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Population Genetics
I. Basic Principles
A. Definitions:
B. Basic computations:
C. Hardy-Weinberg Equilibrium:
D. Utility
1. If no real populations can explicitly meet these assumptions, how can the
model be useful? It is useful for creating an expected model that real populations can be
compared against to see which assumption is most likely being violated.
2. Also, If HWCE is assumed and the frequency of homozygous recessives can
be measured, then the number of heterozygous carriers can be estimated.
Example:
Cystic fibrosis (cc) has a frequency of 1/2500 = 0.0004 in people of northern
European ancestry.
More than 1,000
different mutations in
the CFTR gene have
been identified in cystic
fibrosis patients. The
most common mutation
(observed in 70% of
cystic fibrosis patients)
is a three-base deletion
in the DNA sequence,
causing an absence of a
single amino acid in the
protein. = 0.0004 x 0.7 =
0.00028
Water follows salt flow by osmosis
and dilutes mucus
Example:
Cystic fibrosis (cc) has a frequency of 1/2500 = 0.0004 in people of northern
European ancestry; common allele = 0.00028.
Mucus in lungs reduces
respiration, increases
bacterial infection
In pancreas/liver,
reduces flow/efficacy of
digestive enzymes
In intestine, reduces
nutrient uptake
Example:
Cystic fibrosis (cc) has a frequency of 1/2500 = 0.0004 in people of northern
European ancestry, common allele = 0.00028
How many carriers are there?
q2 = 0.00028, so
q2 = q = 0.017.
p + q = 1, so p = 0.983
So, the frequency of heterozygous carriers for this allele = 2pq = 0.033
This calculation can only be performed if HWE is assumed.
Population Genetics
I. Basic Principles
II. Deviations from HWE
A. Mutation
II. Deviations from HWE
A. Mutation
1. Basics:
II. Deviations from HWE
A. Mutation
1. Basics:
a. Consider a population with:
f(A) = p = .6
f(a) = q = .4
II. Deviations from HWE
A. Mutation
1. Basics:
a. Consider a population with:
f(A) = p = .6
f(a) = q = .4
b. Suppose ‘A' mutates to ‘a' at a realistic rate of:
μ = 1 x 10-5
II. Deviations from HWE
A. Mutation
1. Basics:
a. Consider a population with:
f(A) = p = .6
f(a) = q = .4
b. Suppose ‘A' mutates to ‘a' at a realistic rate of:
μ = 1 x 10-5
c. Well, what fraction of alleles will change?
‘A' will decline by: μp = .6 x 0.00001 = 0.000006
‘a' will increase by the same amount.
II. Deviations from HWE
A. Mutation
1. Basics:
a. Consider a population with:
f(A) = p = .6
f(a) = q = .4
b. Suppose ‘A' mutates to ‘a' at a realistic rate of:
μ = 1 x 10-5
c. Well, what fraction of alleles will change?
‘A' will decline by: μp = .6 x 0.00001 = 0.000006
‘a' will increase by the same amount.
d. So, the new gene frequencies will be:
q1 = q + μp = .400006
p1 = p - μp = p(1-μ) = .599994
At this realistic rate, it takes thousands of generations to cause appreciable
change. Mutation is the source of new alleles, but it does not change the
frequency of alleles very much. Were the mutationists wrong?
II. Deviations from HWE
A. Mutation
1. Basics:
2. Other Considerations:
II. Deviations from HWE
A. Mutation
1. Basics:
2. Other Considerations:
- Selection:
Selection can BALANCE mutation... so a deleterious allele
might not accumulate as rapidly as mutation would predict,
because it is eliminated from the population by selection each
generation.
II. Deviations from HWE
A. Mutation
1. Basics:
2. Other Considerations:
- Selection:
- Drift:
The probability that a new allele (produced by mutation)
becomes fixed (q = 1.0) in a population = 1/2N (basically, it's
frequency in that population of diploids). In a small population,
this chance becomes measureable and likely. So, NEUTRAL
mutations have a reasonable change of becoming fixed in small
populations... and then replaced by new mutations.
II. Deviations from HWE
A. Mutation
B. Migration
1. Basics:
- Consider two populations:
p2 = 0.7
p1 = 0.2
q1 = 0.8
q2 = 0.3
II. Deviations from HWE
A. Mutation
B. Migration
1. Basics:
- Consider two populations:
p2 = 0.7
p1 = 0.2
q2 = 0.3
q1 = 0.8
suppose migrants immigrate at a rate
such that the new immigrants
represent 10% of the new population
II. Deviations from HWE
A. Mutation
B. Migration
1. Basics:
- Consider two populations:
p1 = 0.2
q1 = 0.8
p2 = 0.7
q2 = 0.3
suppose migrants immigrate at a rate
such that the new immigrants
represent 10% of the new population
II. Deviations from HWE
IMPORTANT EFFECT, BUT MAKES
POPULATIONS SIMILAR AND INHIBITS
DIVERGENCE AND ADAPTATION TO LOCAL
CONDITIONS (EXCEPT IT MAY INTRODUCE
NEW ADAPTIVE ALLELES)
A. Mutation
B. Migration
1. Basics:
- Consider two populations:
p1 = 0.2
q1 = 0.8
p(new) = p1(1-m) + p2(m)
P(new) = (0.2).9 + (0.7)0.1 = 0.25
p2 = 0.7
q2 = 0.3
suppose migrants immigrate at a rate
such that the new immigrants
represent 10% of the new population
Frequency of the ‘B’ allele of the ABO blood group locus,
largely as a result of the Mongol migrations following the
fall of the Roman Empire
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
1. Positive Assortative Mating
"like phenotype mates with like phenotype"
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
1. Positive Assortative Mating
"like phenotype mates with like phenotype"
a. Pattern:
offspring
F1
AA
Aa
aa
.2
.6
.2
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
1. Positive Assortative Mating
"like phenotype mates with like phenotype"
a. Pattern:
offspring
F1
AA
Aa
aa
.2
.6
.2
ALL AA
1/4AA:1/2Aa:1/4aa
ALL aa
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
1. Positive Assortative Mating
"like phenotype mates with like phenotype"
a. Pattern:
offspring
F1
AA
Aa
aa
.2
.6
.2
ALL AA
1/4AA:1/2Aa:1/4aa
ALL aa
.2
.15 + .3 + .15
.2
.35
.3
.35
a. Pattern:
offspring
F1
AA
Aa
aa
.2
.6
.2
ALL AA
1/4AA:1/2Aa:1/4aa
ALL aa
.2
.15 + .3 + .15
.2
.35
.3
.35
b. Effect:
- reduction in heterozygosity at this locus; increase in homozygosity.
