Transcript population_genetics_unrevised

1
1
The Gene Pool
•Members of a
species can
interbreed & produce
fertile offspring
Species have a
shared gene pool
Gene pool – all of
the alleles of all
individuals in a
population
•
•
2
2
The Gene Pool
•Different species
do NOT exchange
genes by
interbreeding
Different species
that interbreed
often produce
sterile or less viable
offspring e.g. Mule
•
3
3
Populations
•A group of the
same species living
in an area
No two individuals
are exactly alike
(variations)
More Fit
individuals survive &
pass on their traits
•
•
4
4
Speciation
•Formation of new
species
•One species may
split into 2 or more
species
A species may
evolve into a new
species
Requires very long
periods of time
•
•
5
5
Modern
Evolutionary
Thought
6
Modern Synthesis Theory
• Combines Darwinian
•
•
selection and
Mendelian inheritance
Population genetics study of genetic
variation within a
population
Emphasis on
quantitative
characters
7
7
Modern Synthesis Theory
• 1940s –
•
•
comprehensive theory
of evolution (Modern
Synthesis Theory)
Introduced by Fisher
& Wright
Until then, many did
not accept that
Darwin’s theory of
natural selection could
drive evolution
S. Wright
A. Fisher
8
8
Modern Synthesis Theory
• Today’s theory on evolution
• Recognizes that GENES are responsible
for the inheritance of characteristics
• Recognizes that POPULATIONS, not
•
individuals, evolve due to natural
selection & genetic drift
Recognizes that SPECIATION usually is
due to the gradual accumulation of small
genetic changes
9
9
Microevolution
• Changes occur in gene pools due to
•
•
•
mutation, natural selection, genetic
drift, etc.
Gene pool changes cause more
VARIATION in individuals in the
population
This process is called
MICROEVOLUTION
Example: Bacteria becoming unaffected
by antibiotics (resistant)
10
10
Allele Frequencies Define Gene Pools
500 flowering plants
480 red flowers
320 RR
160 Rr
20 white flowers
20 rr
As there are 1000 copies of the genes for color,
the allele frequencies are (in both males and females):
320 x
(80%)
160 x
(20%)
2 (RR) + 160 x 1 (Rr) = 800 R; 800/1000 = 0.8
R
1 (Rr) + 20 x 2 (rr) = 200 r; 200/1000 = 0.2
r
11
11
Species & Populations
• Population - a localized group of
individuals of the same species.
• Species - a group of populations whose
•
individuals have the ability to breed and
produce fertile offspring.
Individuals near a population center are,
on average, more closely related to one
another than to members of other
populations.
12
12
13
13
Gene Pools
•A population’s gene pool is the total
of all genes in the population at any
one time.
If all members of a population are
homozygous for a particular allele,
then the allele is fixed in the gene
pool.
•
14
14
The Hardy-Weinberg Theorem
•Used to describe a non-evolving
population.
•Shuffling of alleles by meiosis and
random fertilization have no
effect on the overall gene pool.
Natural populations are NOT
expected to actually be in HardyWeinberg equilibrium.
•
15
15
The Hardy-Weinberg Theorem
•Deviation from Hardy-Weinberg
equilibrium usually results in
evolution
Understanding a non-evolving
population, helps us to understand
how evolution occurs
•
16
16
Assumptions of the H-W Theorem
1.Large population size
- small populations can have chance
fluctuations in allele frequencies (e.g., fire,
storm).
2.No migration
- immigrants can change the frequency of an
allele by bringing in new alleles to a
population.
3.No net mutations
- if alleles change from one to another, this
will change the frequency of those alleles
17
17
Assumptions of the H-W Theorem
3.Random mating
- if certain traits are more desirable,
then individuals with those traits will be
selected and this will not allow for random
mixing of alleles.
4.No natural selection
- if some individuals survive and
reproduce at a higher rate than others,
then their offspring will carry those
genes and the frequency will change for
the next generation.
