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Population Genetics

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Title: Population Genetics


1
Population Genetics
2
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

3
Species
  • Different species do NOT exchange genes by
    interbreeding
  • Different species that interbreed often produce
    sterile or less viable offspring e.g. Mule

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
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
Modern Synthesis Theory
  • Todays 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

8
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)

9
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

10
Allele Frequencies Define Gene Pools
500 flowering plants
480 red flowers
20 white flowers
320 RR
160 Rr
20 rr
As there are 1000 copies of the genes for color,
the allele frequencies are (in both males and
females) 320 x 2 (RR) 160 x 1 (Rr) 800 R
800/1000 0.8 (80) R 160 x 1 (Rr) 20 x 2 (rr)
200 r 200/1000 0.2 (20) r
11
Gene Pools
  • A populations gene pool is the total of all
    genes in the population at any one time. 
  • Each allele occurs with a certain frequency (.01
    1).

12
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 Hardy-Weinberg equilibrium.

13
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
  •                        
  • .

14
Sources of genetic variation(Disruption of H-W
law)
  • Mutations- if alleles change from one to
    another, this will change the frequency of those
    alleles
  • 2. Genetic recombination - crossing over
    independent assortment
  • 3. Migration- immigrants can change the
    frequency of an allele by bringing in new alleles
    to a population.
  • - emigrants can change allele frequencies by
    taking alleles out of the population

15
Sources of genetic variation(Disruption of H-W
law)
  • 4. Genetic Drift- small populations can have
    chance fluctuations in allele frequencies (e.g.,
    fire, storm).
  • - bottleneck founder effect
  • 5. 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.

16
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
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19
  • 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
  • Natural selection (1 2 are most important)
  • Gene flow
  • Mutation

20
  • 1) Genetic drift
  • Genetic drift the alteration of the gene pool
    of a small population due to chance.
  • Two factors may cause genetic drift
  •                                     
  • 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.
  • Founder effect may lead to reduced variability
    when a few individuals from a large population
    colonize an isolated habitat.

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23
Yes, I realize that this is not really a cheetah.
24
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.  
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4) Mutation                                    
Mutation is a change in an organisms 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.
27
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 individuals phenotype e.g., the
hydrangea we saw before, and Map butterflies
(color changes are due to seasonal difference in
hormones).
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  • 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.

30
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.
31
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.
32
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?
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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.
35
  • 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).

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  • 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.)

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Neutral variation is genetic variation that
results in no competitive advantage to any
individual.                                    
- Example  human fingerprints.
41
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,
42
  • b.  Relative fitness
  • - Contribution of a genotype to the next
    generation, compared to the contributions of
    alternative genotypes for the same locus.
  • Survival doesnt 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.

43
Directional selection
44
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.
45
Diversifying selection
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  • 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.           

48
All asexual individuals are female (blue). With
sex, offspring half female/half male. Because
males dont reproduce, the overall output is
lower for sexual reproduction.
49
  • 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.

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52
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.
53
Genes Within Populations
  • Chapter 21

54
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.

55
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

56
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

57
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.

58
Hardy-Weinberg Equilibrium
Population of cats n100 16 white and 84
black bb white B_ black
Can we figure out the allelic frequencies of
individuals BB and Bb?
59
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

60
Hardy-Weinberg Principle
  • Calculate genotype frequencies with a binomial
    expansion
  • (pq)2 p2 2pq q2
  • p2 individuals homozygous for first allele
  • 2pq individuals heterozygous for alleles
  • q2 individuals homozygous for second allele

61
Hardy-Weinberg Principle
  • p2 2pq q2
  • and
  • pq 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 v.16
    q0.4
  • 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

62
Hardy-Weinberg Equilibrium
63
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

64
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.

65
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

66
Genetic Drift - Bottleneck Effect
67
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

68
Five Agents of Evolutionary Change
  • Selection pressures
  • avoiding predators
  • matching climatic condition
  • pesticide resistance

69
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.

70
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.

71
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.

72
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.

