POPULATION GENETICS

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POPULATION GENETICS

• Population Genetics is the study of genetics at
  the population level
• Mendelian Population is a group of sexually
  reproducing organisms with a close degree of
  genetic relationship
• Gene Pool is a mixture of the genetic units
  (Genes or Gametes) produced by a Mendelian
  population from which the next generation arises.
  Alleles occur in this pool
• Evolution Through events such as natural
  selection, migration, or mutation, the gene pool
  changes as new alleles enter or existing alleles
  exit the pool. These changes are the basis for
  evolution

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Probability works for individuals but how about
populations?

• You are a plant breeder and were given a field
  with 1000 plants
• 450 red, 300 pink, and 250 white
• Assuming these plants mate randomly, what will
  the proportions of these colors be in the next
  generation?

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Definitions

• Frequency
• The number (count) of an item within a population
• Example 450 red snapdragons
• Relative Frequency
• The proportion (fraction) of an item within a
  population
• Example 450 / 1000 0.45 45 red snapdragons

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What will the proportions of these colors be in
the next generation?

• How do we solve this problem?
• Determine the relative frequency of each genotype
  and allele
• relative frequency of RR x RR / individuals
  (N)
• x 450/1000 0.45
• relative frequency of RW y RW / individuals
  (N)
• y 300/1000 0.30
• relative frequency of WW z WW / individuals
  (N)
• z 250/1000 0.25
• Note x y z 1

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What will the proportions of these colors be in
the next generation?

• Calculating relative allele frequency
• Frequency of allele R p
• p(R) total of R alleles from each genotype
  divided by total of alleles (2N)
• p(R) (2 RR) ( RW) / (2N)
• p(R) (2 450) (300) / (2 1000) 0.6
• Frequency of allele W q
• q(W) total of W alleles from each genotype
  divided by sample size (N)
• q(W) (2 WW) ( RW) / (2N)
• q(W) (2 250) (300) / (2 1000) 0.4
• Note p q 1

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What have we done so far?

• Calculated the relative frequency of each
  genotype in the population (x, y, z)
• Calculated the relative frequency of each allele
  in the population (p q)
• What next?

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What will the proportions of these colors be in
the next generation?

• Now examine all possible mating types. How many
  are there?
• 3 types of male (RR, RW, WW) ? 3 types of
  female (RR, RW, WW) 9 possible crosses
• Calculate the probability each type of cross will
  occur

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Perhaps a table would be helpful...

• What is the probability that heterozygotes will
  mate?
• frequency RW males ? frequency RW females
• 0.30 ? 0.30 0.09 (this is the middle cell of
  the table)
• Therefore, mating among heterozygotes is expected
  to occur 9 of the time

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What will the proportions of these colors be in
the next generation?

• Weve calculated the probability of each mating
  type
• What next?
• We need to determine what type of offspring will
  come from each mating type
• We already know how to do this

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Probability of each genotype in the offspring

• To predict genotype frequencies in the offspring
  we use
• frequency of each mating type
• RW ? RW 0.3 ? 0.3 0.09
• frequency of offspring resulting from each mating
  type
• 25 RR, 50 RW, 25 WW

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Probability of each genotypein the offspring
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Probability of each genotypein the offspring
GENOTYPE FREQUENCY OF RESULTING OFFSPRING
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• How do we combine these? (AND or OR) is the
  question
• Probability RW male RR female AND RR male RW
  female
• Probability RW male RR female OR RR male RW
  female

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Probability of each genotypein the offspring
.25?.09.0225

• If we consider all possible matings, the
  genotypic frequencies of the offspring will be
• x(RR) 0.36
• y(RW) 0.48
• z(WW) 0.16

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What are the allele frequencies?

• p(R) (rel freq RR) 0.5 (rel freq RW)
• p(R) 0.36 (0.5 0.48) 0.6
• q(r) (rel freq WW) 0.5 (rel freq RW)
• q(W) 0.16 (0.5 0.48) 0.4
• NOTE THESE ARE THE SAME AS WE SAW IN THE PARENTS
• They are in equilibrium
• What will the relative genotypic frequencies be
  in the next generation?
• x(RR) 0.36, y(RW) 0.48, z(WW) 0.16
• Genotypic frequencies achieve equilibrium after
  one generation of random mating
• Try this yourself at home to check