Genetic analysis of population
Definitions
Population,a group of interbreeding individuals
Genotypic frequency,The frequency of a specific
genotype in a given population (AA,Aa,aa)
Allele frequency,The frequency of a specific
allele within a given population
Gene pool,The collective gene frequencies of a
specific population
Genetic variation
Changes in the DNA sequence of a gene produce
genetic variation.
Experiments indicate all natural populations contain
a great deal of genetic variation.
Genotype and allele frequencies
Genotype and allele frequencies are the
“genotype” of a population,
Frequencies of three genotypes,
AA (100) Aa (250) aa (50)
f(AA) = #AA/total = 100/400 =,250 (P)
f(Aa) = #Aa/total = 250/400 =,625 (H)
f(aa) = #aa/total = 50/400 =,125 (Q)
Allele frequencies
Allele frequencies are used to describe populations.
Frequencies of alleles of one gene:
AA (100) Aa (250) aa (50)
p = f(A) = (2AA + Aa)/ 2total = (200 + 250)/800
=,5625
q = f(a) = (2aa + Aa)/ 2total = (100 + 250)/800
=,4375
p + q = 1
Hardy-Weinberg Law
Assumptions:
Infinitely large population
Random mating
No mutation,migration,selection
In an ideal population the allele and genotype
frequencies do not change from generation to
generation.
The genotype frequencies can be described by the
equation:
p2 + 2pq + q2 = 1
Using Hardy-Weinberg
Is the following population in Hardy-Weinberg
equilibrium?
MM 345 MN 490 NN 165
(1) What are the allele frequencies?
(2) What are the expected genotype frequencies?
(3) Is the difference significant?
Another example,An population starts with 250 MM
and 150NN individuals,what will be the genotype
and allele frequencies at equilibrium?
Allele frequencies =
p = f(M) =
q = f(N) =
Genotype frequencies =
p2 = 2pq = q2 =
In a population of 1000 individuals how many will be
of each genotype?
MM = MN = NN =
Calculation of allele frequencies
of recessive traits
The allele frequency can be calculated using
the fraction of homozygous recessive individuals in the
population.
Example:
Albinos are present in the population at a frequency of 1
in 20,000,What is heterozygote frequency?
q = 1/20,000,therefore q = 1/141
p = 140/141
heterozygous = 2(1/141 x 140/141) = 1/71
1/71 x 1/71 x 1/4 = 1/20,000,therefore most
births are from matings of heterozygous.
2
External forces can affect Hardy-Weinberg
equilibrium
A Hardy-Weinburg equilibrium population has no
mutation,migration,sampling error (genetic drift),or
selection,All of these can change the allele frequencies
in the next generation.
How do these forces change allele frequencies,and
which have major effects on real populations?
Mutation
Mutations are the source of new alleles.
p = frequency of A q = frequency of a
A -> a = forward mutation,rate = u
a -> A = reverse mutation,rate = v
up = number of new a alleles
vq = number of new A alleles
p = vq - up,q = up - vq
Migration,gene flow
Natural populations are not
closed.
Migration between two
populations can change allele
frequencies.
ex,(A)p1 = 0.8,(A)p2 = 0.5
migration from p1 to p2
produces a new population
with p3 = mp1 + (1-m)p2
What is p3 if m = 0.2?
Population 1
f(A) = p1
Population 2
f(A) = p2
1-m
f(A) = p2
Population 3
m
f(A) = p1
m
The new frequency is:
p3 = mp1 + (1-m)p2
p3 = 0.2 (0.8) + (1- 0.2) 0.5 = 0.56
The rate of change depends on the rate of mating
between p1 and p2.
Migration eventually produces new equilibrium
allele frequencies if random mating occurs between
the two populations.
Gene Flow
Gene flow distributes
new alleles
throughout the
population.
Restricting gene flow
can lead to formation
of new species.
Speciation
Mechanisms that block gene flow are
reproductive isolating mechanisms
(RIM).
RIMs lead to genetically distinct
subpopulations.
Accumulation of enough genetic
differences produces new species.
RIM may be genetic (inversions,
translocations) or physical.
Selection
Natural or artificial selection results from differences in
reproductive fitness.
All organisms produce more offspring than survive
Organisms differ in their ability to survive
Favored genotypes are selected and reproduce
Direct selection of a bacterial strain for antibiotic resistance is
an example of survival of mutant offspring.
