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POPULATION GENETICS
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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
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?
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
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
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
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?
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
Perhaps a table would be helpful...
Females
Note: All
the cells add
up to 1!
•
•
•
•
Males
RR (0.45)
RW (0.30)
WW (0.25)
RR (0.45)
0.2025
0.1350
0.1125
RW (0.30)
0.1350
0.0900
0.0750
WW (0.25)
0.1125
0.0750
0.0625
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
What will the proportions of these
colors be in the next generation?
•We’ve 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…
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
Probability of each genotype
in the offspring
PARENTS
MATING (type) FREQUENCY
RR x RR
RR x RW
RR x WW
RW x RW
RW x WW
WW x WW
RESULTING GENOTYPE OF OFFSPRING
RR
RW
WW
Males
Females
RR (0.45)
RW (0.30)
WW (0.25)
RR (0.45)
0.2025
0.1350
0.1125
RW (0.30)
0.1350
0.0900
0.0750
WW (0.25)
0.1125
0.0750
0.0625
Probability of each genotype
in the offspring
PARENTS
MATING (type) FREQUENCY
RR x RR
0.2025
RR x RW
RR x WW
RW x RW
RW x WW
WW x WW
GENOTYPE FREQUENCY OF RESULTING OFFSPRING
RR
0.2025
RW
WW
Males
Females
RR (0.45)
RW (0.30)
WW (0.25)
RR (0.45)
0.2025
0.1350
0.1125
RW (0.30)
0.1350
0.0900
0.0750
WW (0.25)
0.1125
0.0750
0.0625
How do we combine these? (AND or OR) is the question:
1.
2.
Probability: RW male & RR female AND RR male & RW female
Probability: RW male & RR female OR RR male & RW female
OR = add the probabilities
Probability of each genotype
in the offspring
GENOTYPE FREQUENCY OF RESULTING OFFSPRING
PARENTS
MATING (type) FREQUENCY
RR
RW
WW
RR x RR
0.2025
0.2025
.135 + .135 = .27 .5.27 = .135 .5.27=.135
RR x RW
RR x WW
0.225
0.225
RW x RW
0.09
.25.09=.0225 .5.09=.045 .25.09=.0225
RW x WW
0.15
.5.15=.075 .5.15=.075
WW x WW
0.0625
0.0625
1
0.36
0.48
0.16
• 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
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