18
18
Hardy-Weinberg Equilibrium
The gene pool of a non-evolving population remains
constant over multiple generations; i.e., the allele
frequency does not change over generations of time.
The Hardy-Weinberg Equation:
1.0 = p2 + 2pq + q2
where p2 = frequency of AA genotype; 2pq = frequency of
Aa plus aA genotype; q2 = frequency of aa genotype
19
19
20
20
21
21
But we know that evolution does occur within populations.
Evolution within a species/population = microevolution.
Microevolution refers to changes in allele frequencies in a
gene pool from generation to generation. Represents a
gradual change in a population.
Causes of microevolution:
1) Genetic drift
2) Natural selection (1 & 2 are most important)
3) Gene flow
4) Mutation
22
22
1) Genetic drift
Genetic drift = the alteration of the gene pool of a small
population due to chance.
Two factors may cause genetic drift:
a) Bottleneck effect may lead to reduced genetic
variability following some large disturbance that
removes a large portion of the population. The
surviving population often does not represent the
allele frequency in the original population.
b) Founder effect may lead to reduced variability when a
few individuals from a large population colonize an
isolated habitat.
23
23
24
24
25
25
*Yes, I realize that this is not really a cheetah.
26
26
2) Natural selection
As previously stated, differential success in reproduction
based on heritable traits results in selected alleles being
passed to relatively more offspring (Darwinian
inheritance).
The only agent that results in adaptation to environment.
3) Gene flow
-is genetic exchange due to the migration of fertile
individuals or gametes between populations.
27
27
28
28
4) Mutation
Mutation is a change in an organism’s DNA and is
represented by changing alleles.
Mutations can be transmitted in gametes to offspring,
and immediately affect the composition of the gene pool.
The original source of variation.
29
29
Genetic Variation, the Substrate for Natural Selection
Genetic (heritable) variation within and between
populations: exists both as what we can see (e.g., eye
color) and what we cannot see (e.g., blood type).
Not all variation is heritable.
Environment also can alter an individual’s phenotype [e.g.,
the hydrangea we saw before, and…
…Map butterflies (color changes are due to seasonal
difference in hormones)].
30
30
31
31
Variation within populations
Most variations occur as quantitative characters (e.g.,
height); i.e., variation along a continuum, usually
indicating polygenic inheritance.
Few variations are discrete (e.g., red vs. white flower
color).
Polymorphism is the existence of two or more forms of
a character, in high frequencies, within a
population. Applies only to discrete characters.
32
32
Variation between populations
Geographic variations are differences between gene pools
due to differences in environmental factors.
Natural selection may contribute to geographic variation.
It often occurs when populations are located in different
areas, but may also occur in populations with isolated
individuals.
33
33
Geographic variation
between isolated
populations of house
mice.
Normally house mice are
2n = 40. However,
chromosomes fused in
the mice in the example,
so that the diploid
number has gone down.
34
34
Cline, a type of geographic variation, is a graded variation
in individuals that correspond to gradual changes in the
environment.
Example: Body size of North American birds tends to
increase with increasing latitude. Can you think of a
reason for the birds to evolve differently?
Example: Height variation in yarrow along an altitudinal
gradient. Can you think of a reason for the plants to
evolve differently?
35
35
36
36
Mutation and sexual recombination generate genetic
variation
a. New alleles originate only by mutations (heritable only in
gametes; many kinds of mutations; mutations in functional
gene products most important).
- In stable environments, mutations often result in little or
no benefit to an organism, or are often harmful.
- Mutations are more beneficial (rare) in changing
environments. (Example: HIV resistance to antiviral drugs.)
b. Sexual recombination is the source of most genetic
differences between individuals in a population.
- Vast numbers of recombination possibilities result in
varying genetic make-up.
37
37
Diploidy and balanced polymorphism preserve variation
a. Diploidy often hides genetic variation from selection in
the form of recessive alleles.
Dominant alleles “hide” recessive alleles in heterozygotes.
b. Balanced polymorphism is the ability of natural
selection to maintain stable frequencies of at least two
phenotypes.