Groth, J. 1993. Call matching and
positive assortative mating in Red
Crossbills. The Auk 110L: 398-401.
male
female
Type 2
Type 1
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
1. Positive Assortative Mating
2. Inbreeding
- reduction of heterozygosity across the entire genome, at a rate that
correlates with the degree of relatedness.
- full sibs, parent/offspring: lose 25%of heterozygosity each generation.
BigCatRescue
White tigers in the U.S. are all descendants of a brother-sister pair from
the Cincinnati Zoo. The AZA has outlawed captive breeding of white
tigers.
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
1. Positive Assortative Mating
2. Inbreeding
- reduction of heterozygosity across the entire genome, at a rate that
correlates with the degree of relatedness.
- full sibs, parent/offspring: lose 50%of heterozygosity each generation.
CAN INCREASE PROBABILITY OF DIVERGENCE BETWEEN
POPULATIONS, AND CAN ALSO BE A WAY TO PURGE
DELETERIOUS ALLELES (ALTHOUGH AT A COST TO
REPRODUCTIVE OUTPUT).
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
D. Genetic Drift - Sampling Error
1. The organisms that actually reproduce in a population may not be
representative of the genetics structure of the population; they may vary just due to
sampling error (chance).
D. Genetic Drift - Sampling Error
1. The organisms that actually reproduce in a population may not be
representative of the genetics structure of the population; they may vary just
due to sampling error (chance).
- most dramatic in small samples.
2. effects:
D. Genetic Drift - Sampling Error
1. The organisms that actually reproduce in a population may not be
representative of the genetics structure of the population; they may vary just
due to sampling error (chance).
- most dramatic in small samples.
2. effects:
1 - small pops will differ more, just by chance, from the original
population
D. Genetic Drift - Sampling Error
1. The organisms that actually reproduce in a population may not be
representative of the genetics structure of the population; they may vary just
due to sampling error (chance).
- most dramatic in small samples.
2. effects:
1 - small pops will differ more, just by chance, from the original
population
2 - small pops will vary more from one another than large populations
D. Genetic Drift - Sampling Error
1. most dramatic in small samples.
2. effects
3. circumstances when drift is very important:
D. Genetic Drift - Sampling Error
1. most dramatic in small samples.
2. effects
3. circumstances when drift is very important:
- “Founder Effect”
The Amish, a very small, close-knit
group decended from an intial
population of founders, has a high
incidence of genetic abnormalities such
as polydactyly
- “Founder Effect” and Huntington’s Chorea
HC is a neurodegenerative disorder caused by
an autosomal lethal dominant allele.
The fishing villages around Lake Maracaibo in
Venezuela have the highest incidence of
Huntington’s Chorea in the world, approaching
50% in some communities.
- “Founder Effect” and Huntington’s Chorea
HC is a neurodegenerative disorder caused by
an autosomal lethal dominant allele.
The fishing villages around Lake Maracaibo in
Venezuela have the highest incidence of
Huntington’s Chorea in the world, approaching
50% in some communities.
The gene was mapped to chromosome 4, and
found the HC allele was caused by a repeated
sequence of over 35 “CAG’s”. Dr. Nancy Wexler
found homozygotes in Maracaibo and described
it as the first truly dominant human disease
(most are incompletely dominant and cause
death in the homozygous condition).
- “Founder Effect” and Huntington’s Chorea
HC is a neurodegenerative disorder caused by
an autosomal lethal dominant allele.
The fishing villages around Lake Maracaibo in
Venezuela have the highest incidence of
Huntington’s Chorea in the world, approaching
50% in some communities.
By comparing pedigrees, she traced the
incidence to a single woman who lived 200
years ago. When the population was small, she
had 10 children who survived and reproduced.
Folks with HC now trace their ancestry to this
lineage. Also a nice example of “coalescence” –
convergence of alleles on a common ancestral
allele.
D. Genetic Drift - Sampling Error
1. most dramatic in small samples.
2. effects
3. circumstances when drift is very important:
- “Founder Effect”
- “Bottleneck”
- “Genetic Bottleneck”
If a population crashes (perhaps as the result of a plague) there will be both
selection and drift. There will be selection for those resistant to the disease
(and correlated selection for genes close to the genes conferring resistance),
but there will also be drift at other loci simply by reducing the size of the
breeding population.
European Bison, hunted
to 12 individuals, now
number over 1000.
Cheetah have very
low genetic diversity,
suggesting a severe
bottleneck in the
past. They can even
exchange skin grafts
without rejection.
Fell to 100’s in the 1800s,
now in the 100,000’s
II. Deviations from HWE
A. Mutation
B. Migration
C. Non-Random Mating
D. Genetic Drift - Sampling Error
E. Selection