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Section 9 and 10
Microevolution refers to changes in
the gene pool
• Hardy Weinberg equation
• P2 + 2pq
+ q2 = 1
The Hardy-Weinberg equation can be used to test
whether a population is evolving
– Sexual reproduction alone does not lead to
evolutionary change in a population
– Although alleles are shuffled, the frequency of alleles and
genotypes in the population does not change
– Similarly, if you shuffle a pack of cards, you’ll deal out
different hands, but the cards and suits in the deck do not
change
The Hardy-Weinberg equation can be used to test
whether a population is evolving
– The Hardy Weinberg principle states that allele and
genotype frequencies within a sexually reproducing,
population will remain in equilibrium unless outside
forces act to change those frequencies….this is known
as Hardy-Weinberg equilibrium
Allele are the different versions of the trait. An organism has 2 alleles for each trait.
Genotype frequency refers to the different occurrence of each genotype (AA, Aa, aa).
The Hardy-Weinberg equation can be used to test
whether a population is evolving
– Imagine that there are two alleles in a blue-footed
booby population: W and w
– W is a dominant allele for a nonwebbed booby foot
– w is a recessive allele for a webbed booby foot
Webbing w
No webbing W
The Hardy-Weinberg equation can be used to test
whether a population is evolving
– Consider the gene pool of a population of 500 boobies
– 320 (64%) are homozygous dominant (WW)
– 160 (32%) are heterozygous (Ww)
– 20 (4%) are homozygous recessive (ww)
Copyright © 2009 Pearson Education, Inc.
Phenotypes
Genotypes
WW
Ww
ww
Number of animals
(total = 500)
320
160
20
Genotype frequencies
320
–––
500
160
–––
500
= 0.64
Number of alleles
in gene pool
(total = 1,000)
640 W
Allele frequencies
800
1,000
= 0.32
160 W + 160 w
= 0.8 W
200
1,000
20
–––
500 = 0.04
40 w
= 0.2 w
13.9 The Hardy-Weinberg equation can be used to test
whether a population is evolving
– Frequency of dominant allele (W) = 80% = p
– 80% of alleles in the booby population are W
– Frequency of recessive allele (w) = 20% = q
– 20% of alleles in the booby population are w
Copyright © 2009 Pearson Education, Inc.
13.9 The Hardy-Weinberg equation can be used to test
whether a population is evolving
– Frequency of all three genotypes must be 100% or 1.0
– p2 + 2pq + q2 = 100% = 1.0
– homozygous dominant + heterozygous + homozygous
recessive = 100%
Copyright © 2009 Pearson Education, Inc.
• Thus when gametes combine their alleles to form a
zygote, the probability of generating a WW
genotype is p2 .
• Therefore, in our Bobby population, since p = 0.8,
then the probability of a W sperm fertilizing a W
egg is p2 or 0.64.
• Likewise, since q = 0.2, then the probability of an a
sperm fertilizing an a egg is q2 or 0.04.
• What is more, since there are two ways in which an
Aa genotype can arise, the frequency of
heterozygous individuals is 2 pq or 2( 0.8 x 0.2) or
0.32.
Gametes reflect
allele frequencies
of parental gene pool
W egg
p = 0.8
Eggs
w egg
q = 0.2
Sperm
W sperm
w sperm
p = 0.8
q = 0.8
WW
Ww
p2 = 0.64
pq = 0.16
ww
q2 = 0.04
wW
qp = 0.16
Next generation:
Genotype frequencies
Allele frequencies
0.64 WW
0.32 Ww
0.8 W
0.04 ww
0.2 w
The Hardy-Weinberg equation can be used to test
whether a population is evolving
 What is the probability of a booby chick with a
homozygous dominant genotype (WW)?
 What is the probability of a booby chick with a
homozygous recessive genotype (ww)?
 What is the probability of a booby chick with a
heterozygous genotype (Ww)?
Answers
• WW (.8)2 = .64 (64%)
• Ww 2 (.8 x .2) = .0.32 (32%)
• ww (.2)2 = 0.04 (4%)
.8 for egg and .8 for sperm
Try this one…
• PKU is a recessive disorder.
• If it shows an occurrence of 1 per 10,000
births, what is the frequency of the allele?
• Frequency of the genotype would be
q2 = 0.0001
• To determine frequency of allele take square root
of q……0.01.
• Since p + q = 1, the frequency of dominant allele
is 0.99.
• Therefore, the frequency of heterozygote is
0.1098…about 2% of population carries gene for
PKU
•
•
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Microevolution
What conditions are required for gene frequencies
to remain constant and for the Hardy-Weinberg
equilibrium to be maintained in a population?
1. Very large population size.
2. No gene flow (population isolation).
3. No mutations.
4. Mating must be random.
5. No natural selection.
• Are each of these conditions met?