Heterozygote advantage is one example of a balanced
polymorphism, where the heterozygote has greater
survival and reproductive success than either homozygote
(Example: Sickle cell anemia where heterozygotes are
resistant to malaria).
38
38
39
39
Frequency-dependent selection = survival of one
phenotype declines if that form becomes too common.
(Example: Parasite-Host relationship. Co-evolution
occurs, so that if the host becomes resistant, the
parasite changes to infect the new host. Over the time,
the resistant phenotype declines and a new resistant
phenotype emerges.)
40
40
41
41
42
42
Neutral variation is genetic variation that results in no
competitive advantage to any individual.
- Example: human fingerprints.
43
43
A Closer Look: Natural Selection as the Mechanism of
Adaptive Evolution
Evolutionary fitness - Not direct competition, but instead
the difference in reproductive success that is due to many
variables.
Natural Selection can be defined in two ways:
a. Darwinian fitness- Contribution of an individual to the
gene pool, relative to the contributions of other
individuals.
And,
44
44
b. Relative fitness
- Contribution of a genotype to the next generation,
compared to the contributions of alternative genotypes
for the same locus.
- Survival doesn’t necessarily increase relative fitness;
relative fitness is zero (0) for a sterile plant or animal.
Three ways (modes of selection) in which natural selection
can affect the contribution that a genotype makes to the
next generation.
a. Directional selection favors individuals at one end of
the phenotypic range. Most common during times of
environmental change or when moving to new habitats.
45
45
Directional selection
46
46
Diversifying selection favors extreme over intermediate
phenotypes.
- Occurs when environmental change favors an extreme
phenotype.
Stabilizing selection favors intermediate over extreme
phenotypes.
- Reduces variation and maintains the current average.
- Example = human birth weights.
47
47
Diversifying selection
48
48
49
49
Natural selection maintains sexual reproduction
-Sex generates genetic variation during meiosis and
fertilization.
-Generation-to-generation variation may be of greatest
importance to the continuation of sexual reproduction.
-Disadvantages to using sexual reproduction: Asexual
reproduction produces many more offspring.
-The variation produced during meiosis greatly outweighs
this disadvantage, so sexual reproduction is here to
stay.
50
50
All asexual individuals are female (blue). With sex,
offspring = half female/half male. Because males
don’t reproduce, the overall output is lower for sexual
reproduction.
51
51
Sexual selection leads to differences between sexes
a. Sexual dimorphism is the difference in appearance
between males and females of a species.
-Intrasexual selection is the direct competition between
members of the same sex for mates of the opposite sex.
-This gives rise to males most often having secondary
sexual equipment such as antlers that are used in
competing for females.
-In intersexual selection (mate choice), one sex is choosy
when selecting a mate of the opposite sex.
-This gives rise to often amazingly sophisticated
secondary sexual characteristics; e.g., peacock feathers.
52
52
53
53
54
54
Natural selection does not produce perfect organisms
a. Evolution is limited by historical constraints (e.g., humans
have back problems because our ancestors were 4-legged).
b. Adaptations are compromises. (Humans are athletic due
to flexible limbs, which often dislocate or suffer torn
ligaments.)
c. Not all evolution is adaptive. Chance probably plays a huge
role in evolution and not all changes are for the best.
d. Selection edits existing variations. New alleles cannot
arise as needed, but most develop from what already is
present.
55
55
Genes Within
Populations
56
Gene Variation is Raw Material
Natural selection and evolutionary change
Some individuals in a population possess certain inherited
characteristics that play a role in producing more surviving
offspring than individuals without those characteristics.
The population gradually includes more individuals with
advantageous characteristics.
57
57
Gene Variation In Nature
Measuring levels of genetic variation
blood groups – 30 blood grp genes
Enzymes – 5% heterozygous
Enzyme polymorphism
A locus with more variation than can be explained by mutation is
termed polymorphic.
