Population Genetics

1
Population Genetics
2
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

3
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

4
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
  

5
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

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Modern Evolutionary Thought
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Modern Synthesis Theory

• Combines Darwinian selection and Mendelian
  inheritance
  
• Population genetics - study of genetic variation
  within a population
  
• Emphasis on quantitative characters

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Modern Synthesis Theory

• 1940s comprehensive theory of evolution (Modern
  Synthesis Theory)
  
• Introduced by Fisher Wright
• Until then, many did not accept that Darwins
  theory of natural selection could drive evolution

S. Wright
A. Fisher
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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

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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)

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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 fe
males) 320 x 2 (RR) 160 x 1 (Rr) 800 R 8
00/1000 0.8 (80) R 160 x 1 (Rr) 20 x 2 (rr)
200 r 200/1000 0.2 (20) r
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Population - a localized group of individuals of
the same species.  Species - a group of populati
ons 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.
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A populations gene pool is the total of all
genes in the population at any one time.
  If all members of a population are homozygous f
or a particular allele, then the allele is fixed
in the gene pool.
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• 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. 
  
• Deviation from H-W equilibrium usually results in
  evolution.
  
• Understanding a non-evolving population, helps us
  to understand how evolution occurs.

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Assumptions of the H-W Theorem
- Large population size small populations can
have chance fluctuations in allele frequencies
(e.g., fire, storm). - No migration immigrants
can change the frequency of an allele by bringing
in new alleles to a population.
- No net mutations if alleles change from one
to another, this will change the frequency of
those alleles. - Random mating if certain trait
s are more desirable, then individuals with those
traits will be selected and this will not allow
for random mixing of alleles. - No natural select
ion 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.
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Hardy-Weinberg Equilibrium                       
              The gene pool of a non-evolving pop
ulation 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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• 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

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• 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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Yes, I realize that this is not really a cheetah.
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2) Natural selection                            
         As previously stated, differential succ
ess in reproduction based on heritable traits
results in selected alleles being passed to
relatively more offspring (Darwinian
inheritance). The only agent that results in ad
aptation 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 offs
pring, and immediately affect the composition of
the gene pool. The original source of variation
.
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Genetic Variation, the Substrate for Natural
Selection             Genetic (heritable) varia
tion 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 seaso
nal difference in hormones).
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Variation within populations Most variations occ
ur 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 o
f two or more forms of a character, in high
frequencies, within a population.  Applies only
to discrete characters.
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Variation between populations Geographic variat
ions are differences between gene pools due to
differences in environmental factors. 
Natural selection may contribute to geographic v
ariation.  It often occurs when populations ar
e located in different areas, but may also occur
in populations with isolated individuals.
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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.
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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 tend
s to increase with increasing latitude. Can you
think of a reason for the birds to evolve
differently?   Example Height variation in yar
row 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.  N
ew 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 chan
ging 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.
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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 het
erozygotes.   b.  Balanced polymorphism is the a
bility 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.
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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 define
d in two ways                         a.  Darw
inian fitness- Contribution of an individual to
the gene pool, relative to the contributions of
other individuals. And,
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• 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.

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Directional selection
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Diversifying selection favors extreme over
intermediate phenotypes.  - Occurs when environme
ntal change favors an extreme phenotype.
  Stabilizing selection favors intermediate over
extreme phenotypes.  - Reduces variation and main
tains the current average. - Example human bir
th weights.
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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.           

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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.
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• 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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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 compromis
es. (Humans are athletic due to flexible limbs,
which often dislocate or suffer torn ligaments.)
  c.  Not all evolution is adaptive. Chance prob
ably 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.
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Genes Within Populations

• Chapter 21

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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.

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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

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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

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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.

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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?
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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

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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

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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

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Hardy-Weinberg Equilibrium
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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

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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.

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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

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Genetic Drift - Bottleneck Effect
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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

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Five Agents of Evolutionary Change

• Selection pressures
• avoiding predators
• matching climatic condition
• pesticide resistance

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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.

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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.
  

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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.

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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.

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Sickle Cell and Malaria
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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.

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Kinds of Selection
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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.

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Evolution of Coloration in Guppies
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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.

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Evolutionary Change in Spot Number
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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 ca
n interbreed
Patterns of genetic variation in populations
Changes in genetic structure through time
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Describing genetic structure

• genotype frequencies
• allele frequencies

rr white Rr pink RR r
ed

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Describing genetic structure

• genotype frequencies
• allele frequencies

genotype frequencies
200 white 500 pink 300 r
ed

200/1000 0.2 rr 500/1000 0.5 Rr 300/1000 0
.3 RR
total 1000 flowers
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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
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for a populationwith genotypes
calculate
Genotype frequencies Phenotype frequencies
Allele frequencies
100 GG 160 Gg 140 gg
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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
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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
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Population genetics Outline
What is population genetics?

Calculate

• genotype frequencies

• allele frequencies

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

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Why is genetic variation important?
variation
EXTINCTION!!
no variation
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Why is genetic variation important?
variation
no variation
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Why is genetic variation important?
divergence
variation
NO DIVERGENCE!!
no variation
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Natural selection
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Natural selection
Resistance to antibacterial soap
Generation 1 1.00 not resistant
0.00 resistant
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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!
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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
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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
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Natural selection can cause populations to diverg
e
divergence
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Selection on sickle-cell allele
aa abnormal ß hemoglobin sickle-cell a
nemia
very low fitness
AA normal ß hemoglobin vulnerable to m
alaria
intermed. fitness
Aa both ß hemoglobins resistant to mal
aria
high fitness
Selection favors heterozygotes (Aa).
Both alleles maintained in population (a at low
level).
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How does genetic structure change?

• mutation
• migration
• natural selection
• genetic drift
• non-random mating

genetic change by chance alone

• sampling error

• misrepresentation
• small populations

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Genetic drift
Before
8 RR 8 rr
After
2 RR 6 rr
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How does genetic structure change?

• mutation
• migration
• natural selection
• genetic drift
• non-random mating

cause changes in allele frequencies
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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

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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 A
a 2(0.8 x0.2) 0.32
aa 0.2 x 0.2 0.04
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Example Coat color

• B__ black
• bb red
• Herd of 200 cows
• 100 BB, 50 Bb and 50 bb

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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

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• 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

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• 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)

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• 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

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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).

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• 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

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Expected genotypic, phenotypic and allele
frequencies in the offspring?
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Expected frequencies in offspring

• Genotypic
• .35 BB
• .50 Bb
• .15 bb

• Phenotypic
• .85 brown
• .15 platinum

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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

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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

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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)
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Assumptions for equilibrium

• large population (no random drift)
• Random mating
• no selection
• no migration (closed population)
• no mutation

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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!!!!!

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Hardy-Weinberg Theorem

• Therefore
• It can be used to estimate frequencies when the
  genotypic frequencies are unknown.
  
• Predict frequencies on the next generation.

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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.

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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

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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

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)

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• 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

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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.

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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.

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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)

136
Random (genetic) drift

• Changes in allele frequency due to random
  segregation.
  
• Aa ? .5 A, .5 a gametes
• Important only in very small pop.

137
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.

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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?

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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

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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.

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• 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.

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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.

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• 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.

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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

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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)