Download q 2 = 0.81

Population genetics and evolution
• What is evolution?
Population genetics and evolution
• What is evolution?
– Descent with modification
Population genetics and evolution
• What is evolution?
– Descent with modification
– A change in the characteristics of a population
over time
Population genetics and evolution
• What is evolution?
– Descent with modification
– A change in the characteristics of a population
over time
– A change in the frequency of genes in a
population over time
Population genetics and evolution
• Some genetics terminology
– Chromosomes…
Population genetics and evolution
Population genetics and evolution
• Some genetics terminology
– Chromosomes…
– Homologous chromosomes…
Population genetics and evolution
• Some genetics terminology
– Chromosomes…
– Homologous chromosomes…
– Locus…
Population genetics and evolution
• Some genetics terminology
–
–
–
–
Chromosomes…
Homologous chromosomes…
Locus…
Alleles…
Population genetics and evolution
• Some genetics terminology
– Alleles may be dominant and recessive
Population genetics and evolution
• Some genetics terminology
– Alleles may be dominant and recessive
– In Biston betularia, the gene for melanism is
dominant (M)
Population genetics and evolution
• Some genetics terminology
– Alleles may be dominant and recessive
– In Biston betularia, the gene for melanism is
dominant (M)
– The gene for typical color is recessive (m)
Population genetics and evolution
• Some genetics terminology
– Alleles may be dominant and recessive
– In Biston betularia, the gene for melanism is
dominant (M)
– The gene for typical color is recessive (m)
– Each individual moth has two alleles:
– MM and Mm are melanic, mm are typical
Population genetics and evolution
• Gene frequencies
– The frequency of all of the alleles at a particular
locus in a population = 100% or 1.0
Population genetics and evolution
• Gene frequencies
– The frequency of all of the alleles at a particular
locus in a population = 100% or 1.0
– If there are two alleles, the frequency of one = p
and the frequency of the other = q
Population genetics and evolution
• Gene frequencies
– The frequency of all of the alleles at a particular
locus in a population = 100% or 1.0
– If there are two alleles, the frequency of one = p
and the frequency of the other = q
– p + q = 1.0
Population genetics and evolution
• Gene frequencies
– The frequency of all of the alleles at a particular
locus in a population = 100% or 1.0
– If there are two alleles, the frequency of one = p
and the frequency of the other = q
– p + q = 1.0
– With sexual reproduction, p + q alleles in the
eggs are combined with p + q alleles in the
sperm
Population genetics and evolution
• Gene frequencies
– (p + q) x (p + q) = (p + q)2 = p2 + 2pq + q2
Population genetics and evolution
• Gene frequencies
– (p + q) x (p + q) = (p + q)2 = p2 + 2pq + q2
– In Biston betularia:
– p2 = MM, 2pq = 2Mm, q2 = mm
Population genetics and evolution
• Gene frequencies
–
–
–
–
(p + q) x (p + q) = (p + q)2 = p2 + 2pq + q2
In Biston betularia:
p2 = MM, 2pq = 2Mm, q2 = mm
The population is composed of p2 homozygous
melanic individuals, 2pq heterozygous
individuals (which are melanic), and q2
homozygous typical individuals
Population genetics and evolution
• Gene frequencies
– (p + q) x (p + q) = (p + q)2 = p2 + 2pq + q2
– In Biston betularia:
– p2 = MM, 2pq = 2Mm, q2 = mm
– Phenotype frequencies:
– Let’s say for argument’s sake that the
population consists of 81% typical individuals
and 19% melanic individuals…
Population genetics and evolution
• Gene frequencies
– If p2 = MM, 2pq = 2Mm, and q2 = mm
– And if q2 = .81, what is q, the frequency of m?
Population genetics and evolution
• Gene frequencies
– If p2 = MM, 2pq = 2Mm, and q2 = mm
– And if q2 = .81, what is q, the frequency of m?
– q = 0.9 (0.92 = 0.81)
Population genetics and evolution
• Gene frequencies
– If p2 = MM, 2pq = 2Mm, and q2 = mm
– And if q2 = .81, what is q, the frequency of m?
– q = 0.9 (0.92 = 0.81)
– What is p, the frequency of M?
Population genetics and evolution
• Gene frequencies
– If p2 = MM, 2pq = 2Mm, and q2 = mm
– And if q2 = .81, what is q, the frequency of m?
– q = 0.9 (0.92 = 0.81)
– What is p, the frequency of M?
– p = 0.1 (p + q = 1.0)
Population genetics and evolution
• Gene frequencies
– If p2 = MM, 2pq = 2Mm, and q2 = mm
– And if q2 = .81, what is q, the frequency of m?