Similarly,diploid organisms can be selected for by the presence
of insecticides,fungacides,etc.
The selective disadvantage of a disfavored genotype is called
the selection coefficient,and varies from 0 to 1,where 1
represents the most disfavored,Fitness varies from 1 to 0,
where 1 represents the most fit.
Hbs
In an area of
high malaria
infestation the
heterozygotes
for Hbs have a
selective
advantage.
The frequency of
Hbs is high in
areas where
malaria is
common,
Selection can change a population very quickly,and can
maintain a recessive lethal allele at high frequencies.
Allele Freq,Genotype Frequencies
HbA Hbs HbAHbA HbAHbs HbsHbs
p0,99,01,98,02,0001
p1,91,09,83,16,008
p2,67,33,45,44,11
p3,55,45,30,50,20
p4,53,47,28,50,22
Neutral Alleles
If an allele is selectively neutral,it’s frequency will
change by chance from generation to generation,
Genetic Drift leads to
fixation
Genetic drift can lead
to fixation of one
allele,
400 populations of 8
individuals,with a =
0.5 and A = 0.5,Most
populations were fixed
for one allele after 32
generations.
Inbreeding co-efficiency
Defined as the percentage of homozygousity due to
common ancesters
Brother and sister mating?
First cousin 1/16
Problem
A recessive genetic disease happens around
1/1,000,000,What will be the disease frequency for a
first cousin marriage?
Analyzing the quantitative variation of
multifactorial traits
Quantitative Traits and Polygenic Inheritance
Quantitative traits
Continuous traits (quantitative) individuals vary in the
quantity of the characteristic.
ex,Length of ear in corn.
ex,Height in humans
Discontinuous traits (qualitative) individuals have
qualitative phenotypic differences.
ex,Eye color in Drosophila,white vs red.
ex,Seed shape in peas,round vs wrinkled.
Quantitative traits show a characteristic,Non-Mendelian
pattern of inheritance.
F2
Qualitative
(Mendelian)
Quantitative
P
F1
1/4 3/4
Are quantitative traits controlled by Mendelian genes?
X X
Nilsen Ehle,polygenic hypothesis
Red kernel wheat
crossed with white
kernel produces an
intermediate F1.
The F2 show a range of
colors.
Conclusion,color is a
polygenic trait.
X
1/64 6/64 20/64 15/64 1/64
P
F1
F2
15/ 64 6/64
Phenotypes for quantitative traits are measured in
populations
Samples are taken from
a population.
The phenotype of each
individual in the sample
is measured.
The results can be
shown as a frequency
distribution.
Fig 5.6
Describing a quantitative trait
Phenotype is measured in terms of the mean and
variance of the frequency?x/n
variance = S2= V = a numerical measure of the range:
(x - x)2
n - 1
standard deviation = s = V?
Analysis of Variance
The variance is equal to the sum of its components.
The phenotypic variance of a quantitative trait has two
components,Vp = Vg + Ve
phenotypic variance = genotypic variance + environmental
variance.
Heritability
h2 = heritability = VG / Vp
Heritability indicates how much of the variance is caused
by genetic differences.
organism trait Heritability
Humans stature 0.65
IQ 0.7 -,80
Cattle milk yield 0.35
body weight 0.65
pigs back-fat thickness 0.70
poultry egg weight 0.50
egg production 0.10
frog size 0.69
development rate 0.31
Examples of heritability
Selection for a trait in a population
Repeated
selection for a
specific
phenotype in a
population is
possible if
genetic
variation
exists,and the
trait is
governed by
multiple genes,
Selection differential and response to selection
Heritabity can be calculated from selection
experiments,
Selection response (R) = h2 X selection differential
(S)
h2 = R/S
X P
O
R
s
X = old
population
P = parents
O = offspring
Heritability can be calculated from selection experiments
Ex,Two fish with a length of 25 cm are crossed,These
are from a population with a mean length of 16 cm,
The F1 have a mean length of 22.8 cm,
What is h2 for this trait in this population?
S = selection differential =
R = response to selection =
h2 =
25
16
22.8
R
s
Heterosis
Hybrid corn was
first utilized in the
early part of the
last century,
Corn yields have
gone from 40
bu/acre to 140
bu/acre.
