Transcript AP Biology - Cloudfront.net

Measuring
Evolution of
Populations
AP Biology
5 Agents of evolutionary change
Mutation
Gene Flow
Genetic Drift
AP Biology
Non-random mating
Selection
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
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Evolution of populations
 Evolution = change in allele frequencies
in a population


hypothetical: what conditions would
cause allele frequencies to not change?
non-evolving 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)
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Hardy-Weinberg equilibrium
 Hypothetical, non-evolving population

preserves allele frequencies
 Serves as a model (null hypothesis)


natural populations rarely in H-W equilibrium
useful model to measure if forces are acting on
a population
 measuring evolutionary change
G.H. Hardy
AP mathematician
Biology
W. Weinberg
physician
Hardy-Weinberg theorem
 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 theorem
 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
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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
MustWhat
assume
are the
population
genotype
is frequencies?
in H-W equilibrium!
AP Biology
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 = HsHs
 normal allele = Hb

low oxygen levels causes
RBC to sickle
 breakdown of RBC
 clogging small blood vessels
 damage to organs

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often lethal
Sickle cell frequency
 High frequency of heterozygotes
1 in 5 in Central Africans = HbHs
 unusual for allele with severe
detrimental effects in homozygotes

 1 in 100 = HsHs
 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: HsHs

heterozygote carriers are relatively free of both: HbHs
 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
Practice Question
 A population called the “founder generation”, consisting of
2000 AA individuals, 2000 Aa individuals, and 6000 aa
individuals is established on a remote island. Mating within
this population occurs at random, the three genotypes are
selectively neutral, and mutations occur at a negligible rate.
a) What are the frequencies of the alleles A and a in the
founder generation?
b) Is the founder generation at Hardy-Weinberg Equilibrium?
c) What is the frequency of the A allele in the second
generation (that is, the generation subsequent to the
founder generation)?
d) What are the frequencies of the AA, Aa, and aa genotypes
in the second generation?
AP Biology
AP Biology
For each of the following problems in population genetics
use the Hardy-Weinberg equation. Show all of
your work and label each frequency, probability, and
allele.
1. Suppose that in a breeding experiment, 7,000 AA individuals
and 3,000 aa individuals mate at random. In the first
generation of offspring, what would be the frequencies of the
three genotypes (AA, Aa, and aa)? What would be the
frequencies of the two alleles? What would be the values in
the second generation?
AP Biology
2. Among African-Americans, the frequency of sickle-cell
anemia (which, as you will recall is a homozygous recessive
condition) is about 0.0025. What is the frequency of
heterozygotes? When on African-American marries another,
what is the probability that both will be heterozygotes? If
both are heterozygotes, what is the probability that their first
child will have sickle-cell anemia?
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3. If q = 0.3 and there are Hardy-Weinberg
proportions, what is the most common genotype and
what is its frequency? What is the least frequent
genotype and its frequency?
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4. In a large, randomly mating population with no forces
acting to change gene frequencies, the frequency of
homozygous recessive individuals for the character extralong eyelashes is 90 per 1000, or 0.09. What percentage of
the population carries this trait but displays the dominant
phenotype, short eyelashes? Would the frequency of the
extra-long-lash allele increase, decrease, or remain the
same if long-lashed individuals preferentially mated with
each other and no one else?
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Any Questions??
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