Chpt. 23 The Evolution
of Populations-Population Genetics
Individuals are
selected…
Populations
evolve
Individuals are selected…
Populations evolve
Populations
=
unit of evolution
Natural selection = mechanism of
evolution
Gradualism
=
accumulation of
small changes in
gene pool over
LONG periods of
time
Hardy-Weinberg Theorem
Hardy-Weinberg Theorem
 examines the gene
structure of a
NON-evolving
population
Hardy-Weinberg Theorem
examines the gene structure of a NON-evolving
population.
Obviously, this is not common,
however, gives a base-line / model
NULL HYPOTHESIS
for determining if and why
populations evolve
Hardy-Weinberg Theorem
even though alleles are
shuffled and recombined
during meiosis and random
fertilization.
This has no effect on the overall
gene pool percentages.
A
a
a
A
A
a
A
a
A
A
a
A
a
Not SWIMMING pool….
a GENE
Hardy-Weinberg Theorem
Gene pool frequencies
(percentages) will remain
unchanged if no mechanism that
can cause evolution to occur
acts on a population.
Hardy-Weinberg Theorem
Gene pool frequencies will
remain unchanged if:
Mutations are not
occurring
Hardy-Weinberg Theorem
Gene pool frequencies will
remain unchanged if:
Natural selection is
not occurring
Hardy-Weinberg Theorem
Gene pool frequencies will
remain unchanged if:
Population is LARGE
Hardy-Weinberg Theorem
Gene pool frequencies will
remain unchanged if:
EVERYONE breeds…
Hardy-Weinberg Theorem
Gene pool frequencies will
remain unchanged if:
EVERYONE randomly
mates…
Hardy-Weinberg Theorem
Gene pool frequencies will
remain unchanged if:
EVERYONE produces
the same number of
offspring
Hardy-Weinberg Theorem
Gene pool frequencies will
remain unchanged if:
NOONE migrates in
or out of the
population…
Hardy-Weinberg Theorem
5 Agents of evolutionary change:
Mutation
Gene Flow (migration)
Genetic Drift (same # of offspring)
Non-random mating
Selection
Hardy-Weinberg Theorem
remember:
H.W. explains: the
frequency of alleles remains
constant in a population… unless
acted upon by agents
OTHER THAN sexual
recombination.
Hardy-Weinberg Principle
Mathematical statement about
the relative frequency of alleles
(genotypes) in a population.
p +q = 1
p2 + 2pq + q2 = 1
Hardy-Weinberg Theorem
Frequency of alleles remains
constant in a population, unless
acted upon by agents OTHER
THAN sexual recombination.
Inheritance does not cause
changes in allele frequency.
Hardy-Weinberg Principle
p = frequency of dominant
allele
p+q=1
Hardy-Weinberg Principle
q = frequency of recessive
allele
p+q=1
Hardy-Weinberg Principle
Mathematical statement about
the relative frequency of alleles
(genotypes) in a population.
in most cases, we only
know the phenotypic
frequencies
Hardy-Weinberg Principle
q2 = frequency of homozygote
recessive individuals
2
q =
# of aa individuals
Hardy-Weinberg Principle
p2 = frequency of homozygote
dominant individuals
2
p =
# of AA individuals
Hardy-Weinberg Principle
p = frequency of dominant
allele
p = # of (AA) + 2 (# Aa)
Hardy-Weinberg Principle
q = frequency of recessive
allele
q = # of (aa) + 2 (# Aa)
Hardy-Weinberg Principle
2pq = frequency of heterozygote
individuals
2pq = # of Aa individuals
Hardy-Weinberg Principle
by comparing genotypic
frequencies from one generation
to the next, you can learn
whether or not evolution has
occurred…
Hardy-Weinberg Principle
if genotypic frequencies have
changed from your original
count…
evolution has occurred!