– q = 0.9 (0.92 = 0.81)
– What is p, the frequency of M?
– p = 0.1
– p2 = 0.01 (MM), 2pq = 0.18 (Mm)
Population genetics and evolution
• Gene frequencies
– If p2 = MM, 2pq = 2Mm, and q2 = mm
– And if q2 = .81, what is q, the frequency of m?
– q = 0.9 (0.92 = 0.81)
–
–
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What is p, the frequency of M?
p = 0.1
p2 = 0.01 (MM), 2pq = 0.18 (Mm)
19% of individuals are melanic
Population genetics and evolution
• To summarize:
– Homozygous dominants = MM = p2
– Heterozygotes = Mm = 2pq
– Homozygous recessives = mm = q2
Population genetics and evolution
• What happens during reproduction?
– Meiosis separates alleles into gametes
Population genetics and evolution
• What happens during reproduction?
– Meiosis separates alleles into gametes
– Gametes bear alleles in proportion to their
frequency in the population…
Population genetics and evolution
• What happens during reproduction?
– Meiosis separates alleles into gametes
– Gametes bear alleles in proportion to their
frequency in the population…
– there are p sperm with M and q sperm with m
Population genetics and evolution
• What happens during reproduction?
– Meiosis separates alleles into gametes
– Gametes bear alleles in proportion to their
frequency in the population…
– there are p sperm with M and q sperm with m
– there are p eggs with M and q eggs with m
Population genetics and evolution
• What happens during reproduction?
– Meiosis separates alleles into gametes
– Gametes bear alleles in proportion to their
frequency in the population…
– there are p sperm with M and q sperm with m
– there are p eggs with M and q eggs with m
– Eggs and sperm combine to form zygotes…
Population genetics and evolution
• What happens during reproduction?
EGGS
SPERM
M (p = 0.1)
m (q = 0.9)
M (p = 0.1)
MM (p2 = 0.01)
Mm (pq = 0.09)
m (q = 0.9)
Mm (pq = 0.09)
mm (q2 = 0.81)
Population genetics and evolution
• After reproduction:
– Homozygous dominants = MM = p2 = 0.01
– Heterozygotes = Mm = 2pq = 0.18
– Homozygous recessives = mm = q2 = 0.81
– Melanics = 0.19 (0.01 + 0.18)
– Typicals = 0.81
Population genetics and evolution
• After reproduction:
– Homozygous dominants = MM = p2 = 0.01
– Heterozygotes = Mm = 2pq = 0.18
– Homozygous recessives = mm = q2 = 0.81
– Melanics = 0.19 (0.01 + 0.18)
– Typicals = 0.81
– THIS IS WHAT WE STARTED WITH!!
Population genetics and evolution
• What is evolution? A change in gene
frequency within a population
Population genetics and evolution
• What is evolution? A change in gene
frequency within a population
• What processes lead to changes in gene
frequency?
Population genetics and evolution
• processes that lead to changes in gene
frequency:
Population genetics and evolution
• processes that lead to changes in gene
frequency:
– Mutation (the ultimate source of all genetic
variation)
Population genetics and evolution
• processes that lead to changes in gene
frequency:
– Mutation
– Gene flow (usually accomplished by migration
of individuals from one population to another)
Population genetics and evolution
Population genetics and evolution
• processes that lead to changes in gene
frequency:
– Mutation
– Gene flow
– Non-random mating (inbreeding may increase
the production of homozygotes with recessive
alleles, which may be selected against)
Population genetics and evolution
• processes that lead to changes in gene
frequency:
–
–
–
–
Mutation
Gene flow
Non-random mating
Selection (the most powerful agent of
evolutionary change)
Population genetics and evolution
• processes that lead to changes in gene
frequency:
–
–
–
–
–
Mutation
Migration
Non-random mating
Selection
Genetic drift (changes in gene frequency in
small populations due to random sampling error)
Population genetics and evolution
• Genetic drift:
– Changes in gene frequency in small populations
due to random sampling error
Population genetics and evolution
• Genetic drift:
– Population bottlenecks - reduction of
population size results in loss of genetic
variation and potentially in the loss of alleles
from the population
– Reduction of population size must be
catastrophic and non-selective
Population genetics and evolution
• Genetic drift: Population bottleneck
Population genetics and evolution
• Genetic drift:
– The Founder Effect - a small population
disperses from a larger population, and founds a
new population in another geographic location.
The gene frequencies in the founding
population are not representative of the larger
population.
– Especially important in speciation on
archipelagoes
Population genetics and evolution