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Finding Variation
Gene frequency
Richard Lewontin
To understand evolution we must identify
changes in gene frequency within populations.
Population Genetics is the branch of Biology
explicitly concerned with gene frequencies.
• In the 1960’s, electrophoresis was first employed as a
method for examining protein diversity.
• The astounding finding of this early work was the
ubiquity of genetic diversity.
•
genetic diversity extensive: many protein alleles and high levels of
polymorphism within populations.
•
protein estimates << DNA sequence reality
PCR
Thermus aquaticus
• Polymerase Chain Reaction
technique has revolutionised
molecular biology.
–
TAQ polymerase
DNA polymerase + specific primers used to amplify specific sequence DNA
–
Thermal cycles used to melt target DNA, allow primers to attach, and then
replica of target DNA to be formed.
–
Cut the DNA with restriction enzymes & run fragments on gel.
Kary
Mullis
4
Calculating Gene Frequencies
.
• How common is CCR5-D32?
• Example: In Icelanders, 102 people were
see Table 5.3 F&H
screened for this genotype. 75 +/+; 24 +/D32;
3 D32/D32
• 204 alleles, 24 + 6 = 30 of which were D32.
• i.e., 14.7% D32 in the population.
Genetic Diversity
• Several measures exist, e.g.,
• heterozygosity (frequency of heterozygotes in a population)
• proportion of genes polymorphic
• F&H first emphasize classical allelomorph data
from protein electrophoresis.
• allozyme heterozygosity data suggest that 1/3 - 1/2 of loci
coding for enzymes are polymorphic in a typical population.
• average individual is heterozygous at 4-15% of loci.
Genetic Diversity
• Sequencing of DNA is a more direct method
• of course many changes in sequence are silent & do not
present themselves as a phenotype
• CFTR is a gene linked to cystic fibrosis.
• helps cells in lung destroy Pseudomonas aeruginosa.
• over 500 different loss of function mutants found in screen
of 30 000 chromosomes of CF-sufferers.
• an example of how dozens or hundreds of alleles may be
typical for a given locus.
•
•
neutralists maintain that most alleles are equivalent; diversity results from genetic drift.
selectionists argue that forces like shifting NS, heterozygote advantage, frequencydependence (advantage to being rare) supports variation.
Genes in Populations
Loss-of-function mutations in the human CFTR gene
Godfrey
Hardy
the
equilibrium
principle
Wilhelm
Weinberg
“A fundamental principle in population genetics stating that
the genotype frequencies and gene frequencies of a large,
randomly mating population remain constant providing
that mutation, immigration, and selection do not take
place” -- American Heritage Dictionary
SCIENCE
JULY 10, 1908
DISCUSSION AND CORRESPONDENCE
Mendelian Proportions in a Mixed Population
To The Editor of Science: I am reluctant to intrude
in a discussion concerning matters of which I have
no expert knowledge, and I should have expected
the very simple point which I wish to make to have
been familiar to biologists. However, some
remarks of Mr. Udny Yule, to which Mr. R. C.
Punnett has called my attention, suggest that it
may still be worth making.
In the Proceedings of the Royal Society of
Medicine (Vol I., p. 165) Mr. Yule is reported to
have suggested, as a criticism of the Mendelian
position, that if brachydactyly is dominant “in the
course of time one would expect, in the absence of
counteracting factors, to get three brachydactylous
persons to one normal.”
It is not difficult to prove, however, that such an
expectation would be quite groundless. Suppose
that Aa is a pair of Mendelian characters, A being
dominant, and that in any given generation the
numbers of pure dominants (AA), heterozygotes
(Aa), and pure recessives (aa) are as p:2q:r.
Finally, suppose that the numbers are fairly large,
so that the mating may be regarded as random,
that the sexes are evenly distributed among the
three varieties, and that all are equally fertile. A
little mathematics of the multiplication-table type
is enough to show that in the next generation the
numbers will be as
2
2
(p + q) : 2(p + q)(q + r) : (q + r) ,
or as p1:2q1:r1, say.
The interesting question is – in what circumstances will this distribution be the same as that in
the generation before? It is easy to see that the
condition for this is q2 = pr. And since q = p1r1,
whatever the values of p, q, and r may be, the
distribution will in any case continue unchanged
after the second generation.
Suppose, to take a definite instance, that A is
brachydactyly, and that we start from a population
of pure brachydactylous and pure normal persons,
say in the ratio of 1:10,000. Then p = 1, q = 0, r =
10,000 and p1 = 1, q1 = 10,000, r1 = 100,000,000.
If brachydactyly is dominant, the proportion of
brachydactylous persons in the second generation
is 20,001:100,020,001, or practically 2:10,000,
twice that in the first generation; and this
proportion will afterwards have no tendency
whatever to increase. If, on the other hand,
brachydactyly were recessive, the proportion in the
second generation would be 1:100,020,001, or
N. S. Vol. XXVIII:49-50
Allele vs. Genotype
practically 1:100,000,000, and this proportion
would afterwards have no tendency to decrease.
In a word, there is not the slightest foundation
for the idea that a dominant character should show
a tendency to spread over a whole population, or
that a recessive should tend to die out.
