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Chapter 7: Evolution at multiple
loci

Evolution at two loci: Linkage equilibrium and
linkage disequilibrium.

Locus is location on a chromosome where a gene
occurs.

Single locus Hardy-Weinberg models are simple.
However, many traits are controlled by combined
influence of many genes.
Pair of loci located on same chromosome.
 (Recall locus is location on chromosome of
a gene).
 Gene at locus A has two alleles A and a
 Gene at locus B has two alleles B and b


In two-locus Hardy-Weinberg analysis we
track allele and chromosome frequencies.
Thus 4 possible chromosome genotypes:
 AB, Ab, aB, ab
 Multilocus genotype referred to as a
haplotype (from haploid genotype).


Does selection on locus A affect our ability
to make predictions about evolution at locus
B?

Sometimes. Depends on whether loci are in
linkage equilibrium or linkage
disequilibrium.

Two loci in a population are in linkage
equilibrium when genotype of a chromosome at
one locus is independent of the genotype at the
other locus on the same chromosome.

I.e. knowing genotype at one locus is of no use in
predicting genotype at the other locus.
Example

Two hypothetical populations each
containing 25 chromosomes.
Allele frequencies are identical in both
populations.
 A = 0.6, a = 0.4; B = 0.8, b = 0.2


If studying only locus A or locus B we
would conclude populations were identical.

However, populations not identical when
we look at haplotypes.
Population 1
 AB = 0.48
 Ab = 0.12
 aB = 0.32
 ab = 0.08

Population 2
AB = 0.44
Ab = 0.16
aB = 0.36
ab = 0.04
Population 1 is in linkage equilibrium.
 Frequency of B on chromosomes carrying A
is 12/15 or 0.8, frequency of B on
chromosomes carrying a is 8/10 or 0.8.
 Frequency of B is same on chromosomes
carrying A as on chromosomes carrying a.


Population 2 is in linkage disequilibrium.

Frequency of B on chromosomes carrying A
is 11/15 or 0.73, frequency of B on
chromosomes carrying a is 9/10 or 0.9.
Conditions for linkage
equilibrium
1. Frequency of B on chromosomes
carrying allele A is equal to frequency of B
on chromosomes carrying allele a.
 2. Frequency of a chromosome haplotype
can be calculated by multiplying
frequencies of constituent alleles, i.e.
frequency of AB is = freq. A X freq. B.

Conditions for linkage
equilibrium

3. Coefficient of linkage disequilibrium (D)
is equal to zero. Box 7.1
D
= gABgab - gAbgaB
 (gAB = frequency of chromosome AB,
etc.)
Coefficient of linkage
disequilibrium
D can range from - 0.25 to 0.25.
 0.25 when AB and ab only genotypes and
both at frequency of 0.5
 Similarly -0.25 when Ab and aB only
genotypes and both at frequency of 0.5
 If D = 0, then population in linkage
equilibrium and value of D is a measure of
the degree of linkage disequilibrium.

What creates linkage
disequilibrium in populations?
Three mechanisms:
 Selection on multilocus genotypes.
 Genetic drift
 Population mixing

Selection on multilocus
genotypes.

Scenario: Locus A and locus B in linkage
equilibrium. Gametes combine at random to
from zygotes.
Selection on multilocus
genotypes.

Assume genotype ab/ab is of size 10 units.

For all other genotypes every copy of A or B
adds one unit of size (e.g. Ab/aB is size 12).

Assume predators eat all genotypes of < 13
units size.
Selection on multilocus
genotypes.

Survivors (65.3% of population) in linkage
disequilibrium by all 3 criteria because
some genotypes missing.

E.g. criterion 3: D= gABgab
- gAbgaB

D = 0.4416*0 - (0.0576*0.1536) = - 0.0088
Genetic drift
Scenario: Small population with two
genotypes AB and Ab. No copies of allele
a.
 Single Ab chromosome mutation converts
an A to an a. This single ab chromosome
puts population in linkage disequilibrium.

