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Population Genetics:
Hardy-Weinberg Principle
AP Biology
2007-2008
5 Agents of evolutionary change
Mutation
Gene Flow
Genetic Drift
AP Biology
Non-random mating
Selection
 Mutation: A permanent, heritable change in the




nucleotide sequence in a gene or a chromosome
Gene flow: The transfer of alleles of genes from
one population to another
Non-random mating: Any mating system in which
males are not randomly assigned to females.
Genetic drift: The process of change in the
genetic composition of a population due to
chance or random events rather than by natural
selection, resulting in changes in allele
frequencies over time.
Selection: Natural selection chooses the fittest to
survive.
AP Biology
Populations & gene pools
 Concepts
A population is a localized group of
interbreeding individuals
 Gene pool is collection of alleles in the
population

 remember difference between alleles & genes!

Allele frequency is how common is that
allele in the population
 how many A vs. a in whole population
AP Biology
Evolution of populations
 Evolution = change in allele frequencies
in a population

Hypothetical ?: what conditions would
cause allele frequencies to not change
in a population?
REMOVE all agents of evolutionary change
1. very large population size (no genetic drift)
2. no migration (no gene flow in or out)
3. no mutation (no genetic change)
4. random mating (no sexual selection)
5. no natural selection (everyone is equally fit)
AP Biology
Hardy-Weinberg equilibrium
 Hypothetical, non-evolving population
preserves allele frequencies
 Serves as a model (null hypothesis) –


States that both allele and genotype frequencies in a
population remain constant from generation to generation
unless specific disturbing influences are introduced.
 Those disturbing influences include non-random mating,
mutations, selection (from nature), limited population
size/genetic drift, and gene flow. It is important to
understand that outside the lab, one or more of these
"disturbing influences" are always in effect.
Hardy–Weinberg equilibrium is impossible in nature. Genetic
equilibrium is an ideal state that provides a baseline against
which to measure change.
AP Biology
Natural populations rarely fit into H-W
equilibrium
 H-W is a useful model to measure the
forces acting on a population and as a
measure of evolutionary change

G.H. Hardy
mathematician
AP Biology
W. Weinberg
physician
Hardy-Weinberg equation
 Counting Alleles
assume 2 alleles = B, b
 frequency of dominant allele (B) = p
 frequency of recessive allele (b) = q

 frequencies must add to 1 (100%), so:
p+q=1
BB
AP Biology
Bb
bb
Hardy-Weinberg equation
 Counting Individuals



frequency of homozygous dominant: p x p = p2
frequency of homozygous recessive: q x q = q2
frequency of heterozygotes: (p x q) + (q x p) = 2pq
 frequencies of all individuals must add to 1 (100%), so:
p2 + 2pq + q2 = 1
BB
AP Biology
Bb
bb
H-W formulas
 Alleles:
p+q=1
B
 Individuals:
p2 + 2pq + q2 = 1
BB
BB
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b
Bb
Bb
bb
bb
Using Hardy-Weinberg equation
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
Must assume population is in H-W
equilibrium!
AP Biology
What are the genotype frequencies?
Using Hardy-Weinberg equation
p2=.36
Assuming
H-W equilibrium
2pq=.48
q2=.16
BB
Bb
bb
p2=.20
=.74
BB
2pq=.64
2pq=.10
Bb
q2=.16
bb
Null hypothesis
Sampled data
How do you
explain
the data?
AP
Biology
Application of H-W principle
 Sickle cell anemia

inherit a mutation in gene coding for
hemoglobin
 oxygen-carrying blood protein
 recessive allele = HbHb
 normal allele = HB

low oxygen levels causes
RBC to sickle
 breakdown of RBC
 clogging small blood vessels
 damage to organs

AP Biology
often lethal
Sickle cell frequency
 High frequency of heterozygotes
1 in 5 in Central Africans = HBHb
 unusual for allele with severe
detrimental effects in homozygotes

 1 in 100 = HbHb
 usually die before reproductive age
Why is the Hs allele maintained at such high
levels in African populations?
Suggests some selective advantage of
being heterozygous…
AP Biology
Single-celled eukaryote parasite
(Plasmodium) spends part of its
life cycle in red blood cells
Malaria
1
2
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3
Heterozygote Advantage
 In tropical Africa, where malaria is common:

homozygous dominant (normal)
 die or reduced reproduction from malaria: HBHB

homozygous recessive
 die or reduced reproduction from sickle cell anemia: HbHb

heterozygote carriers are relatively free of both: HBHb
 survive & reproduce more, more common in population
Hypothesis:
In malaria-infected
cells, the O2 level is
lowered enough to
cause sickling which
kills the cell & destroys
the
parasite.
AP Biology
Frequency of sickle cell allele &
distribution of malaria