Four highly
inbred lines are
crossed,and the
two hybrids are
crossed to give a
double cross
hybrid,
X
XXParents
Single cross
hybrid
Double cross
hybrid
Definitions
Population,a group of interbreeding individuals
Genotypic frequency,The frequency of a specific
genotype in a given population (AA,Aa,aa)
Allele frequency,The frequency of a specific
allele within a given population
Gene pool,The collective gene frequencies of a
specific population
Genetic variation
Changes in the DNA sequence of a gene produce
genetic variation.
Experiments indicate all natural populations contain
a great deal of genetic variation.
Genotype and allele frequencies
Genotype and allele frequencies are the
“genotype” of a population,
Frequencies of three genotypes,
AA (100) Aa (250) aa (50)
f(AA) = #AA/total = 100/400 =,250 (P)
f(Aa) = #Aa/total = 250/400 =,625 (H)
f(aa) = #aa/total = 50/400 =,125 (Q)
Allele frequencies
Allele frequencies are used to describe populations.
Frequencies of alleles of one gene:
AA (100) Aa (250) aa (50)
p = f(A) = (2AA + Aa)/ 2total = (200 + 250)/800
=,5625
q = f(a) = (2aa + Aa)/ 2total = (100 + 250)/800
=,4375
p + q = 1
Hardy-Weinberg Law
Assumptions:
Infinitely large population
Random mating
No mutation,migration,selection
In an ideal population the allele and genotype
frequencies do not change from generation to
generation.
The genotype frequencies can be described by the
equation:
p2 + 2pq + q2 = 1
Using Hardy-Weinberg
Is the following population in Hardy-Weinberg
equilibrium?
MM 345 MN 490 NN 165
(1) What are the allele frequencies?
(2) What are the expected genotype frequencies?
(3) Is the difference significant?
Another example,An population starts with 250 MM
and 150NN individuals,what will be the genotype
and allele frequencies at equilibrium?
Allele frequencies =
p = f(M) =
q = f(N) =
Genotype frequencies =
p2 = 2pq = q2 =
In a population of 1000 individuals how many will be
of each genotype?
MM = MN = NN =
Calculation of allele frequencies
of recessive traits
The allele frequency can be calculated using
the fraction of homozygous recessive individuals in the
population.
Example:
Albinos are present in the population at a frequency of 1
in 20,000,What is heterozygote frequency?
q = 1/20,000,therefore q = 1/141
p = 140/141
heterozygous = 2(1/141 x 140/141) = 1/71
1/71 x 1/71 x 1/4 = 1/20,000,therefore most
births are from matings of heterozygous.
2
External forces can affect Hardy-Weinberg
equilibrium
A Hardy-Weinburg equilibrium population has no
mutation,migration,sampling error (genetic drift),or
selection,All of these can change the allele frequencies
in the next generation.
How do these forces change allele frequencies,and
which have major effects on real populations?
Mutation
Mutations are the source of new alleles.
p = frequency of A q = frequency of a
A -> a = forward mutation,rate = u
a -> A = reverse mutation,rate = v
up = number of new a alleles
vq = number of new A alleles
p = vq - up,q = up - vq
Migration,gene flow
Natural populations are not
closed.
Migration between two
populations can change allele
frequencies.
ex,(A)p1 = 0.8,(A)p2 = 0.5
migration from p1 to p2
produces a new population
with p3 = mp1 + (1-m)p2
What is p3 if m = 0.2?
Population 1
f(A) = p1
Population 2
f(A) = p2
1-m
f(A) = p2
Population 3
m
f(A) = p1
m
The new frequency is:
p3 = mp1 + (1-m)p2
p3 = 0.2 (0.8) + (1- 0.2) 0.5 = 0.56
The rate of change depends on the rate of mating
between p1 and p2.
Migration eventually produces new equilibrium
allele frequencies if random mating occurs between
the two populations.
Gene Flow
Gene flow distributes
new alleles
throughout the
population.
Restricting gene flow
can lead to formation
of new species.
Speciation
Mechanisms that block gene flow are
reproductive isolating mechanisms
(RIM).
RIMs lead to genetically distinct
subpopulations.
Accumulation of enough genetic
differences produces new species.
RIM may be genetic (inversions,
translocations) or physical.
Selection
Natural or artificial selection results from differences in
reproductive fitness.
All organisms produce more offspring than survive
Organisms differ in their ability to survive
Favored genotypes are selected and reproduce
Direct selection of a bacterial strain for antibiotic resistance is
an example of survival of mutant offspring.