Natural populations tend to have more polymorphic loci than can be
accounted for by mutation.
15% Drosophila
5-8% in vertebrates
58
58
Hardy-Weinberg Principle
Population genetics - study of properties of genes in
populations
blending inheritance phenotypically intermediate (phenotypic
inheritance) was widely accepted
new genetic variants would quickly be diluted
59
59
Hardy-Weinberg Principle
Hardy-Weinberg - original proportions of genotypes in
a population will remain constant from generation to
generation
Sexual reproduction (meiosis and fertilization) alone will not
change allelic (genotypic) proportions.
60
60
Hardy-Weinberg Equilibrium
Population of cats
n=100
16 white and 84 black
bb = white
B_ = black
Can we figure out the allelic frequencies of individuals BB and Bb?
61
61
Hardy-Weinberg Principle
Necessary assumptions
Allelic frequencies would remain constant if…
population size is very large
random mating
no mutation
no gene input from external sources
no selection occurring
62
62
Hardy-Weinberg Principle
Calculate genotype frequencies with a binomial expansion
(p+q)2 = p2 + 2pq + q2
p2 = individuals homozygous for first allele
2pq = individuals heterozygous for alleles
q2 = individuals homozygous for second allele
63
63
Hardy-Weinberg
Principle
2
2
p + 2pq + q
and
p+q = 1 (always two alleles)
16 cats white = 16bb then (q2 = 0.16)
This we know we can see and count!!!!!
If p + q = 1 then we can calculate p from q2
Q = square root of q2 = q
√.16
q=0.4
p + q = 1 then p = .6 (.6 +.4 = 1)
P2 = .36
All we need now are those that are heterozygous (2pq)
(2 x .6 x .4)=0.48
.36 + .48 + .16
64
64
Hardy-Weinberg Equilibrium
65
65
Five Agents of Evolutionary Change
Mutation
Mutation rates are generally so low they have little effect on
Hardy-Weinberg proportions of common alleles.
ultimate source of genetic variation
Gene flow
movement of alleles from one population to another
tend to homogenize allele frequencies
66
66
Five Agents of Evolutionary Change
Nonrandom mating
assortative mating - phenotypically similar individuals mate
Causes frequencies of particular genotypes to differ from those
predicted by Hardy-Weinberg.
67
67
Five Agents of Evolutionary Change
Genetic drift – statistical accidents.
Frequencies of particular alleles may change by chance alone.
important in small populations
founder effect - few individuals found new population (small allelic pool)
bottleneck effect - drastic reduction in population, and gene pool size
68
68
Genetic Drift - Bottleneck Effect
69
69
Five Agents of Evolutionary Change
Selection – Only agent that produces adaptive
evolutionary change
artificial - breeders exert selection
natural - nature exerts selection
variation must exist among individuals
variation must result in differences in numbers of viable offspring
produced
variation must be genetically inherited
natural selection is a process, and evolution is an outcome
70
70
Five Agents of Evolutionary Change
Selection pressures:
avoiding predators
matching climatic condition
pesticide resistance
71
71
Measuring Fitness
Fitness is defined by evolutionary biologists as the
number of surviving offspring left in the next
generation.
relative measure
Selection favors phenotypes with the greatest fitness.
72
72
Interactions Among Evolutionary Forces
Levels of variation retained in a population may be
determined by the relative strength of different
evolutionary processes.
Gene flow versus natural selection
Gene flow can be either a constructive or a constraining force.
Allelic frequencies reflect a balance between gene flow and natural
selection.
73
73
Natural Selection Can Maintain
Variation
Frequency-dependent selection
Phenotype fitness depends on its frequency within the population.
Negative frequency-dependent selection favors rare phenotypes.
Positive frequency-dependent selection eliminates variation.
Oscillating selection
Selection favors different phenotypes at different times.
74
74
Heterozygote Advantage
Heterozygote advantage will favor heterozygotes, and
maintain both alleles instead of removing less successful
alleles from a population.
