Transcript Selection

Selection
Dan Graur
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Conditions for maintaining
Hardy-Weinberg equilibrium:
1.
2.
3.
4.
5.
random mating
no migration
no mutation
no selection
infinite population size
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2 mathematical approaches
to studying genetic changes
in populations:
Deterministic models
Stochastic models
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Deterministic models assume that changes
in allele frequencies from generation to
generation occur in a unique manner and
can be unambiguously predicted from
knowledge of initial conditions.
Strictly speaking, this approach applies
only when: (1) the population is infinite in
size, and (2) the environment either
remains constant with time or changes
according to deterministic rules.
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Stochastic models assume that changes
in allele frequencies occur in a
probabilistic manner, i.e., from
knowledge of the conditions in one
generation one cannot predict
unambiguously the allele frequencies
in the next generation, but can only
determine the probabilities with which
certain allele frequencies are likely to
be attained.
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Stochastic models are preferable to
deterministic ones, since they are
based on more realistic
assumptions.
However, deterministic models are
easier mathematically and, under
certain circumstances, they yield
sufficiently accurate insights.
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Selection
The deterministic approach
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Natural selection
The differential reproduction of genetically
distinct individuals (genotypes) within a
population.
Differential reproduction is caused by
differences among individuals in such traits
as (1) mortality, (2) fertility (offspring), (3)
fecundity (gametes), (4) mating success, and
(5) viability of offspring.
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Is the fitness of
slim men higher
than that of fat
men?
Dixson et al. 2003.
Masculine somatotype
and hirsuteness as
determinants of sexual
attractiveness to women.
Archives of Sexual
Behavior 32:29–39.
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Variability
Non-Genetic
Genetic
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Arashnia levana
Non-genetic variability.
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Helix aspersa
Genetic variability.
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Variability
Non-Genetic
Fitness-related
Genetic
Fitness-unrelated
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Genetic? No
Fitness related? Yes
Does selection operate?
Hair color
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Sperm morphology
Genetic? Yes
Fitness related? Yes
Does selection operate?
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Genetic?
Fitness related?
Does selection operate?
Wealth
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Darwinian
selection
requires
variation.
Lamarkian
selection
does not
require
variation.
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Natural selection is
predicated on the
availability of genetic
variation among individuals
in characters related to
reproductive success
(variation in fitness).
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Synonymous and nonsynonymous
genetic variability.
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Evolutionary Success
Ryan Kremer
Carlos Slim Helú
(richest person on
earth)
6 children
Linus Pauling
(Only person to win
2 unshared Nobel
prizes)
4 children
The fitness (w) of a genotype is a measure
of the individual’s ability to survive and
reproduce.
The size of a population is constrained by
the carrying capacity of the environment.
Thus, an individual’s evolutionary success
is determined not by its absolute fitness,
but by its relative fitness in comparison
to the other genotypes in the population.
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Finite Niche (Carrying) Capacity
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In nature, the fitness of a genotype is not
expected to remain constant for all
generations and under all conditions.
However, by assigning a constant value of
fitness to each genotype, we are able to
formulate simple models, which are useful
for understanding the dynamics of change
in the genetic structure of a population
brought about by natural selection.
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• We assume that fitness is determined
solely by the genetic makeup.
• We assume that all loci contribute
independently to fitness (i.e., the
different loci do not interact with one
another in a manner that affects
fitness), so that each locus can be dealt
with separately.
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A very simple model (1):
One locus
=
A
Two alleles
=
A 1 & A2
The old allele
=
A1
The new allele is =
A2
Three genotypes =
A 1 A 1 , A1 A 2 & A 2 A 2
Each genotype has a typical fitness (w)
We are interested in the fate of A2
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A very simple model (2):
The fitness of the old genotype (A1A1) is
set at 1.
The relative fitnesses of the two new
possible genotypes (A1A2 & A2A2) are
defined comparatively as 1 + s or 1 + t,
where s and t are the selection coefficients.
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In comparison with A1, A2 may
deleterious, neutral, or
advantageous, and it will be
subject to purifying
selection, no selection, or
positive Darwinian
selection, respectively.
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Genotype
A1A1
Fitness
w11
Frequency p2
A1A2
A2A2
w12
w22
2pq
q2
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Change in A2 allele frequency per
generation
pq[ p(w  w )+ q(w  w )]
12
11
22
12
q 
2
2
p w  2pqw  q w
11
12
22
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Genotype
A1A1
A1A2
A2A2
Fitness
w11
w12
w22
2pq
q2
Frequency p2
These are the variables we fiddle with
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Dominance & Recessiveness
At the phenotypic level
At the fitness level
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A1 dominance
Genotype
A1A2
A2A2
w11
w11
w22
Frequency p2
2pq
q2
Fitness
A1A1
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A1 dominance
Genotype
Fitness
A1A1
1
A1A2
1
A2A2
1+s
A2
pq2s
q 
2
1 q s
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A2 dominance
Genotype
A1A1
A1A2
A2A2
Fitness
w11
w22
w22
2pq
q2
Frequency p2
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codominance
A2 dominance
Genotype
Fitness
A1A2
1+s
A2A2
1+s
2
p qs
2
1 s  p s
A2
q 
A1A1
1
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Codominance (genic selection)
Genotype
A1A1
Fitness
w11
Frequency p2
A1A2
A2A2
(w11 + w22)/2 w22
2pq
q2
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codominance
Genotype
Fitness
A1A2
1+s
A2A2
1 + 2s
spq
1 2spq 2sq 2
A2
q 
A1A1
1
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codominance
A1 dominance
A2 dominance
A1 = old mutant
A2 = new mutant
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Selection intensities
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Initial Frequencies
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Industrial
Melanism
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A2
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Selection against recessive lethal alleles
b-hexosaminidase A is a
dimeric lysosomal protein
consisting of two a-subunits. It
is encoded by a gene on
chromosome 15.