Suppose there are 1,000 individuals in a
population
Genotype
Number
Genotypic Frequency
AA
490
0.49
Aa
420
0.42
aa
90
0.09
1000
1.00
total
Suppose there are 1,000 individuals in a
population
Genotypic Frequency
Genotypic frequency =
the proportion of a particular
genotype found in a
population
total
0.49
AA
0.42
Aa
0.09
aa
1.00
Suppose there are 1,000 individuals in a
population
Phenotype
Number
dominant
910
0.91
recessive
90
0.09
1000
1.00
total
Phenotypic Frequency
Suppose there are 1,000 individuals in a
population
Phenotypic Frequency
Phenotypic frequency =
the proportion of a particular
phenotype found in a
population
total
0.91
0.09
1.00
Suppose there are 1,000 individuals in a
population
Allele
Number
A
1400
0.7
a
420
0.3
2000
1.00
total
Allele Frequency
q=
frequency
of
recessive
allele
However,
we do not
know how
many a’s
there are
just by
looking at
phenotype
480
Allele frequency
Pssst…(There are 1,000 copies of the flower color
gene in this population of 500 total flowers…)
q=
q2 =
frequency
of
recessive
genotype
480
Genotypic frequency
q2 = 20/500
q2 =
frequency
of
recessive
genotype
480
Genotypic frequency
q2 = .04
q=
frequency
of
recessive
allele
480
Allele frequency
q = .04
q=
frequency
of
recessive
allele
480
Allele frequency
q = .2
q=
frequency
of
recessive
allele
p=
frequency
of
dominant
allele
480
q = .2
Allele frequency
p+q=1
p + .2 = 1
p = 1 - .2
p = .8
480
p = .8
q = .2
Some of the pink flowers
will be AA and some will be
Aa
p2 + 2pq + q2 = 1
480
Some of the pink flowers
will be AA and some will be
Aa
.64 + .32 + .04 = 1
480
How many of the pink
flowers will be AA and how
many will be Aa
.64 X 500 individuals
320 individuals are AA
480
How many of the pink
flowers will be AA and how
many will be Aa
.32 X 500 individuals
160 individuals are Aa
480
320 are AA
160 are Aa
480 total
.8 x .8 = .64
Genetic structure of next generation
.2 x .2 = .04
Genetic structure of next generation
.2 x .8 = .16 aA
.8 x .2 = .16 Aa
.32
Genetic structure of next generation
Hardy-Weinberg Principle
Under ideal conditions, the
relative allele frequencies are
the same in the offspring
generation as in the parent
generation.
2
p
+ 2pq +
2
q
=1
IF: frequencies in a
population deviate from
Hardy-Weinberg (these
are set numbers)…
THEN: we know the
population is evolving.
Oh Hardy, why did
you quit your job
at
ABERCRO
MBIE?
Weinburg, I keep
telling you, I got
sick of changing
genes!!!
change over time is a
result of changes in a
population’s frequency
of genotypes /
genetic
Lets Hardy!!
What percentage of the human population
are carriers for the allele for PKU?
1 out of 10,000 babies are born with this recessive
disease
Most of the time you will begin by
determining the frequency of the
homozygous recessive genotype
Find q2 (frequency of homo recessive)
Lets Hardy!!
What percentage of the human population
are carriers for the allele for PKU?
1 out of 10,000 babies are born with this recessive
disease
Hint: q2 = 1 / 10,000 (frequency of aa)
Find q
Find p
Find pq
AP Problems Using
Hardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio
exam (but no calculators are
allowed).
AP Problems Using
Hardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio
exam (but no calculators are
allowed).
AP Problems Using
Hardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio
exam (but no calculators are
allowed).
AP Problems Using
Hardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio
exam (but no calculators are allowed)
AP Problems Using
Hardy-Weinberg
population:
100 cats
84 black, 16 white
How many of each
genotype?
p2=.36
BB
q2 (bb): 16/100 = .16
q (b): √.16 = 0.4
p (B): 1 - 0.4 = 0.6
2pq=.48
Bb
q2=.16
bb
AP Problems Using
Hardy-Weinberg
p2=.36
Assuming
H-W equilibrium
2pq=.48
q2=.16
BB
Bb
bb
p2=.20
BB
2pq=.64
Bb
q2=.16
bb
Null hypothesis
Sampled data
How do you
explain the data?