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Population Genetics and Evolution
Lecture topics
 Genotype
and allele frequencies
 Hardy-Weinberg equilibrium
 Causes of evolution
 Fitness and natural selection
 Modes of selection
 Maintenance of genetic diversity
Key Concepts
The Hardy-Weinberg principle acts as a null hypothesis when
researchers want to test whether evolution or nonrandom mating
is occurring at a particular gene.
Each of the four evolutionary mechanisms has different
consequences. Only natural selection produces adaptation.
Genetic drift causes random fluctuations in allele frequencies.
Gene flow equalizes allele frequencies between populations.
Mutation introduces new alleles.
Inbreeding changes genotype frequencies but does not change
allele frequencies.
Sexual selection leads to the evolution of traits that help
individuals attract mates. It is usually stronger on males than on
females.
© 2011 Pearson Education, Inc.
Population Genetics: study of allelic
and genotypic frequencies in a
population.
 Allele
frequency = Proportional
representation of different alleles in a
population
 Genotype frequency = proportional
representation of different genotypic
combinations in a population.
 Evolution = change in allelic or
genotypic frequencies over generations
Distinction between Mendelian and
Population Genetics
Mendelian genetics deals with crosses
between two individuals
– Probabilities always 0.5 of getting one or
other allele from segregation of alleles
 Population genetics addresses large
interbreeding population with the probability of
obtaining a given allele dependent on allele’s
frequency in the gene pool

Calculating genotype frequencies
from a sample of a population
 Simple
proportion of individuals in a
population with a given genotype
 E.g., in a sample of 100 individuals,
25 are AA, 25 are Aa, and 50 are aa
 Frequency of AA is 25/100 = 0.25
 Frequency of Aa also 0.25
 Frequency of aa is 50/100 = 0.50
 Sum rule: all frequencies must sum to 1
Calculating allele frequencies from a
sample of a population
 Count individuals of each genotype
 Frequency of first allele (e.g., A) is
denoted by the symbol p
 p = (2*#AA individuals) + #Aa
2*(#AA + #Aa + #aa)
 2 x AA because each has 2 A alleles at
the A locus (really just counting A alleles)
 Divide by 2n (where n = sample size)
because that's how many alleles in
sample
Frequency of the second allele
(e.g., a) is denoted by q
q
= 1-p (unless there are more than 2
different alleles)
 e.g., if 49 AA, 42 Aa and 9 aa individuals
 p = (2*49) + 42
(2*100)
= (98+42)/200 = 140/200 = 0.7
 q = 1 - 0.7 = 0.3
Alternative to counting homozygotes
twice is to divide heterozygotes by 2
since only half their alleles are A or a
Question: How do you get these
numbers from nature?...
 Take
 E.g.,
a sample and count!
collect a random sample of 120
salamanders and determine genotypes
e.g., if 30 AA: 60 Aa: 30 aa
 0.25 AA, 0.5 Aa, 0.25 aa
 0.5A, 0.5a
Can also go from Allele
frequency to genotype frequency
 Or
at least can calculate
expected genotype frequencies
for a given allele frequency
Hardy-Weinberg Equilibrium
 Predicts
genotype frequencies next
generation if no forces at work to
change them, i.e., if not evolving
 Assumptions of H-W model
–No Mutation
–No gene flow (No migration)
–Large population size
–Random mating
–No selection
Assume alleles drawn at random from
gene pool to determine genotype
frequencies in next generation
 P(AA) = P(first allele A) * P(second A)
= p*p = p2
 P(Aa) = 2pq
–P(A first) *P(a second)=pq
–P(a first) *P(A second)=qp
–P(Aa or aA) = pq + pq = 2pq
 P(aa) = q2
Result is
H-W equilibrium genotype
frequencies: p2 + 2pq + q2
H-W equilibrium genotype
2
2
frequencies: p + 2pq + q
 p2
AA, 2pq Aa, and q2 aa
 Equilibrium is reached in a single
generation if assumptions of model
are met
 If not in equilibrium, then population is
either undergoing evolution or
something is maintaining current
disequilibrium
How to detect disequilibrium
 Compare
OBSERVED genotype
frequency to the EXPECTED frequency
if in equilibrium
 Expected GENOTYPE frequency is
calculated from observed ALLELE
frequencies
 Test using Chi-square statistic
–Requires counts instead of
proportions
Chi-square example
 Observe:
25AA, 25Aa, 50aa
 Allele frequencies:
–p = ((2*25)+25)/200 = 0.375
–q = ((2*50)+25)/200 = 0.625
 Expected genotype frequencies:
–p2 = 0.3752 = 0.1406
–2pq = 2*0.375*0.625 = 0.4688
–q2 = 0.6252 = 0.3906
Convert proportions to counts
before doing chi-square test
 Expected
genotype frequencies:
0.1406 AA, 0.4688 Aa, 0.3906 aa
 Multiply
by sample size (in this case
100) to get expected counts
–0.1406 AA * 100 = 14 AA
–0.4688 Aa * 100 = 47Aa
–0.3906 aa * 100 = 39aa
Chi-square test
 Expected
genotype counts:
14AA, 47Aa, 39aa
 Observed genotype counts:
25AA, 25Aa, 50aa
 2 =  ((O-E)2/E)
= (25-14)2 +(25-47)2 +(50-39)2 =22.03
14
47
39
(compare with critical  2 for 2 d.f. = 5.9)
 Significantly different than H-W equilibrium
If not in equilibrium, why not?