Sickle cell anemia
Homozygotes exhibit severe anemia, have abnormal blood cells, and
usually die before reproductive age.
Heterozygotes are less susceptible to malaria.
75
75
Sickle Cell and Malaria
76
76
Forms of Selection
Disruptive selection
Selection eliminates intermediate types.
Directional selection
Selection eliminates one extreme from a phenotypic array.
Stabilizing selection
Selection acts to eliminate both extremes from an array of
phenotypes.
77
77
Kinds of Selection
78
78
Selection on Color in Guppies
Guppies are found in small northeastern streams in
South America and in nearby mountainous streams in
Trinidad.
Due to dispersal barriers, guppies can be found in pools below
waterfalls with high predation risk, or pools above waterfalls
with low predation risk.
79
79
Evolution of Coloration in Guppies
80
80
Selection on Color in Guppies
High predation environment - Males exhibit drab
coloration and tend to be relatively small and
reproduce at a younger age.
Low predation environment - Males display bright
coloration, a larger number of spots, and tend to be
more successful at defending territories.
In the absence of predators, larger, more colorful fish may
produce more offspring.
81
81
Evolutionary Change in Spot Number
82
82
Limits to Selection
Genes have multiple effects
pleiotropy
Evolution requires genetic variation
Intense selection may remove variation from a population at a
rate greater than mutation can replenish.
thoroughbred horses
Gene interactions affect allelic fitness
epistatic interactions
83
83
84
84
Population genetics
• genetic structure of a population
• alleles
• genotypes
group of individuals
of the same species
that can interbreed
Patterns of genetic variation in populations
Changes in genetic structure through time
85
85
Describing genetic structure
• genotype frequencies
• allele frequencies
rr = white
Rr = pink
RR = red
86
86
Describing genetic
structure
• genotype frequencies
• allele frequencies
200 white
500 pink
genotype
frequencies:
200/1000 = 0.2 rr
500/1000 = 0.5 Rr
300 red
total = 1000 flowers
300/1000 = 0.3 RR
87
87
Describing genetic
structure
• genotype frequencies
• allele frequencies
200 rr = 400 r
500 Rr= 500 r
= 500 R
300 RR= 600 R
allele
frequencies:
900/2000 = 0.45 r
1100/2000 = 0.55 R
total = 2000 alleles
88
88
for a population
with genotypes:
calculate:
Genotype frequencies
100 GG
160 Gg
140 gg
Phenotype frequencies
Allele frequencies
89
89
for a population
with genotypes:
100 GG
160 Gg
calculate:
Genotype frequencies
260
100/400 = 0.25 GG
0.65
160/400 = 0.40 Gg
140/400 = 0.35 gg
Phenotype frequencies
260/400 = 0.65 green
140/400 = 0.35 brown
140 gg
Allele frequencies
360/800 = 0.45 G
440/800 = 0.55 g
90
90
another way to calculate
allele frequencies:
Genotype frequencies
100 GG
160 Gg
0.25 GG
0.40 Gg
0.35 gg
G 0.25
G 0.40/2 = 0.20
g 0.40/2 = 0.20
g 0.35
Allele frequencies
140 gg
360/800 = 0.45 G
440/800 = 0.55 g
OR [0.25 + (0.40)/2] = 0.45
[0.35 + (0.40)/2] = 0.65
91
91
Population genetics – Outline
 What is population genetics?
 Calculate
- genotype frequencies
- allele frequencies
Why is genetic variation important?
How does genetic structure change?
92
92
Genetic variation in space and time
Frequency of Mdh-1 alleles in snail colonies in two city blocks
93
93
Genetic variation in space and
time
Changes in frequency of allele F at the Lap locus
in prairie vole populations over 20 generations
94
94
Genetic variation in space and
time
Why is genetic variation important?
potential for change in genetic structure
• adaptation to environmental change
- conservation
•divergence of populations
- biodiversity
95
95
Why is genetic variation
important?
variation
global
warming
survival
EXTINCTION!!
no variation
96
96
Why is genetic variation
important?
variation
no variation
97
97
Why is genetic variation
important?
divergence
variation
no variation
NO DIVERGENCE!!
