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Transcript
Measuring
Evolution of Populations
5 Agents of evolutionary change
Mutation
Gene Flow
Genetic Drift
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
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)
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
mathematician
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
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
Bb
bb
H-W formulas
 Alleles:
p+q=1
B
 Individuals:
p2 + 2pq + q2 = 1
BB
BB
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
What assume
Must
are the genotype
population
frequencies?
is in H-W
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?
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

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…
Single-celled eukaryote parasite
(Plasmodium) spends part of its
life cycle in red blood cells
Malaria
1
2
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.
Frequency of sickle cell allele
& distribution of malaria
Any Questions??
2005-
Practice Problem #1
In a population of foxes, 85% of the
alleles for fur color are for red (R) and
15% are for brown (r). What percentage
of the population of foxes is
heterozygous if the population is in
equilibrium?
What do you know?
 85% of the alleles are R
 15% of the alleles are r
p = .85
q = .15
What do you want to know?
 Percentage of the population that is
heterozygous
2pq
2pq = 2(.85)(.15) = .255
Practice Problem #1
In a population of foxes, 85% of the
alleles for fur color are for red (R) and
15% are for brown (r). What percentage
of the population of foxes is
heterozygous if the population is in
equilibrium?
26% of the population of foxes
is heterozygous.
Practice Problem #2
In guppies, the allele for blue scales (B) is
dominant over red scales (b). In a
population of 1000 guppies, 960 blue and
40 are red.
A. What are the frequencies of the two
alleles in this population if the
population is in Hardy-Weinberg
equilibrium?
B. How many homozygous dominant
individuals are there in the
population?
What do you know?
 960 out of 1000 fish are blue (.96)
 40 out of 1000 fish are red (.04)
q2 = .04
What do you want to know?
 Frequencies of the alleles in the
population
p+q=1
p and q
q2 = .04
q = .2; p = .8
Practice Problem #2
In guppies, the allele for blue scales (B) is
dominant over red scales (b). In a
population of 1000 guppies, 960 blue and
40 are red.
A. What are the frequencies of the two
alleles in this population if the
population is in Hardy-Weinberg
80% of the alleles are B,
equilibrium? and 20% of the alleles are b.
B. How many homozygous dominant
individuals are there in the
population?
What do you know?
 960 out of 1000 fish are blue (.96)
 40 out of 1000 fish are red (.04)
q2 = .04
What do you want to know?
 How many homozygous dominant
individuals?
p2
p2 = (.8)2 = .64
.64 x 1000 = 640
Practice Problem #2
In guppies, the allele for blue scales (B) is
dominant over red scales (b). In a
population of 1000 guppies, 960 blue and
40 are red.
A. What are the frequencies of the two
alleles in this population if the
population is in Hardy-Weinberg
80% of the alleles are B,
equilibrium? and 20% of the alleles are b.
B. How many homozygous dominant
individuals are there in the
population? 640 fish are homozygous dominant.
Practice Problem #3
Flower color in snapdragons shows incomplete
dominance. When pure-breeding red flowering
plants are cross with pure-breeding white
flowering plants, all of the offspring have pink
flowers. In a garden of 100 snapdragon plants,
30 plants have red flowers (RR), 20 plants have
pink flowers (RW), and 50 plants have white
flowers (WW).
A.What are the frequencies of the R and W
alleles?
B.Is the population in Hardy-Weinberg
equilibrium? Explain.
What do you know?
 30 out of 100 snapdragons are red/RR
(.3)
 20 out of 100 snapdragons are pink/RW
(.2)
 50 out of 100 snapdragons are
white/WW (.5)
p and q
What
do
you
want
to
know?
 Frequencies of the alleles in the
population
q = .2; p = .8