73
Sickle Cell and Malaria
74
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.

75
Kinds of Selection
76
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.

77
Evolution of Coloration in Guppies
78
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.

79
Evolutionary Change in Spot Number
80
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

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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
83
Describing genetic structure
  • genotype frequencies
  • allele frequencies

rr white Rr pink RR red
84
Describing genetic structure
  • genotype frequencies
  • allele frequencies

genotype frequencies
200 white 500 pink 300 red
200/1000 0.2 rr 500/1000 0.5 Rr 300/1000
0.3 RR
total 1000 flowers
85
Describing genetic structure
  • genotype frequencies
  • allele frequencies

200 rr 500 Rr 300 RR
400 r 500 r 500 R 600 R
allele frequencies
900/2000 0.45 r 1100/2000 0.55 R
total 2000 alleles
86
for a populationwith genotypes
calculate
Genotype frequencies Phenotype
frequencies Allele frequencies
100 GG 160 Gg 140 gg
87
for a populationwith genotypes
calculate
Genotype frequencies Phenotype
frequencies Allele frequencies
100/400 0.25 GG 160/400 0.40 Gg 140/400
0.35 gg
100 GG 160 Gg 140 gg
260/400 0.65 green 140/400 0.35 brown
360/800 0.45 G 440/800 0.55 g
88
another way to calculateallele frequencies
Genotype frequencies Allele frequencies
0.25 GG 0.40 Gg 0.35 gg
0.25
100 GG 160 Gg 140 gg
0.40/2 0.20
0.40/2 0.20
0.35
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
89
Population genetics Outline
What is population genetics?

Calculate
  • genotype frequencies
  • allele frequencies

Why is genetic variation important?
How does genetic structure change?
90
Genetic variation in space and time
Frequency of Mdh-1 alleles in snail colonies in
two city blocks
91
Genetic variation in space and time
Changes in frequency of allele F at the Lap
locus in prairie vole populations over 20
generations
92
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

93
Why is genetic variation important?
variation
EXTINCTION!!
no variation
94
Why is genetic variation important?
variation
no variation
95
Why is genetic variation important?
divergence
variation
NO DIVERGENCE!!
no variation
96
Natural selection
97
Natural selection
Resistance to antibacterial soap
Generation 1 1.00 not resistant 0.00
resistant
98
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!
99
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
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
Generation 3 0.76 not resistant 0.24
resistant
Generation 4 0.12 not resistant 0.88
resistant
101
Natural selection can cause populations to diverge
divergence
102
Selection on sickle-cell allele
aa abnormal ß hemoglobin sickle-cell
anemia
very low fitness
AA normal ß hemoglobin vulnerable to
malaria
intermed. fitness
Aa both ß hemoglobins resistant to
malaria
high fitness
Selection favors heterozygotes (Aa). Both alleles
maintained in population (a at low level).
103
How does genetic structure change?
  • mutation
  • migration
  • natural selection
  • genetic drift
  • non-random mating

genetic change by chance alone
  • sampling error
  • misrepresentation
  • small populations

104
Genetic drift
Before
8 RR 8 rr
After
2 RR 6 rr
105
How does genetic structure change?
  • mutation
  • migration
  • natural selection
  • genetic drift
  • non-random mating

cause changes in allele frequencies
106
How does genetic structure change?
  • mutation
  • migration
  • natural selection
  • genetic drift
  • non-random mating

mating combines alleles into genotypes
  • non-random mating
  • non-random
  • allele combinations


107
A
A
aa x aa aa
A
AA x AA AA
a
A
A
A
A
a
A
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
108
Example Coat color
  • B__ black
  • bb red
  • Herd of 200 cows
  • 100 BB, 50 Bb and 50 bb

109
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

110
  • 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

111
  • 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)

112
  • 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

113
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).