Similarly,diploid organisms can be selected for by the presence
of insecticides,fungacides,etc.
The selective disadvantage of a disfavored genotype is called
the selection coefficient,and varies from 0 to 1,where 1
represents the most disfavored,Fitness varies from 1 to 0,
where 1 represents the most fit.
Hbs
In an area of
high malaria
infestation the
heterozygotes
for Hbs have a
selective
advantage.
The frequency of
Hbs is high in
areas where
malaria is
common,
Selection can change a population very quickly,and can
maintain a recessive lethal allele at high frequencies.
Allele Freq,Genotype Frequencies
HbA Hbs HbAHbA HbAHbs HbsHbs
p0,99,01,98,02,0001
p1,91,09,83,16,008
p2,67,33,45,44,11
p3,55,45,30,50,20
p4,53,47,28,50,22
Neutral Alleles
If an allele is selectively neutral,it’s frequency will
change by chance from generation to generation,
Genetic Drift leads to
fixation
Genetic drift can lead
to fixation of one
allele,
400 populations of 8
individuals,with a =
0.5 and A = 0.5,Most
populations were fixed
for one allele after 32
generations.
Inbreeding co-efficiency
Defined as the percentage of homozygousity due to
common ancesters
Brother and sister mating?
First cousin 1/16
Problem
A recessive genetic disease happens around
1/1,000,000,What will be the disease frequency for a
first cousin marriage?
Analyzing the quantitative variation of
multifactorial traits
Quantitative Traits and Polygenic Inheritance
Quantitative traits
Continuous traits (quantitative) individuals vary in the
quantity of the characteristic.
ex,Length of ear in corn.
ex,Height in humans
Discontinuous traits (qualitative) individuals have
qualitative phenotypic differences.
ex,Eye color in Drosophila,white vs red.
ex,Seed shape in peas,round vs wrinkled.
Quantitative traits show a characteristic,Non-Mendelian
pattern of inheritance.
F2
Qualitative
(Mendelian)
Quantitative
P
F1
1/4 3/4
Are quantitative traits controlled by Mendelian genes?
X X
Nilsen Ehle,polygenic hypothesis
Red kernel wheat
crossed with white
kernel produces an
intermediate F1.
The F2 show a range of
colors.
Conclusion,color is a
polygenic trait.
X
1/64 6/64 20/64 15/64 1/64
P
F1
F2
15/ 64 6/64
Phenotypes for quantitative traits are measured in
populations
Samples are taken from
a population.
The phenotype of each
individual in the sample
is measured.
The results can be
shown as a frequency
distribution.
Fig 5.6
Describing a quantitative trait
Phenotype is measured in terms of the mean and
variance of the frequency?x/n
variance = S2= V = a numerical measure of the range:
(x - x)2
n - 1
standard deviation = s = V?
Analysis of Variance
The variance is equal to the sum of its components.
The phenotypic variance of a quantitative trait has two
components,Vp = Vg + Ve
phenotypic variance = genotypic variance + environmental
variance.
Heritability
h2 = heritability = VG / Vp
Heritability indicates how much of the variance is caused
by genetic differences.
organism trait Heritability
Humans stature 0.65
IQ 0.7 -,80
Cattle milk yield 0.35
body weight 0.65
pigs back-fat thickness 0.70
poultry egg weight 0.50
egg production 0.10
frog size 0.69
development rate 0.31
Examples of heritability
Selection for a trait in a population
Repeated
selection for a
specific
phenotype in a
population is
possible if
genetic
variation
exists,and the
trait is
governed by
multiple genes,
Selection differential and response to selection
Heritabity can be calculated from selection
experiments,
Selection response (R) = h2 X selection differential
(S)
h2 = R/S
X P
O
R
s
X = old
population
P = parents
O = offspring
Heritability can be calculated from selection experiments
Ex,Two fish with a length of 25 cm are crossed,These
are from a population with a mean length of 16 cm,
The F1 have a mean length of 22.8 cm,
What is h2 for this trait in this population?
S = selection differential =
R = response to selection =
h2 =
25
16
22.8
R
s
Heterosis
Hybrid corn was
first utilized in the
early part of the
last century,
Corn yields have
gone from 40
bu/acre to 140
bu/acre.
Four highly
inbred lines are
crossed,and the
two hybrids are
crossed to give a
double cross
hybrid,
X
XXParents
Single cross
hybrid
Double cross
hybrid