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Selection against recessive lethal alleles
b-hexosaminidase-A catalyzes the removal of Nacetylgalactosamine from GM2 ganglioside, thereby
degrading and removing it from the nervous system.
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Absence of b-hexosaminidase-A
 Accumulation of GM2 ganglioside in neurons.
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Selection against recessive lethal alleles
Tay-Sachs disease results from a
defect in the HEXA gene encoding the
a subunit of b-hexosaminidase A.
Warren Tay (1843-1927)
Bernard Sachs (1858-1944)
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Tay-Sachs is a recessive… allele
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Tay-Sachs is a recessive & lethal alleles
Symptoms of classical Tay-Sachs disease first appear
at 4 to 6 months of age when an apparently healthy
baby gradually stops smiling, crawling or turning
over, loses its ability to grasp or reach out and,
eventually, becomes blind, paralyzed and unaware of
its surroundings. Death occurs by age 3-5.
Cherry-red spot from an
infant with Tay-Sachs
disease.
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Selection against recessive lethal alleles
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Inefficiency of selection against
recessive allele
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It is difficult to rid a population of recessive
alleles, because they hide behind the back
of dominant alleles, and are not exposed to
selection.
If q = 50%, then 50% of all recessive
alleles are in heterozygous state.
If q = 10%, then 98% of all recessive
alleles are in heterozygous state.
If q = 1%, then 99.98% of all recessive
alleles are in heterozygous state.
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Selection against dominant lethal alleles
Dr. George Sumner Huntington
1850-1916
Protein: huntingtin
Gene: 180 Kb (chromosome 4)
Exons: 67
Amino acids: 3,141
Mode: autosomal dominant
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Selection against dominant lethal alleles
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It should be easy to rid a population of
dominant alleles, because all of them are
exposed to selection at all frequencies.
So why are
there dominant
lethal diseases?
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1.
2.
3.
4.
Recurrent mutations.
Late age of onset.
Variable expressivity.
Incomplete penetrance.
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Overdominance
Genotype
A1A1
Fitness
w11
Frequency p2
A1A2
A2A2
w12 > w11,w22
w22
2pq
q2
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Underdominance
Genotype
A1A1
Fitness
w11
Frequency p2
A1A2
A2A2
w12 < w11,w22
w22
2pq
q2
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The change in the frequency of A2 from
generation to generation is:
pq(2sq- tq - s)
q 
2
1 2spq tq
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At equilibrium, i.e.,
when ∆q = 0.
s
qˆ 
2s  t
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overdominance
s = 0.04 and t = 0.02
underdominance
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s = - 0.02 and t = - 0.01
Overdominant selection is inherently
inefficient, even if the two homozygotes
are not viable.
RIP
Powderpuff
Chinese Crested
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The peculiar case of
sickle-cell anemia
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Glutamic acid
Valine
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alahkyh
147aa
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147aa
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Intuitive Model
normal fitness
b
b
H H  normal
somewhat reduced fitness
b
s
H H sickle cell trait
reduced fitness
s
s
H H sickle cell anemia
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In theory, the end result
should have been
directional selection — a
S
drastic reduction in H
allele frequency in the
population.
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Worldwide distribution of sickle-cell anemia
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In practice, the
frequency of the
S
H allele may
reach enormous
values in some
populations.
>20%
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Plasmodium falciparum
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An evolutionary “experiment”: Slave trade
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West Africa Frequency= >20%
Curaçau
no malaria
HS frequency = 5%
Surinam
endemic malaria
HS frequency = 20%
300 years = 10-15 generations
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Genotype HH
Fitness
1
S
HH
1.27
S
S
H H
0.25
• With malaria in the background, heterozygotes have
a huge advantage over the wild type homozygotes.
• In the absence of malaria, the heterozygotes have a
slight disadvantage in comparison to wild type
homozygotes.
• The fitness of the HsHs homozygotes is not affected
by the presence or absence of malaria.
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Modiano D, Luoni G, Sirima BS,
Simpore J, Verra F, Konate A, Rastrelli
E, Olivieri A, Calissano C, Paganotti
GM, D'Urbano L, Sanou I, Sawadogo
A, Modiano G, Coluzzi M. 2001.
Haemoglobin C protects against
clinical Plasmodium falciparum
malaria. Nature 414:305-308.
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Hemoglobin C
E to V = HS
E to K = HC
codon
position
6!
Glutamic acid
Lysine
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Genotype HH
Fitness
1
S
HH
1.27
S
S
H H
0.25
Genotype HH
Fitness
1
C
C
C
HH
1.27
H H
0.75
“…in the long term and in the absence of malaria
control, HbC would replace HbS in central West Africa.”
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The peculiar case of
Rh-blood groups
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Underdominant selection?
Why does Rh– still exist?
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Typ e of mutation Typ e of resulting
selection
Deleterious
Purifying selection
Detrimental
Neutral
No selection
Advantageous
Positive Darwinian
Adaptive
Selection
Beneficial
Overdominant
Stable balancing
selection
Underdominant Unstable balancing
selection
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A summary:
Selection may lead to changes in allele
frequencies over time.
A mere change in allele frequencies from
generation to generation does not necessarily
indicate that selection is at work.
A lack of change in allele frequencies does not
necessarily indicate that selection is absent.
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Selection is a very
important evolutionary
force.
At least, in principle…
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