114
  • 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

115
Expected genotypic, phenotypic and allele
frequencies in the offspring?
116
Expected frequencies in offspring
  • Genotypic
  • .35 BB
  • .50 Bb
  • .15 bb
  • Phenotypic
  • .85 brown
  • .15 platinum

117
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

118
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

119
Hardy-Weinberg Theorem
  • Population gene and genotypic frequencies dont
    change over generations if is at or near
    equilibrium.

Population in equilibrium means that the
populations isnt under evolutionary forces
(Assumptions for Equilibrium)
120
Assumptions for equilibrium
  • large population (no random drift)
  • Random mating
  • no selection
  • no migration (closed population)
  • no mutation

121
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!!!!!

122
Hardy-Weinberg Theorem
  • Therefore
  • It can be used to estimate frequencies when the
    genotypic frequencies are unknown.
  • Predict frequencies on the next generation.

123
Hardy-Weinberg Theorem
  • If predicted frequencies differ from observed
    frequencies Population is not under
    Hardy-Weinberg Equilibrium.
  • Therefore the population is under selection,
    migration, mutation or genetic drift.
  • Or a particular locus is been affected by the
    forces mentioned above.

124
Hardy-Weinberg Theorem (2 alleles at 1 locus)
  • Allele freq.
  • f(A) p
  • f(a) q
  • p q 1
  • Sum of all alleles 100
  • 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

125
Hardy-Weinberg Theorem
  • Allele freq.
  • f(A) p
  • f(a) q
  • p q 1
  • Sum of all alleles 100
  • 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

Gametes A (p) a(q)
A(p) AA (pp) Aa (pq)
a(q) aA (qp) aa (qq)
AA pp p2 Aa pq qp 2pq Aa
qq q2
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Example use of H-W theorem
  • 1000-head sheep flock. No selection for color.
    Closed to outside breeding.
  • 910 white (B_)
  • 90 black (bb)

127
  • Start with known f(black) f(bb) .09 q2
  • Then, p 1 q .7 f(B)
  • f(BB) p2 .49
  • f(Bb) 2pq .42
  • f(bb) q2 .09

128
In summary
  • Allele freq.
  • f(B) p .7 (est.)
  • f(b) q .3 (est.)
  • Phenotypic freq.
  • f(white) .91 (actual)
  • f(black) .09 (actual)
  • Genotypic freq.
  • f(BB) p2 .49 (est.)
  • f(Bb) 2pq .42 (est.)
  • f(bb) q2 .09 (actual)

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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

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Forces that affect allele freq.
  • 1. Mutation
  • 2. Migration
  • 3. Selection
  • 4. Random (genetic) drift
  • Selection and migration most important for
    livestock breeders.

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Mutation
  • Change in base DNA sequence.
  • Source of new alleles.
  • Important over long time-frame.
  • Usually undesirable.

132
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.

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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.

134
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)

135
Random (genetic) drift
  • Changes in allele frequency due to random
    segregation.
  • Aa ? .5 A, .5 a gametes
  • Important only in very small pop.

136
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.

137
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?

138
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

139
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.

140
  • Genotypic Allele freq.
  • freq (HH) .2/.4 .5 f(H) .5 1/2(.5)
    .75
  • freq (Hh) .2/.4 .5 f(h) 0 1/2(.5) .25
  • freq (hh) 0
  • ? p .75 - .3 .45
  • Note more change can be made when the initial
  • frequency of desirable gene is low.

141
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.

142
  • Genotypic Allele freq.
  • f (HH) .2/.7 .2857 f(H) .2857 1/2(.2857)
    .429
  • f (Hh) .2/.7 .2857 f(h) .4286 1/2(.2857)
    .571
  • f (hh) .3/.7 .4286
  • ? p .429 - .3 .129
  • Note the higher proportion that can be culled,
    the
  • more you can change allele freq.

143
Selection Against Recessive Allele
  • Allele Freq. Genotypic Freq.
  • A a AA Aa aa
  • .1 .9 .01 .18 .81
  • .3 .7 .09 .42 .49
  • .5 .5 .25 .50 .25
  • .7 .3 .49 .42 .09
  • .9 .1 .81 .18 .01

144
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)
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