Introduction to Population Genetics

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Introduction to Population Genetics

• Hardy-Weinberg Equilibrium

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Darwin and Evolution

• Descent with modification
• Change over time 4 conditions that lead to
  evolution
  
• There are differences among individuals within
  populations
  
• differences are passed from parent offspring
• more offspring are born than will survive and
  reproduce.
  
• Some variants are more successful at surviving
  and/or reproducing than others
  
• If all 4 met Population is evolving.

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• Population genetics incorporates Mendelian
  Genetics into the study of Evolution
  
• The goal of population genetics is to understand
  the genetic composition of a population and the
  forces that determine and change that
  composition
• Microevolution a change in the genetic
  composition of a population

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So what exactly is a population?

• A population a group of interbreeding
  individuals of the same species living within a
  prescribed geographical area
  
• A Gene Pool the complete set of genetic
  information contained within all the individuals
  in a population

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Describing the genetic composition of a population

• Genotypic frequencies the proportion of
  individuals in a population with a given
  genotype
  
• Example Gene A with two alleles, A and a

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Genotypic frequencies
Frequency (AA) 2/10 0.2 20
Frequency (Aa) 5/10 0.5 50
Frequency (aa) 3/10 0.3 30
Note The total 1.0 or 100
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Describing the genetic composition of a population

• Allelic frequencies the proportion of alleles of
  a particular gene locus in a gene pool that are
  of a specific type
  
• Example Gene A with two alleles, A and a

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Allelic frequencies
Frequency (A) 9/20 0.45 45
Frequency (a) 11/20 0.55 55
Note The total 1.0 or 100
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Polymorphic Loci
A genetic locus is said to be polymorphic
if that locus has more than one allele occurring
at a frequency greater than 5 (for example if
for gene A, f(A) 0.06, f(a) 0.94
Most populations of insects and plants are
polymorphic at more than half of their enzyme-
encoding loci (vertebrates are somewhat less)
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Why do we have polymorphic loci?
Shouldnt dominant alleles replace
recessive ones? Shouldnt natural selection eli
minate
genetic variation?
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The Hardy-Weinberg Principle

• Allele frequencies and genotypic frequencies will
  remain constant from generation to generation as
  long as
  
• The population size is large
• Mating is random
• No mutation takes place
• There is no migration in or out of the
  population
  
• There is no natural selection
• If these conditions are met, the population is
  said to be in Hardy-Weinberg Equilibrium
  

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How does it work?-Allelic frequencies

• By convention, for a given gene the frequency of
  the dominant allele is symbolized by p, the
  frequency of the recessive allele is represented
  by q
• So for our previous example, p f(A) 0.45, q
  f(a) 0.55
  
• If these are the only two alleles for the gene in
  the population then
  
• p q 1.0

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How does it work? -Genotypic frequencies
Imagine a population in which p 0.2, q 0.8
The gene pool of this population
can be pictured as a container full
of gametes. The frequency of gametes carryin
g the A allele 0.2 The frequency of gametes
carrying the a allele 0.8
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How does it work? -Genotypic frequencies
Imagine a population in which p 0.2, q 0.8
To get a zygote/adult, we need to pull
out 2 gametes to unite them
genotype AA

Prob(A) x Prob(A)
p x p p2 0.2
x 0.2 0.04
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How does it work? -Genotypic frequencies
Imagine a population in which p 0.2, q 0.8
To get a zygote/adult, we need to pull
out 2 gametes to unite them
genotype aa

Prob(a) x Prob(a)
q x q q2 0.8
x 0.8 0.64
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How does it work? -Genotypic frequencies
Imagine a population in which p 0.2, q 0.8
To get a zygote/adult, we need to pull
out 2 gametes to unite them
genotype Aa

genotype Aa

2 x P(A) x P(a)
2 x p x q 2pq 2
x 0.2 x 0.8 0.32
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So

• For a population where p f(A) and q f(a)
• p q 1
• The frequency of the genotypes in H-W equilibrium
  will be
  