Genetic drift

If selection favors a and its frequency
increases, degree of linkage disequilibrium
increases too.
Population mixing

If two populations, which are in linkage
equilibrium, are merged resulting
population may not be in linkage
equilibrium.
What eliminates linkage
disequilibrium from population?

Sexual reproduction steadily reduces
linkage disequilibrium.

Crossing over during meiosis breaks up old
combinations of alleles and creates new
combinations.
Genetic recombination

Genetic recombination tends to randomize
genotypes in relation to other genotypes
(i.e., it reduces linkage disequilibrium.)

Rate of decline in linkage disequilibrium is
proportional to rate of recombination.
Empirical example of genetic
recombination

Clegg et al. (1980) established fruit fly
populations that were in linkage
disequilibrium.
Population 1 AB and ab each 0.5 frequency.
 Population 2 aB and Ab each 0.5 frequency.

Empirical example of genetic
recombination
Populations of about 1,000 individuals
maintained for 48-50 generations.
 Flies allowed to mate freely.
 Populations sampled every 1-2 generations
to count frequencies of 4 haplotypes.

Empirical example of genetic
recombination

Crossing-over created missing haplotypes in
each population and linkage disequilibrium
disappeared.

In general, in random-mating populations
sex is efficient enough at eliminating
linkage disequilibrium that most alleles are
in linkage equilibrium most of the time.
Practical reasons to measure linkage
disequilibrium

There are two major uses of measures of
linkage disequilibrium.
– Can be used to reconstruct history of genes and
populations
– Can be used to identify alleles recently favored
by positive selection
Reconstructing history of the
CCR5-Δ32 locus

Where did the CCR5-Δ32 allele come from
and when did it originate?

CCR5-Δ32 is the allele that provides a
selective advantage against HIV.
Reconstructing history of the
CCR5-Δ32 locus

CCR5-Δ32 is located on chromosome 3 and
near two short-tandem repeat sites called
GAAT and AFMB.

GAAT and AFMB are non-coding and have
no effect on fitness. Both GAAT and
AFMB have a number of different alleles.
Reconstructing history of the
CCR5-Δ32 locus
Stephens et al. (1998) examined haplotypes
of 192 Europeans.
 Found that GAAT and AFMB alleles in
close to linkage equilibrium with each other.

Reconstructing history of the
CCR5-Δ32 locus
However, CCR5 is in strong linkage
disequilibrium with both GAAT and AFMB.
 Almost all chromosomes carrying CCR5Δ32 also carry allele 197 at GAAT and
allele 215 at AFMB.

Reconstructing history of the
CCR5-Δ32 locus
Most likely reason for observed linkage
disequilibrium is genetic drift.
 Hypothesis: in past was originally only one
CCR5 allele the CCR5+ allele, a mutation
on a chromosome with the haplotype
CCR5--GAAT-197--AFMB-215 created the
CCR5Δ32 allele.

Reconstructing history of the
CCR5-Δ32 locus

The CCR5Δ32 allele was favored by selection and
rose to high frequency dragging the other two
alleles with it.

Since its appearance and increase crossing over
and mutation have been breaking down the
linkage disequilibrium. Now about 15% of Δ32197-215 haplotypes have changed to other
haplotypes.
Reconstructing history of the
CCR5-Δ32 locus

Based on rates of crossing over and
mutation rates, Stephens et al. (1998)
estimate the CCR5-Δ32 allele first appeared
about 700 years ago (range of estimates
275-1875 years)
Reconstructing history of the
CCR5-Δ32 locus

Because the CCR5-Δ32 increased in frequency so
rapidly selection must have been strong.

Most obvious candidate is an epidemic disease.

Myxoma virus a relative of smallpox uses CCR5
protein on cell surface to enter host cell, which
suggests the epidemic disease that favored CCR5Δ32 may have been smallpox.
Using linkage disequilibrium to
detect strong positive selection.