Some assumption must be
violated
a. Mutation
b. Gene flow (migration)
c. Small population size
d. Non-random mating
e. Selection
Mutation?
 Mutations
are the ultimate source of
all genetic variation
 Mutation alone unlikely to cause
serious deviation from H-W, but can
introduce new alleles
–Mutations random Aa  a A
–Mutation rate
~ 1-250/locus/million gametes
(Humans: >108 sperm/ejaculate)
Migration? (AKA Gene flow)
 Makes
populations more similar
 Tends to increase genetic variation
in “importing” population
 Can introduce novel alleles
 Effect on equilibrium likely to be
small - except for small isolated
populations
 Or if migration is non-random
e.g., source-sink populations
Gene Flow in Natural Populations


On the island of Vlieland, great tits breed in
two sets of woodlands.
– Females hatched in the eastern woodland
appear to be more well adapted.
Gene flow is higher in the western woodland;
thus birds coming from the mainland are
introducing alleles at a higher rate into the
western population.
– These mainland alleles result in individuals
less well-adapted to the island
environment.
Small population size?
 Genetic drift = change in allele
frequency due to sampling error in
small population
 Small samples are not likely to
reflect genetic composition of
population (remember coin-tossing
demo of confidence in test cross?)
 Changes dues to drift are evolution,
but not necessarily adaptive
Founder effect = Effect of being
founded by a small group of colonists
 E.g.,
Finns, Native Americans
Genetic bottleneck
 Effect
of a temporary reduction in
population size  lower genetic
variation in descendents
 Can create problems for rare species
 Cheetahs are thought to have passed
through a genetic bottleneck around
10,000 years ago  less genetic
variation than inbred laboratory mice!
Non-Random Mating?
 H-W
model assumes mating is
completely random, like drawing pairs of
marbles
 Assortative mating
–Positive: mate with similar individuals,
e.g., Inbreeding, selfing. Tends to
increase frequency of homozygotes
–Negative: mate with dissimilar
individuals e.g., Inbreeding avoidance.
Tends to increase frequency of
heterozygotes
Sexual Selection results from
non-random mating
 Differential
contribution of alleles to next
generation because of differential
mating success
 This is a major driver of evolutionary
change
 Often one or a few individuals of one sex
obtain the majority of matings
Biggest male elephant seals
monopolize most matings
Natural Selection is the primary cause
of evolution and deviation from H-W
 Differential
reproduction of individuals
with different genotypes
 Note: Sexual selection is really a special
case of natural selection
 Perhaps better to think of fecundity
selection and viability selection if you
seek a dichotomy
 Reproductive success quantified as
fitness
Fitness
 An
individual’s reproductive contribution
to the next generation is its fitness
 All that really matters is relative fitness,
 = contribution of individuals of a
particular genotype relative to other
genotypes
 i.e., mean number of offspring produced
by a given genotype/mean number of
offspring produced by the genotype
producing the most offspring
Calculating relative fitness
If:
AA
Aa
aa
Then:
AA
Aa
aa
has 3 offspring
has 4 offspring
has 2 offspring
= 3/4
= 0.75
= 4/4
=1
= 2/4
= 0.5
Can use relative fitness and H-W freq
to model effects of selection
 We
will develop such a model in lab.
 Start with H-W to produce zygotes
 Multiply genotype frequencies by relative
fitnesses to get abundances after
selection
 Calculate new allele and genotype
frequencies for “survivors/breeders”
 Repeat for multiple generations
Question: How do you get fitness
values from nature?
 Estimate
lifetime reproductive
success of individuals (not easy!)
 Determine genotypes of those same
individuals
 Take average reproductive success
for each genotype and divide as
above by output of most successful
genotype
Key Concepts
Evolution by natural selection is not
progressive, and it does not change the
characteristics of the individuals that are
selected―it changes only the characteristics of
the population. Animals do not do things for the
good of the species, and not all traits are
adaptive. All adaptations are constrained by
trade-offs and genetic and historical factors.
© 2011 Pearson Education, Inc.
© 2011 Pearson Education, Inc.
© 2011 Pearson Education, Inc.
Not progressive?