98
98
Natural selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant
0.00 resistant
99
99
Natural
selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant
0.00 resistant
100
100
Natural
selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant
0.00 resistant
Generation 2: 0.96 not resistant
0.04 resistant
mutation!
101
101
Natural
selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant
0.00 resistant
Generation 2: 0.96 not resistant
0.04 resistant
Generation 3: 0.76 not resistant
0.24 resistant
102
102
Natural
selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant
0.00 resistant
Generation 2: 0.96 not resistant
0.04 resistant
Generation 3: 0.76 not resistant
0.24 resistant
Generation 4: 0.12 not resistant
0.88 resistant
103
103
Natural selection can cause
populations to diverge
divergence
104
104
Selection on sickle-cell allele
HbSHbS – abnormal ß hemoglobin
very low
fitness
sickle-cell anemia
HbAHbA – normal ß hemoglobin intermed.
fitness
vulnerable to malaria
HbAHbS – both ß hemoglobins
resistant to malaria
high
fitness
Selection favors heterozygotes (HbAHbS ).
Both alleles maintained in population (HbS at low level
105
105
How does genetic structure
change?
• mutation
• migration
genetic change by chance alon
• natural selection
• genetic drift
• sampling error
• misrepresentation
• small populations
• non-random mating
106
106
Genetic drift
Before:
8 RR
0.50 R
8 rr
0.50 r
After:
2 RR
6 rr
0.25 R
0.75 r
107
107
How does genetic structure
change?
• mutation
• migration
• natural selection
cause changes in
allele frequencies
• genetic drift
• non-random mating
108
108
How does genetic structure
change?
• mutation
• migration
• natural selection
• genetic drift
mating combines alleles
into genotypes
• non-random mating
• non-random mating
non-random
allele combinations
109
109
A A A
A A a
A
A
a
A
A
0.8
A
0.8
a
0.2
AA
0.8 x 0.8
aA
0.2 x 0.8
aa xAA
aa x AA
a
0.2
Aa
0.8 x 0.2
aa
0.2 x 0.2
aa AA
allele frequencies:
A = 0.8
A = 0.2
genotype frequencies:
AA = 0.8 x 0.8 = 0.64
Aa = 2(0.8 x0.2) = 0.32
aa = 0.2 x 0.2 = 0.04
110
110
Example: Coat color
B__ = black
bb = red
Herd of 200 cows:
100 BB, 50 Bb and 50 bb
111
111
Allele frequency
No. B alleles = 2(100) + 1(50) = 250
No. b alleles = 2(50) + 1(50) = 150
Total No. = 400
Allele frequencies:
f(B) = 250/400 = .625
f(b) = 150/400 = .375
112
112
genotypic frequencies
f(BB) = 100/200 = .5
f(Bb) = 50/200 = .25
f(bb) = 50/200 = .25
phenotypic frequencies
f(black) = 150/200 = .75
f(red) = 50/200 = .25
113
113
Previous example: counted alleles to compute
frequencies. Can also compute allele frequency
from genotypic frequency.
f(A) = f(AA) + 1/2 f(Aa)
f(a) = f(aa) + 1/2 f(Aa)
114
114
Previous example, we had
f(BB) = .50, f(Bb) = .25, f(bb) = .25.
allele frequencies can be computed as:
f(B) = f(BB) + 1/2 f(Bb)
= .50 + 1/2 (.25) = .625
f(b)
= f(bb) + 1/2 f(Bb)
= .25 + 1/2 (.25) = .375
115
115
Mink color example:
B_ = brown
bb = platinum (blue-gray)
Group of females (.5 BB, .4 Bb, .1 bb) bred to
heterozygous males (0 BB, 1.0 Bb, 0 bb).