A new mutant allele will be in linkage
disequilibrium when it first appears. If it persists,
it may increase in frequency.

Over time linkage disequilibrium will break down
as a result of recombination from crossing over.

Linkage disequilibrium breaks down fastest for
loci further apart on a chromosome because
crossing over take place more often between
distant loci.
Using linkage disequilibrium to
detect strong positive selection.

High linkage disequilibrium indicates an
allele originated recently.

Also expect a recently mutated allele to be
rare unless selection strongly favoring it.
Using linkage disequilibrium to
detect strong positive selection.

If an allele is common, but has high linkage
disequilibrium, especially with loci that are
located far away on the chromosome, this suggests
that the allele has been strongly selected for and
must have originated recently.

If the allele had arisen a long time ago sex should
have eliminated the linkage disequilibrium.
Using linkage disequilibrium to
detect positive selection.
An allele of G6PD (Glucose-6-phosphate
dehydrogenase) G6PD-202A has a high
frequency (~18% in African populations)
and has a high degree of linkage
disequilibrium.
 Thus, appears to have been strongly
selected for recently.

G6PD and malaria

There are many common G6PD deficiencies
and their distribution corresponds closely
with distribution of malaria.

Appears that G6PD-202A confers strong
protection against malaria.
Adaptive significance of sex
Many risks and costs associated with sexual
reproduction.
 Searching for a mate requires time and
energy and exposes organisms to predators.
 Mate may require investment (food,
territory, defense).
 Risk of sexually transmitted disease.

Adaptive significance of sex
Why not reproduce asexually?
 Many organisms can reproduced both
sexually and asexually.
 E.g. plants, aphids.

Adaptive significance of sex

In populations that can reproduce both
asexually and sexually will one mode of
reproduction replace the other?
Adaptive significance of sex
Maynard-Smith explored the question.
 Considered population in which some
organisms reproduce asexually and the
others sexually.
 Made 2 assumptions.

Maynard Smith’s assumptions
1. Mode of reproduction does not affect
number of offspring she can produce.
 2. Mode of reproduction does not affect
probability offspring will survive.
 (asexually reproducing organisms produce
only females, sexually reproducing produce
both males and females.)

Adaptive significance of sex
Asexually reproducing females under
Maynard-Smith’s assumptions leave twice
as many grandchildren as sexually
reproducing females.
 This is because each generation of sexually
reproducing organisms contains only 50%
females.

Adaptive significance of sex
Ultimately, asexual reproduction should
take over.
 However, in nature this is not the case.
 Most organisms reproduce sexually and
both sexual and asexual modes of
reproduction are used in many organisms

Adaptive significance of sex
Sex must confer benefits that overcome
mathematical reproductive advantage of
asexual reproduction.
 One or both of Maynard-Smith’s
assumptions must be incorrect.

Adaptive significance of sex
Assumption 1 (mode of reproduction does
not affect number of offspring she can
produce) violated in species where male
helps female (humans, birds, many
mammals, some fish).
 However, not likely a general explanation
because in most species male does not help.

Adaptive significance of sex

Most likely advantage of sex is that it
increases offspring’s prospects of survival.
Dunbrack et al. (1995)
experiment
Lab populations of flour beetles
 Mixed populations of red and black strains.
 Strains designated as “sexual” or “asexual”
in experimental replicates.

Dunbrack et al. (1995)
experiment

Asexual strain in culture. Every generation
each adult replaced by 3 new individuals
from reservoir population of sexual strain.
3X reproductive advantage, but no
evolution in response to environment..

Sexual strain allowed to breed and remain
in culture. Could evolve.
Dunbrack et al. (1995)
experiment
Two strains prevented from breeding with
each other.
 Populations tracked for 30 generations.
 8 replicates in experiment. Four different
concentrations of malathion (insecticide).
 Controls: No evolution, but one strain had
3x reproductive advantage.

