Download Hardy-Weinberg Principle

Hardy-Weinberg Principle
SBI3UP
What is it?
• Method to quantify a gene pool (total of all
alleles within a population) by measuring each
allele frequency
• Changes in allele frequencies may help
measure evolutionary change within populations
In order to apply the Hardy-Weinberg
Equilibrium/Population Equilibrium the
following conditions are required:
– Large populations
– Random mating
– No mutation
– No migration
– Equal viability, fertility, and mating ability of
all genotypes
The H-W equations:
p+q=1
p2 + 2pq +q2 = 1
p  frequency of allele A in popl’n
q  frequency of allele a in popl’n
p2  frequency of AA genotype
q2  frequency of aa genotype
2pq  frequency of Aa genotype
• If a pop’n is in Hardy-Weinberg equilibrium (not evolving)
the frequency of the dominant and recessive alleles is
0.5 each (50%)
– E.g. p + q = 1
• so,
0.5 + 0.5 = 1
• If white (b) is recessive to black (B) and 34% of the
alleles are b, what is the frequency of B?
–
–
–
p= 1- q
p = 1 – 0.34
p = 0.66
A Little Math
1 unit
1 unit
A 1 unit by 1 unit square
has an area of 1 unit2
p2
pq
p
1 unit
pq
q2
q
If the sides are (p+q) units
long then the area is
q
p
1 unit
(p+q)2 = p2 + 2pq +q2
Add the squares and
rectangles to get this
formula
Ex.
• If p = 0.8 then q = 0.2
• What is the frequency
of the dominant
phenotype?
–
p2
+ 2pq (both represent
dominant phenotype
– 0.96 or 96%
• What is the frequency
of heterozygous
individuals?
– 2pq
– 0.32 or 32%
p+q=1
p2 + 2pq +q2 = 1
0.8
0.2
p2
0.64
pq
0.16
p
pq
0.16
q2
0.04
q
p
q
0.8
0.2
Ex. If 98 out of 200 individuals in a population
express the recessive phenotype, what percent of
the population would you predict would be
heterozygotes?
Dominant
allele
Recessive
allele
t
Heterozygous
Dominant
phenotype
Homozygous
recessive
p
q
p2
2pq
p2+2pq
q2
0.1
0.8
0.09
0.64
0.25
0.16
0.91
0.96
0.99
For extra practice, complete the table…
Dominant
allele
Recessive
allele
Homozygous
dominant
Heterozygous
Dominant
phenotype
Homozygous
recessive
p
q
p2
2pq
p2+2pq
q2
0.1
0.9
0.01
0.18
0.19
0.81
0.2
0.8
0.04
0.32
0.36
0.64
0.3
0.7
0.09
0.42
0.51
0.49
0.4
0.6
0.16
0.48
0.64
0.36
0.5
0.5
0.25
0.50
0.75
0.25
0.6
0.4
0.36
0.48
0.84
0.16
0.7
0.3
0.49
0.42
0.91
0.09
0.8
0.2
0.64
0.32
0.96
0.04
0.9
0.1
0.81
0.18
0.99
0.01