• f(AA) p2
• f(Aa) 2pq
• f(aa) q2
• Since these are all the possible genotypes
• p2 2pq q2 1

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The next generation
Generation 1 f(AA) p2 f(Aa) 2pq f(aa)
q2
Generation 1s gametes
a

gametes will be produced in their original
frequencies, p and q

a
a
a
A
A
a
a
a
a
a
a
a
A
a
a
a
A
a
a
a
Generation 2 f(AA) p2 f(Aa) 2pq f(aa)
q2
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The Hardy-Weinberg Equilibrium
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Whats the point?

• Hardy-Weinberg tells us that if certain
  conditions are met, there will be no change in
  gene frequencies-- no evolution
  
• The population size is large
• Mating is random
• No mutation takes place
• There is no migration in or out of the
  population
  
• There is no natural selection
• If one or more of these assumptions is violated,
  gene frequencies will change -- evolution occurs

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Agents of evolutionary change
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Other consequences of H-W

• Genotypic/ phenotypic frequencies depend on
  allele frequencies, not on which allele is
  dominant or recessive
  
• Example Achondroplasia gene D dwarfism, d
  normal height
  
• p f(D) 0.00005 q f(d) 0.99995
• Frequency of dwarfs p2 2pq 0.0001 (one in
  ten thousand)
  
• For rare recessive alleles, most individuals with
  the allele will be heterozygotes, and will not
  express it
  
• ExampleCystic fibrosis C normal allele, c
  cystic fibrosis
  
• p f(C) 0.978 q f(c) 0.022
• Freq. of cc individuals q2 0.00048 (1 in
  2000)
  
• Freq.of Cc individuals 2pq 0.043
  (almost 1 in 25)
  

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Lets work through some problems

• In a certain population, 28 individuals are
  genotype aa, 42 are
  
• genotype Aa, and 30 are genotype AA.
• a. What are the genotypic frequencies in this
  population?
  
• b. What are the allele frequencies in this
  population?
  
• c. What genotypic frequencies would H-W predict
  there should be
  
• given your answer to b.? Is this population in
  H-W equilibrium?
  

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Lets work through some problems

• In a certain population, 28 individuals are
  genotype aa, 42 are
  
• genotype Aa, and 30 are genotype AA.
• a. What are the genotypic frequencies in this
  population?
  
• f(aa) 28/(284230) 28/100 0.28 f(Aa)
  42/(284230) 42/100 0.42
  
• f(AA) 30/(284230) 30/100 0.30
• b. What are the allele frequencies in this
  population?
  
• q f(a) ((28x2) 42))/(2x(284230)) 98/200
  0.49
  
• p f(A) ((30x2) 42))/(2x(284230))
  102/200 0.51
  
• c. What genotypic frequencies would H-W predict
  there should be
  
• given your answer to b.? Is this population in
  H-W equilibrium?
  
• According to H-W, genotypic frequencies should
  be
  
• f(aa) q2 (0.49)2 0.24 f(Aa) 2pq 2
  x 0.49 x 0.51 0.50
  
• f(AA) p2 (0.51)2 0.26
• So, no this population is not in H-W equilibrium

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Lets work through some problems
2. In a certain population, 1 in every 2500
babies born are albino (normal pigmentation (S)
is dominant over albinism (s)).
Assume this population is in H-W equilibrium for
this gene. What is the frequency of the albino
allele in this population? What is the freq
uency of heterozygotes in this population?
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Lets work through some problems
2. In a certain population, 1 in every 2500
babies born are albino (normal pigmentation (S)
is dominant over albinism (s)).
Assume this population is in H-W equilibrium for
this gene. What is the frequency of the albino
allele in this population? f(ss) q2 1/2500
0.0004 f(s) q square root (0.0004) 0.02
(so f(S) p 1 - q 0.98) What is the freq
uency of heterozygotes in this population?
f(Ss) 2pq 2 x 0.98 x 0.02 0.0392