I ought perhaps to add a few words on the effect
of the small deviations from the theoretical proportions which will, of course, occur in every generation. Such a distribution as p1:2q1:r1, which
satisfies the condition q = p1r1, we may call a
stable distribution. In actual fact we shall obtain in
the second generation not p1:2q1:r1 but a slightly
different distribution p:2q:r, which is not “stable.”
This should, according to theory, give us in the
third generation a “stable” distribution p2:2q2:r2,
also differing from p1:2q1:r1; and so on. The sense
in which the distribution p1:2q1:r1 is “stable” is
this, that if we allow for the effects of casual
deviations in any subsequent generation, we
should, according to theory, obtain at the next
generation a new “stable” distribution differing but
slightly from the original distribution.
I have, of course, considered only the very simplest hypotheses possible. Hypotheses other that
[sic] that of purely random mating will give
different results, and, of course, if, as appears to be
the case sometimes, the character is not
independent of that of sex, or has an influence on
fertility, the whole question may be greatly
complicated. But such complications seem to be
irrelevant to the simple issue raised by Mr. Yule’s
remarks.
G. H. Hardy
Trinity College, Cambridge,
April 5, 1908
A
a
A
AA
Aa
a
aA
aa
Allele
frequencies
a=0.5
A=0.5
Genotype
frequencies
aa=0.25
Aa=0.50
AA=0.25
P. S. I understand from Mr. Punnett that he
has submitted the substance of what I have said
above to Mr. Yule, and that the latter would accept
it as a satisfactory answer to the difficulty that he
raised. The “stability” of the particular ratio 1:2:1
is recognized by Professor Karl Pearson (Phil.
Trans. Roy. Soc. (A), vol. 203, p. 60).
Reprinted from
Hardy, G. H. 1908. Mendelian proportions in a mixed
population, Science, N. S. Vol. XVIII:49-50. (letter to
the editor)
Available from: Electronic Scholarly Publishing
http://www.esp.org
A
a
A
AA
Aa
a
aA
aa
A
a
A
p2
pq
a
pq
q2
p = 0.6
q = 0.4
population
of zygotes
= 100
Allele
frequencies
a=0.5=q
A=0.5=p
Genotype
frequencies
AA=p2
Aa=2pq
aa=q2
p + q = 1.0
p2 = 0.36
2pq = 0.48
q2 = 0.16
p2 + 2pq + q2 = 1.0
Assume complete mixing & no mate choice.
The next generation
Using H-W
• Assume each zygote grows up, produces 10
• we may use the H-W principle to determine if
gametes and mates randomly.
the population is in equilibrium.
• AA = 36 x 10 = 360
• Aa = 48 x 10 = 480
• aa = 16 x 10 = 160
• The frequency of A = 360 + 1/2*480 = 600/1000 =
0.6
• count allele (gene) frequencies
• calculate expected genotype frequencies
• compare observed number of homozygotes
with expected number.
• The frequency of A = 160 + 1/2*480 = 400/1000 =
0.4
Human Blood Groups
Human Blood Groups
African
American
Obs.
Exp. %
Exp. #
MM
MN
NN
79
138
61
!
278
Euro.
American
freq.
M
0.532
freq.
N
0.468
African
American
Obs.
Exp. %
Exp. #
MM
MN
NN
79
0.28
78.8
138
0.5
138.7
61
0.22
60.8
!
278
freq.
M
freq.
N
0.532
0.468
Euro.
American
Amerind
Amerind
freq. M = (79 + 0.5*138)/278 = 0.532
freq. N = (61 + 0.5*138)/278 = 0.468
expected # of MM = 0.5322 * 278 = 0.28 * 278 = 78.8
expected # of NN = 0.4682 * 278 = 0.22 * 278 = 60.8
expected # of MN = 2 * 0.532 * 0.468 * 278 = 138.7
Human Blood Groups
So who cares?
MM
MN
NN
!
freq.
M
freq.
N
African
American
Obs.
Exp. %
Exp. #
79
0.28
78.8
138
0.5
138.7
61
0.22
60.8
278
0.532
0.468
Euro.
American
Obs.
Exp. %
Exp. #
1787
0.292
1787.2
3039
0.497
3044.9
1303
0.211
1296.9
6129
Amerind
Obs.
Exp. %
Exp. #
123
0.602
123.3
72
0.348
71.4
10
0.05
10.3
205
• H-W is important for three major reasons:
• practically, it serves as a null model.
Deviations from H-W equilibrium point to
interesting problems for investigation.
0.540
0.776
H-W often violated
• The interest value of the H-W calculation is
rarely predictive.
• Populations will often violate one or more of
0.460
0.224
• conceptually, it solved a major dilemma
for early population genetics: how variation
can be maintained.
Sources of Non-Equilibrium
“... the genotype frequencies and gene
frequencies of a large1, randomly mating2
population remain constant providing that
mutation3, immigration4, and selection5 do not
take place”
its assumptions.
• the mechanism of deviation generally of much greater interest
to researchers.
- deviation from equilibrium helps point out
evolution and its sources