Population Genetics
Evolution depends upon mutation
to create new alleles.
Evolution occurs as a result of allele frequency
changes within/among populations.
What evolutionary forces alter
allele frequencies?
How do allele frequencies change
in a population from generation
to generation?
Allele frequencies
in the gene pool:
A: 12 / 20 = 0.6
a: 8 / 20 = 0.4
Alleles Combine to Yield Genotypic Frequencies
Our mice grow-up and generate gametes
for next generations gene pool
Allele frequency across generations:
A General Single Locus, 2 Allele Model
Freq A1 = p
Freq A2 = q
Genotypic frequencies are given
by probability theory
One locus, 2 Allele Model
In a diploid organism, there are two alleles for each locus.
Therefore there are three possible genotypes:
Genotype
A1A1 A1A2 A2A2
Given:
Frequency of allele A1 = p
Frequency of allele A2 = 1 - p = q
Then:
Genotype
A1A1 A1A2 A2A2
Frequency
p2
2pq
q2
A population that maintains such frequencies
is said to be at Hardy-Weinberg Equilibrium
Hardy-Weinberg Principle
When none of the evolutionary forces (selection, mutation, drift,
migration, non-random mating) are operative:
(1) Allele frequencies in a population
will not change, generation after
generation.
(2) If allele frequencies are given by p
and q, the genotype frequencies will
be given by p2, 2pq, and q2
Hardy-Weinberg Principle Depends Upon
the Following Assumptions
1. There is no selection
2. There is no mutation
3. There is no migration
4. There are no chance events
5. Individuals choose their mates at random
The Outcome of Natural Selection Depends Upon:
(1) Relationship between phenotype and fitness.
(2) Relationship between phenotype and genotype.
These determine the relationship between
fitness and genotype.
Outcome determines if there is evolution
12.2 Growth of 2 genotypes in an asexually reproducing
population w/ nonoverlapping generations
% survival to reproduction:
A = 0.05
B = 0.10
Fecundity (eggs produced):
A = 60
B = 40
Fitness A = 0.05 x 60 = 3
Fitness B = 0.01 x 40 = 4
R = Per Capita Growth Rate
= Represents Absolute Fitness
The rate of genetic change in a populations depends upon
relative fitness:
Relative Fitness of A = Absolute fitness A
Highest Absolute Fitness
WA
=
3/4 = 0.75
Often by convention, fitness is
expressed relative to the genotype
with highest absolute fitness.
Thus,
WB = 4/4 = 1.0
The fitness of a genotype is the average lifetime
contribution of individuals of that genotype to the
population after one or more generations, measured
at the same stage in the life history.
12.3 Components of natural selection that may affect the
fitness of a sexually reproducing organism
12.1(2) Modes of selection on a polymorphism consisting of two
alleles at one locus
12.1(1) Modes of selection on a heritable quantitative
character
Incorporating Selection
Individuals may differ in fitness because
of their underlying genotype
Genotype A1A1 A1A2 A2A2
Frequency p2
2pq q2
Fitness
w11
w12 w22
Average fitness of the whole population:
w = p2w11 + 2pqw12 + q2w22
Given variable fitness, frequencies after selection:
Genotype
A1A1
Freq
p2 w11 2pq w12
w
A1A2
A2A2
q2 w22
w
w
New allele frequencies after mating:
p2 w11 + pq w12
w
New Frequency of A1
pq w12 + q2w22
w
New Frequency of A2
Fitness: Probability that one’s genes will be represented
in future generations.
Hard to measure. Often, fitness is indirectly measured:
(e.g. survival probability given a particular genotype)
WAA
1
Fitness is often stated
in relative terms
WAa
1
Waa
1+s
Selection coefficient
gives the selection differential
Persistent Selection Changes Allele Frequencies
Strength of selection is given by the
magnitude of the selection differential
Selection Experiments Show Changes in Allele Frequencies
HW
Cavener and
Clegg (1981)
Food spiked
with ethanol
Selection can drive genotype frequencies
away from Hardy Weinberg Expectations
High frequency (Europe)
High selection/transmisson (Africa)
High frequency (Europe)
Low selection/transmisson (Europe)
Low frequency (Europe)
High selection/transmisson (Africa)
Predicted
change
in allele
frequencies
at CCR5
What is the frequency of A1 in the next generation?
pt + 1 =
p2w11 + pqw12
p2w11 + 2pqw12 + q2w22
What is the change in frequency of A1 per generation?
Dp = pt + 1 - pt =
p / w (pw11 + qw12 - w )
With this equation we can substitute values for relative
fitness and analyze various cases of selection.
Gene Action
Fitness Relationship
Dominance
A 1A 1
1+s
A 1A 2
1+s
A 2A 2
1
Recessivity
A 1A 1
1+s
A 1A 2
1
A 2A 2
1
Overdominance
A 1A 1
1+s
A 1A 2
1
A 2A 2
1+t
Underdominance A1A1
1+s
A 1A 2
1
A 2A 2
1+t
Dominance
Genotype
Fitness
A1A1
1+s
A1A2
1+s
S = 0.01
A1
A2A2
1
Recessive
Genotype
Fitness
A1A1
1+s
S = 0.01
A1
A1A2
1
A2A2
1
Evolution in lab
populations of
flour beetles
support theoretical
predictions.
Dawson (1970)
Overdominance/Heterozygote Superiority
Genotype
Fitness
A1A1
1+s
A1A2
1
A2A2
1+t
S = - 0.02 t = - 0.04
A1
Stable equilibrium
is reached
Genetic diversity
is maintained
Viable allele did not fix
in the population
Mukai and Burdick 1958
Underdominance
Genotype
Fitness
A1A1
1+s
A1A2
1
S = 0.01
A2A2
1+t
t = 0.02
Unstable equilibrium
A1
A1 maybe fixed or
lost from the
population
Frequency-Dependent Selection
Allele frequencies in a population remain near an equilibrium
because selection favors the rarer allele.
As a result, both alleles are maintained in the population.
Frequency-Dependent
Selection
Perissodus
Incorporating Mutation
Mutation alone is a weak
evolutionary force
However, mutation and selection acting in concert
are a powerful evolutionary force