116
116
Allele frequencies among the females?
f(B) = .5 + 1/2(.4) = .7
f(b) = .1 + 1/2(.4) = .3
Allele frequencies among the males?
f(B) = 0 + 1/2(1) = .5
f(b) = 0 + 1/2(1) = .5
117
117
Expected genotypic, phenotypic and allele frequencies in
the offspring?
dams
.7 B
sires
.5 B
.5 b
________________
.35 BB
.35 Bb
.3 b
.15 Bb
.15 bb
118
118
Expected frequencies in offspring
Genotypic
Phenotypic
.35 BB
.50 Bb
.15 bb
.85 brown
.15 platinum
119
119
Allele frequencies in offspring
f(B)
= f(BB) + .5 f(Bb)
= .35 + .5(.50) = .6
f(b)
= f(bb) + .5 f(Bb)
= .15 + .5(.50) = .4
120
120
Also note: allele freq. of offspring =
average of sire and dam
f(B) = 1/2 (.5 + .7) = .6
f(b) = 1/2 (.5 + .3) = .4
121
121
Hardy-Weinberg Theorem
Population gene and genotypic frequencies don’t change
over generations it is at or near equilibrium.
Population in equilibrium means that the
populations isn’t under evolutionary forces
(Assumptions for Equilibrium*)
122
122
Assumptions for equilibrium
large population (no random drift)
Random mating
no selection
no migration (closed population)
no mutation
123
123
Hardy-Weinberg Theorem
Under these assumptions populations remains
stable over generations.
It means: If frequency of allele A in a population
is =.5, the sires and cows will generate gametes
with frequency =.5 and the frequency of allele
A on next generation will be =.5!!!!!
124
124
Hardy-Weinberg Theorem
Therefore:
It can be used to estimate frequencies when the
genotypic frequencies are unknown.
Predict frequencies on the next generation.
125
125
Hardy-Weinberg Theorem
If predicted frequencies differ from observed
frequencies Population is not under HardyWeinberg Equilibrium.
Therefore the population is under selection,
migration, mutation or genetic drift.
Or a particular locus is been affected by the
forces mentioned above.
126
126
Hardy-Weinberg Theorem
(2 alleles at 1 locus)
Allele freq.
Genotypic freq.
f(A) = p
f(a) = q
f(AA) = p2 Dominant homozygous
f(Aa) = 2 pq Heterozgous
f(aa) = q2 Recessive homozygous
p + q = 1
Sum of all alleles = 100%
p2 + 2 pq + q2 = 1
Sum of all genotypes = 100%
127
127
Hardy-Weinberg Theorem
Genotypic freq.
f(AA) = p2 Dominant homozygous
f(Aa) = 2 pq Heterozgous
f(aa) = q2 Recessive homozygous
p2 + 2 pq + q2 = 1
Sum of all genotypes = 100%
Allele freq.
f(A) = p
f(a) = q
p + q = 1
Sum of all alleles = 100%
Gametes
A(p)
a(q)
A (p)
AA
(pp)
aA
(qp)
a(q)
Aa
(pq)
aa
(qq)
AA = p*p
= p2
Aa = pq + qp = 2pq
Aa = q*q
= q2
128
128
Example use of H-W theorem
1000-head sheep flock. No selection for color. Closed
to outside breeding.
910 white (B_)
90 black (bb)
129
129
Start with known: f(black) = f(bb) = .09 =q2
q  q  .09  .3  f (b)
2
Then, p = 1 – q = .7 = f(B)
f(BB) = p2 = .49
f(Bb) = 2pq = .42
f(bb) = q2 = .09
130
130
In summary:
Allele freq.
f(B) = p = .7 (est.)
f(b) = q = .3 (est.)
Genotypic freq.
f(BB) = p2 = .49 (est.)
f(Bb) = 2pq = .42 (est.)
f(bb) = q2 = .09 (actual)
Phenotypic freq.
f(white) = .91 (actual)
f(black) = .09 (actual)
131
131
Mink example using H-W
Group of 2000 (1920 brown, 80 platinum) in
equilibrium. We know f(bb) = 80/2000 = .04 =
q2
f(b) = (q2) = .04 = .2
f(B) = p = 1- q = .8
f(BB) = p2 = .64
f(Bb) = 2pq = .32
132
132
Forces that affect allele freq.