Dunbrack et al. (1995)
experiment
Control results.
 “Asexually” reproducing strain
outcompeted the sexually reproducing
strain.

Dunbrack et al. (1995)
experiment
Experimental cultures: Initially asexual
strain increased in frequency, but eventually
sexual strain took over.
 Rate at which sexual strain took over
proportional to malathion concentration.

Dunbrack et al. (1995)
experiment

Conclusion: Assumption 2 of MaynardSmith’s null model incorrect.

Descendants produced by sexual
reproduction achieve higher fitness than
those produced asexually.
Sex in populations means genetic
recombination

Sex:
– Meiosis with crossing over
– Matings with random individuals
– Consequence is genetic recombination. New
combinations of genes brought together each
generation.
Why is sex beneficial?
1. Genetic drift plus mutation make sex
beneficial
 2. Selection imposed by changing
environments makes sex beneficial

Genetic drift plus mutation:
Muller’s ratchet

An asexually reproducing female will pass a
deleterious mutation to all her offspring.
Back mutation only way to eliminate it.
 Muller’s ratchet: deleterious alleles will
accumulate in asexually reproducing
populations.

Muller’s ratchet
Small, asexually reproducing population.
 Deleterious mutations occur occasionally.
 Mutations selected against.
 Population contains groups of individuals
with zero, one, two, etc. mutations.

Muller’s ratchet
Few individuals in each group. If by chance
no individuals with zero mutations
reproduce in a generation, then zero
mutation group lost.
 Rate of loss of groups by drift will be higher
than rate of back mutation so population
will over time accumulate deleterious
mutations in a ratchet fashion.

Muller’s ratchet

Burden of increased number of deleterious
mutations (genetic load) may eventually
cause population to go extinct.

Sexual reproduction breaks ratchet. E.g.
two individuals each with one copy of a
deleterious mutation will produce 25% of
offspring that are mutation free.
Anderson and Hughes (1996) test
of Muller’s ratchet in bacteria.

Propagated multiple generations of bacterium, but
each generation derived from one indiviual
(genetic drift).

444 cultures. At end of experiment (2 months) 1%
of cultures had reduced fitness (lower than wildtype bacteria), none had increased fitness. Results
consistent with Muller’s ratchet.
Selection favors sex in changing
environments.

Effects of Muller’s ratchet slow and take
many generations to affect asexually
reproducing populations.

However, advantage of sex is apparent in
only a few generations. What short-term
benefit does sex provide?
Selection favors sex in changing
environments.

In constant environments asexual
reproduction is a good strategy (if mother
adapted to it, offspring will be too).

However, if environment changes offspring
may be poorly adapted and all will be
poorly adapted because they are identical.
Selection favors sex in changing
environments.

Sexually reproducing females produce
variable offspring so if environment
changes some may be well adapted to the
new environment.
Selection favors sex in changing
environments.
Red Queen Hypothesis: evolutionary arms
races between hosts and parasites.
 (Red Queen runs to stand still)
 Parasites and hosts in perpetual struggle.
Host evolving defenses, parasites evolving
ways to evade them.
 Different multilocus host genotypes favored
each generation. Sex creates the genotypes.

Do parasites favor sex in hosts?
Lively (1992) studies New Zealand
freshwater snail. Host to parasitic
trematodes.
 Trematodes eat host’s gonads and castrate
it! Strong selection pressure.
 Snail populations contain both obligate
sexually and asexually reproducing females.

Do parasites favor sex in hosts?

Proportion of sexual vs asexual females
varies from population to population.

Frequency of trematode infections varies
also.
Do parasites favor sex in hosts?

If evolutionary arms race favors sex, then
sexually reproducing snails should be
commoner in populations with high rates of
trematode infections.

Results match prediction.
White slice indicates
frequency of males
and thus sexual
reproduction
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