Organisms can only adapt to the past
environments, not the future.
– Any lineage, no matter how well-adapted, can
go extinct, especially if conditions change

Evolution is a bush, not a line
Aristotle and others
proposed that species
were organized into a
sequence based on
increased size and
complexity, with
humans at the top
Humans
Live-bearing
vertebrates
Egg-bearing
vertebrates
Invertebrates
Higher plants
Lower plants
Inanimate
matter
Not progressive?

Organisms can only adapt to the past
environments, not the future.
– Any lineage, no matter how well-adapted, can
go extinct, especially if conditions change
Evolution is a bush, not a line
 But mean fitness of a population increases –
this is the essence of the process of
adaptation

What Maintains Genetic Diversity?
populations are not fixed for the
“best allele – Why not?
 Most modes of selection do not drive a
single allele to fixation
Number of individuals
 Most
Phenotype
(a) No selection
(b) Stabilizing selection
(c) Directional selection
(d) Disruptive selection
No selection
 If
all assumptions of H-W met,
population should remain at equilibrium
 Selectively neutral alleles
–No difference in fitness although
obvious phenotypic difference
–Difference in protein makes no other
difference
–Difference in DNA makes no
difference in amino acid sequence
No Selection
Stabilizing Selection
 Selection
acts against extreme
individuals
 Reduces spread of phenotypic
values
 May increase frequency of
heterozygotes
 Many mechanisms
Stabilizing
E.g., Birth Weight
 Postnatal
survival increases with birth
weight
 Death in childbirth increases with birth
weight
 Trade-off  optimum somewhere in
middle
Percent of infant population
Birth weight
15
30
10
10
5
5
2
2
4
6
8
Body weight in pounds
Percent of infant death (log scale)
100
20
10Fig. 18.06
Heterozygote Advantage
 Heterozygotes
have higher
fitness than either homozygote
 more heterozygotes than
predicted by H-W
 E.g., Sickle-cell
Sickle cell hemoglobin
Sickle cell anemia in heterozygote less
severe than if homozygous for Hbs
 HbHbs confers resistance to the malarial
parasite, Plasmodium falciparum
 If malaria frequent, heterozygote is favored

Figure 18-6
Hybrid Vigor
 Multilocus
heterozygote advantage
 Inbred lines homozygous, which
reveals deleterious recessive alleles
 Hybrids between two inbred lines
tend to be healthier
Directional Selection
 One
phenotypic extreme
favored
 Tends to shift population
mean phenotype in one
direction
 Or one allele toward fixation
Directional
Directional selection is rare or
fluctuates
 Most
populations probably close to
optimum, so stabilizing selection more
likely (very extreme phenotypes likely to
have low fitness)
 Seen mostly when environment changes
 Fluctuating selection
• E.g., Galapagos finches
–Beak size varies with weather
Fig. 21.2
Frequency-dependent
selection
 Which
allele is favored depends
on its relative abundance
 E.g., Scale-eating cichlids
Cichlid with
right-pointing
mouth attacks
prey on its left
flank.
Cichlid with
left-pointing
mouth attacks
prey on its
right flank.
Fig. 18.7a
Prey
species learn
to avoid most
common type
Fig. 18.7b
Frequency of cichlids
with left-pointing mouths
1.0
Cichlid data
0.5
0
1982
1984 1986 1988
Sample year
1990
Even Lethal Recessive Isn’t
Completely Eliminated e.g.,Tailless
locus in mice
TT Normal, Tt Short-tailed, tt Lethal
– tt dies in utero – usually resorbed so never
even born
 Tt x Tt  1TT: 2Tt: (1tt)
 Since heterozygote survives, allele tends to
become less abundant, but only approaches
extinction asymptotically
 Chance event may eliminate it, but new
mutants are constantly generated
Disruptive Selection
 Selection
against the average
phenotype and favoring the extremes
 May produce an excess of both
homozygotes, but random mating
reproduces heterozygotes
 Has been proposed as a mechanism of
speciation
 E.g., Cactus Finches – selection based
on ability to harvest cactus seeds vs.
insect larvae
Disruptive
Major modes of selection
have potential to maintain
genetic variation
Number of individuals
 All
Phenotype
(a) No selection
(b) Stabilizing selection
(c) Directional selection
(d) Disruptive selection
Population Genetics and Evolution
Lecture topics
 Genotype
and allele frequencies
 Hardy-Weinberg equilibrium
 Causes of evolution
 Fitness and natural selection
 Modes of selection
 Maintenance of genetic diversity