1.
2.
3.
4.
Mutation
Migration
Selection
Random (genetic) drift
Selection and migration most important for livestock
breeders.
133
133
Mutation
Change in base DNA sequence.
Source of new alleles.
Important over long time-frame.
Usually undesirable.
134
134
Migration
Introduction of allele(s) into a population from an
outside source.
Classic example: introduction of animals into an isolated
population.
others:
new herd sire.
opening herd books.
“under-the-counter” addition to a breed.
135
135
Change in allele freq. due to migration
 pmig = m(Pm-Po) where
Pm = allele freq. in migrants
Po = allele freq. in original population
m = proportion of migrants in mixed pop.
136
136
Migration example
100 Red Angus (all bb, p0 = 0)
purchase 100 Bb (pm = .5)
 p = m(pm - po) = .5(.5 - 0) = .25
new p = p0 +  p = 0 + .25 = .25 = f(B)
new q = q0 +  q = 1 - .25 = .75 = f(b)
137
137
Random (genetic) drift
Changes in allele frequency due to random segregation.
Aa  .5 A, .5 a gametes
Important only in very small pop.
138
138
Selection
Some individuals leave more offspring than others.
Primary tool to improve genetics of livestock.
Does not create new alleles. Does alter freq.
Primary effect  change allele frequency of desirable
alleles.
139
139
Example: horned/polled cattle
100-head herd (70 HH, 20 Hh, and 10 hh).
Genotypic freq.:
f(HH) = .7, f(Hh) = .2, f(hh) = .1
Allele freq.:
f(H) = .8, f(h) = .2
Suppose we cull all horned cows. Calculate
allele and genotypic frequencies after culling?
140
140
After culling
f(HH) = .7/.9 = .778
f(Hh) = .2/.9 = .222
f(hh) = 0
f(H) = .778 + .5(.222) = .889
f(h) = 0 + .5(.222) = .111
 p = .889 - .8 = .089
141
141
2nd example
Cow herd with 20 HH, 20 Hh, and 60 hh
Initial genotypic freq.: .2HH, .2Hh, .6hh
Initial allele frequencies:
f(H) = .2 + 1/2(.2) = .3
f(h) = .6 + 1/2(.2) = .7
Again, cull all horned cows.
142
142
Genotypic
freq (HH) = .2/.4 = .5
freq (Hh) = .2/.4 = .5
freq (hh) = 0
Allele freq.
f(H) = .5 + 1/2(.5) = .75
f(h) = 0 + 1/2(.5) = .25
 p = .75 - .3 = .45
Note: more change can be made when the initial
frequency of desirable gene is low.
143
143
3rd example
initial genotypic freq. .2 HH, .2 Hh, .6 hh.
Initial allele freq. f(H) = .3 and f(h) = .7
Cull half of the horned cows.
144
144
Genotypic
f (HH) = .2/.7 = .2857
f (Hh) = .2/.7 = .2857
f (hh) = .3/.7 = .4286
Allele freq.
f(H) = .2857 + 1/2(.2857) = .429
f(h) = .4286 + 1/2(.2857) = .571
 p = .429 - .3 = .129
Note: the higher proportion that can be culled, the
more you can change allele freq.
145
145
Selection Against Recessive Allele
Allele Freq.
A
a
.1
.9
.3
.7
.5
.5
.7
.3
.9
.1
Genotypic Freq.
AA
Aa
.01
.18
.09
.42
.25
.50
.49
.42
.81
.18
aa
.81
.49
.25
.09
.01
146
146
Factors affecting response to selection
1. Selection intensity
2. Degree of dominance
(dominance slows progress)
Initial allele frequency (for a one locus)
Genetic Variability (Bell Curve)
147
147