage of heterozygosity is
lost
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Testing Hardy-Weiberg equilibrium for HbA/S
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In the course of a survey conducted in an African hospital, 1000 newborn children
were typed for hemoglobin A and S, and the following genotype counts were
obtained: 778 AA, 205 AS, and 17 SS. Are these frequencies in H-W equilibrium?
Genotypes
AA
AS
SS
Total
Observed Expected
761
225
14
1000
Allele count
A
B
Tot
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1747
253
2000
Chisq
763.0
0.005
221.0
0.073
16.0
0.251
1000.0
0.328
P = 0.56664
Genotypes
AA
AB
BB
Frequency
Total
0.761
0.225
0.014
1
Allele
Frequency
A
B
Tot
0.874
0.127
1.000
The answer is: “Yes, they are; there is no evidence of significant deviation of the
observed frequecies from those expected under the H-W law”
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HWE in an adult population
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In another survey (Edington, 1957) a large sample of the Yoruba adult population
from Ibadan (Nigeria) was typed for hemoglobin A and S, with the following results:
Genotypes
AA
AS
SS
Total
Observed Expected
9365 9523.9
2.7
2993 2675.3
37.7
29
187.9
134.3
12387 12387.0
174.7
P = 0.00000
Allele count
A
B
Tot
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Chisq
21723
3051
24774
Genotypes
AA
AB
BB
Frequency
Total
0.756
0.242
0.002
1
Allele
Frequency
A
B
Tot
0.877
0.123
1.000
Deviation from HWE is now striking. What is going on? Genotype frequencies are
in HW proportion at birth, whereas a large excess of heterozygotes is observed
among adults.
We may hypothesize that homozygote deficiency is due to selection. Increased
mortality of SS homozygotes from severe anemia is obvious; less obvious is an
increased mortality of AA homozygotes.
It has been proven both by direct observation and by experiments that mortality
from malaria is higher among AA than among AS.
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Hetrozygote advantage
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We now proceed to estimate the selection coefficients against the two homozygotes
Genotypes
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Selection coefficients
9365
9523.9
0.983
wAA = 1-t = 0.983/1.119 =
0.879
AS
2993
2675.3
1.119
wmax = 1 = 1.119/1.119 =
1.000
29
187.9
12387 12387.0
0.154
wSS = 1-s = 0.154/1.119 =
0.138
Total
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Relative fitness
AA
SS
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Observed Expected Obs/Exp
t=
0.121
s=
0.862
These estimates are based on higly simplified assumptions; nevertheless, they are
remarkably close to the values required to explain this polymorphism.
In fact, if the fitness of the heterozygote is higher than that of both homozygotes, the
polymorphism is stable. Selection cause the relative frequencies of alleles to rise or
fall until they reach equilibrium with both alleles represented at high frequency in
the population.
A polymorphism such as HbA/HbS, that is maintained by selection in favor of
heterozygotes, is called a balanced polymorphism.
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Equilibrium allele frequencies for balanced polymorphisms
• We can now work out the equilibrium allele frequency of a balanced polymorphism:
Genotypes
AA
Frequency before selection
p2
Fitness
1-t
Frequency after selection p2(1-t)
AS
2pq
1
2pq
SS
q2
1-s
q2(1-s)
Total
1,00
1 - tp2 - sq2
•
After selection, the new frequency of allele HbS is therefore:
pq(tq-sp)
q2 (1-s) + pq
, from which Dq =
q’ =
1 – tp2 -sq2
1-tp2 - sq2
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Equilibrium occurs at Dq = 0, or (tp-sq)=0, from which we find:
s
t
peq=
and
qeq=
(t + s)
(t + s)
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The fact that the values estimated for theseselections coefficients are roughly similar
to those measured for the real genotypes in areas where malaria is endemic means
that the observed allele frequencies may be near their equilibrium values.
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