Genetic variability necessary for evolutionary success

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Why Study Populations and Gene Frequencies?

• Genetic variability necessary for
  evolutionary success
• Measuring genetic variability at many loci
  can characterize a population
• Variability of phenotypic and molecular
  traits are analyzed

Microsatelite analysis for 16 trees in a
population of pines
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Population Genetics

• For a population of individuals to succeed over
  evolutionary time, it must contain genetic
  variability, because changes in gene frequencies
  are at the heart of evolution and speciation.
• Population genetics attempts to describe how
  the frequency of the alleles which control the
  trait change over time, rather than studying the
  inheritance of a trait. To study frequency
  changes, we analyze populations rather than
  individuals.

Cheetas
D. pumilio
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What is a Population?

• A population is a local group belonging to a
  single species.
• A population is not just a group of
  individuals, but a breeding group.
• Therefore, the genetics of a population is
  concerned not only with the genetic constitution
  of the individuals but also with the transmission
  of the genes from one generation to the next.

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Genetic Variability

• One method of expressing variability is by
  analyzing the genetic data and expressing the
  data in terms of gene (or allelic) frequencies.
• The summation of all the allelic frequencies,
  for all the genes that are analyzed in a specific
  population, can be considered a characterization
  of that population and is called the gene pool.
• A population can have a wide range of allelic
  frequencies for each of the genes that are being
  considered and two populations do not necessarily
  have the same set of frequencies even though they
  are the same species.

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First Derive Genotypic Frequencies
Genotypic frequencies - describes the
distribution of genotypes in a population
Example blood type locus two alleles , M or N,
and three MM, MN, NN genotypes are possible (the
following data was collected from a single human
population) Genotye of Individuals
Genotypic Frequencies MM 1787
MM1787/61290.289 MN
3039 MN3039/61290.50 NN
1303 NN1303/61290.21
Total 6129
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Deriving Gene (or Allelic) Frequencies

• To determine the allelic frequencies we simply
  count the number of M or N alleles and divide by
  the total number of alleles.
• f(M) (2 x 1787) 3039/12,258 0.5395
• f(N) (2 x 1303) 3039/12,258 0.4605
• By convention one of the alleles is given the
  designation p and the other q. Also, p q 1.
• p0.5395 and q0.4605
• Furthermore, a population is considered by
  population geneticists to be polymorphic if two
  alleles are segregating and the frequency of the
  most frequent allele is less than 0.99.

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Deriving allelic frequencies from genotypic
frequencies
Percent Allelic
Frequencies Location MM MN NN
p q Greenland 83.5
15.6 0.90 0.913 0.087 Iceland
31.2 51.5 17.30 0.569
0.431 Let pf(M) and qf(N). Thus, pf(MM) ½
f(MN) and qf(NN) ½ f(MN).
Greenland p0.835 ½ (0.156)0.913 and q0.009
½ (0.156)0.087 Iceland p0.312 ½
(0.515)0.569 and q0.173 ½ (0.515)0.431.
Clearly the allelic frequencies vary between
these populations.
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The Hardy-Weinberg Law

• The unifying concept of population genetics
• Under certain assumptions, allele frequencies
  dont change from generation to generation
• - No selection
• - No mutations
• - No migration in or out
• - No sampling errors
• - Individuals mate at random
• Can predict genotype frequencies from allele
  frequencies

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The Hardy-Weinberg Law
The frequencies in the next generation will be
p2 for the AA genotype 2pq for
the Aa genotype, and q2 for the aa
genotype such that, p2 2pq q2 1.

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Demonstration of Hardy-Weinberg Law

• Imagine a single locus with two alleles A
  a
• In the gene pool the frequency of A is 0.7
  and a is 0.3 (note 0.7 0.3 1)
• Remember we are assuming random mating
• Imagine the results of all the matings in
  the population by calculating the probabilities
  of all the possible offspring genotypes

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Results of Matings
AA 0.7 x 0.7 0.49 Aa 0.7 x 0.3 0.21 0.3
x 0.7 0.21 0.21 0.21 0.42 aa 0.3 x 0.3
0.09 0.49 0.42 0.09 1
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Hardy-Weinberg Equilibrium

• A population in which allele frequencies
  remain constant from generation to generation
• The Hardy-Weinberg Law applies for any
  frequencies of A and a as long as they sum to 1
  and the five conditions hold
• H-Ws Five Conditions
• - Natural Selection
• - Mutations
• - Migration
• - Genetic Drift (sampling errors)
• - Mating is random

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Consequences of Hardy-Weinberg Equilibrium

• Dominant traits dont automatically increase
  in the population
• Genetic variability can be maintained
• If H-W holds, when you know the frequency of
  one allele, you can calculate the other allele
  frequencies
• Foundation of population genetics - shows
  main causes of evolution

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Testing for Equilibrium

• Violation of one of the five conditions can be
  detected if the genotypes in a population are not
  in equilibrium
• Step one determine the genotype frequencies
  (from phenotypes or DNA/protein sequences)
• Step two Calculate allele frequencies from
  genotype frequencies
• Step three Use allele frequencies to
  predict genotype frequencies - predicted
  frequencies should match p2 2pq q2 1, if in
  equilibrium

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Using Hardy-Weinberg to calculate the frequency
of heterozygotes

• If you start with the frequency of
  homozygous recessive phenotypes you can calculate
  the rest
• - Example cystic fibrosis - autosomal, recesive
  
• Affected individuals have salty skin,
  produce thick mucus in lungs and are susceptible
  to bacterial infections
• Frequency is 1/2500 or 0.0004 in Northern
  Europeans - how many are carriers?

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Cystic Fibrosis
Equation p2 2pq q2 1 Frequency
of homozygous recessives is q2 0.0004
Provided H-W rules apply we can calculate nunber
of heterozygote carriers (Aa) Frequency of
a q square root of 0.0004 or 0.02 p q
1 then 1 - q p ... 1 - 0.02 p 0.98
Heterozygotes 2pq 2(0.02)(0.98) 0.04
Carriers are 4 or 1/25 even though only 1/2500
are affected
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More than 2 Alleles

• Hardy-Weinberg law can be extended
• - e.g. 3 alleles
• Allele frequencies p q r 1
• Genotype frequencies
• (p q r)2 p2 q2 r2 2pr
  2pq 2qr 1