Population Genetics
(Why do professors torture you with H-W in
evolution classes?)
Questions
• What is a null hypothesis and why do we need it?
• What is the definition of evolution?
• What is the role of the H-W equation in evolutionary
studies?
Allele and genotype frequencies throughout the
life cycle
48
36
Initial allele frequencies
A
a
0.6
0.4
Number
zygotes
Gametes
Final allele frequencies
A
a
0.6
0.4
16
AA Aa aa
Genotype
Zygotes
Juveniles
Adults
48
48
36
Number
adults
36
16
AA Aa aa
Genotype
Number
juveniles
16
AA Aa aa
Genotype
Hardy-Weinberg equilibrium
Sperm
0.6 A
Egg Sperm
0.4 a
Aa
0.6 A
0.36AA
0.24Aa
Eggs
0.4 a
AA
36
0.24Aa
+
Aa
48
+
0.16aa
aa
16 =
Total
100
Zygote Probability
A
A
AA
0.6 x 0.6 = 0.36
A
a
Aa
0.6 x 0.4 = 0.24
a
A
aA
0.6 x 0.4 = 0.24
a
a
aa
0.4 x 0.4 = 0.16
Gamete frequencies
AA
0.36
Aa
aa
0.48 + 0.16 =
+
+
+
+
0.36
+0.24
-----0.6
A
+
Total
1.0
=
=
0.24
+0.16
-----0.4
a
1.0
=
total
Question
• How can we use HW to test whether evolution has
occurred?
How geneticists estimate H-W in a population
AAAACGTCA
AAATCGTCA
AAATCGTCA
AAAACGTCA
AAATCGTCA
AAAACGTCA
AAATCGTCA
AAAACGTCA
AAAACGTCA
AAAACGTCA
AAAACGTCA
AAATCGTCA
AAATCGTCA
AAATCGTCA
AAAACGTCA
AAAACGTCA
AAATCGTCA
AAATCGTCA
AAAACGTCA
AAATCGTCA
Example: Single nucleotide polymorphisms (SNPs)
Hardy-Weinberg equilibrium general case
Sperm
f(A1)=p
f(A1)=p
f(A1A1)=p2
Egg Sperm
f(A2)=q
f(A1A2)=
pq
Eggs
f(A2)=q
A1A1
p2 +
f(A2A1)= pq
A1A2
2pq
A2A2
+ q2 =
f(A2A2)=
q2
Total
1.0
Zygote Probability
A1
A1
A1A1
p x p = p2
A1
A2
A1A2
p x q = pq
A2
A1
A2A1
p x q = pq
A2
A2
A2A2
q x q = q2
•
What would happen to the genotype and hence allele
frequencies under the following scenarios?
A1A1
p2 +
•
•
•
•
A1A2
2pq
A2A2
+ q2 =
Total
1.0
Within a single generation, starfish zygotes with the A2A2
genotype do not metamorphose and settle
Within a single generation, starfish zygotes with the A1A2
genotype do not metamorphose and settle
Within a single generation, starfish zygotes with the A2A2
genotype arrive from another population and settle along
with local genotypes
Within a single generation, a subset of individuals in a
population of starfish are washed above the tidal zone and
die.
Example of other uses of HW
•
Zostera marina (eelgrass) is a marine flowering plant is the
dominant sea grass species of the Northern hemisphere.
•
Populations of Zostera can have both clonal and sexually
reproducing forms. How could you use H-W principles to
determine whether a single population is reproducing mainly
clonally, or through mainly through sexual reproduction?