Selection
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Transcript of Selection
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SelectiSelectionon
Dan Graur
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Conditions for maintaining Hardy-Weinberg equilibrium:
1. random mating2. no migration3. no mutation4. no selection5. 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 easiereasier mathematically and, under certain circumstances, they yield sufficiently accurate insights.
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SelectionSelectionThe deterministic approach
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Natural selectionNatural selection
The The differential redifferential repproductionroduction of genetically distinct of genetically distinct individuals (genotypes) within individuals (genotypes) within a population. a population.
Differential reproduction is Differential reproduction is caused by differences among caused by differences among individuals in such traits as individuals in such traits as (1) (1) mortalitmortality, (2) y, (2) fertilitfertility y (offspring), (3) (offspring), (3) fecunditfecundity y (gametes), (4) (gametes), (4) matinmating g successsuccess, , and (5) and (5) viabilitviability y ofof offsoffspprinring. g.
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Is the fitness of slim men higher than that of fat men?Dixson Dixson et alet al. . 2003. Masculine 2003. Masculine somatotypesomatotype and and hirsutenesshirsuteness as as determinants of determinants of sexual sexual attractiveness to attractiveness to women. women. Archives Archives of Sexual of Sexual BehaviorBehavior 32:29– 32:29–39.39.
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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 Genetic
Fitness-related Fitness-unrelated
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Genetic? NoGenetic? NoFitness related? YesFitness related? Yes
Hair color
Does selection operate? Does selection operate?
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Sperm morphology
Genetic? YesFitness related? Yes
Does selection operate? Does selection operate?
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Genetic?Fitness related?
Wealth
Does selection operate? Does selection operate?
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DarwiniaDarwinian n selectioselection n requires requires variatiovariation.n.
LamarkiaLamarkian n selectioselection does n does not not require require variatiovariation.n.
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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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Carlos Slim Helú(richest person on earth)6 children
Linus Pauling(Only person to win 2 unshared Nobel prizes) 4 children
Ryan Kremer
Evolutionary Success
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The fitness (w)(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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24Finite 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):A very simple model (1):
One locus = A
Two alleles = A1 & A2
The old allele = A1
The new allele is = A2
Three genotypes = A1A1, A1A2 &
A2A2
Each genotype has a typical fitness (w)
We are interested in the fate
of A2
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A very simple model (2):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 deleteriousdeleterious, neutralneutral, or advantageousadvantageous, and it will be subject to
purifying purifying selectionselection, no no selectionselection, or positive Darwinian positive Darwinian selectionselection, respectively.
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GenotypeGenotype AA11AA11 AA11AA22 AA22AA22
FitnessFitness ww1111 ww1212 ww2222
FrequencyFrequency pp22 2 2pqpq qq22
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Δq=pq[p(w12−w11)+q(w22−w12)]
p2w11
+2pqw12
+q2w22
Change in A2 allele frequency per generation
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GenotypeGenotype AA11AA11 AA11AA22 AA22AA22
FitnessFitness ww1111 ww1212 ww2222
FrequencyFrequency pp22 2 2pqpq qq22
These are the variables we fiddle with
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Dominance & Recessiveness Dominance & Recessiveness
At the phenotypic level
At the fitness level
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GenotypeGenotype AA11AA11 AA11AA22 AA22AA22
FitnessFitness ww1111 ww11 11 ww2222
FrequencyFrequency pp22 2 2pqpq qq22
AA1 1 dominancedominance
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Genotype A1A1A1A2A2A2
Fitness 1 1 1 + s
AA1 1 dominancedominance
€
Δq=pq2s
1+q2s
A2
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GenotypeGenotype AA11AA11 AA11AA22 AA22AA22
FitnessFitness ww1111 ww22 22 ww2222
FrequencyFrequency pp22 2 2pqpq qq22
AA2 2 dominancedominance
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Genotype A1A1A1A2A2A2
Fitness 1 1 + s 1 + s
codominanceAA2 2 dominancedominance
€
Δq=p2qs
1−s−p2sA2
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GenotypeGenotype AA11AA11 AA11AA22 AA22AA22
FitnessFitness ww1111 ((ww11 11 + + ww2222)/2 )/2 ww2222
FrequencyFrequency pp22 2 2pqpq qq22
Codominance (genic selection)Codominance (genic selection)
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Genotype A1A1A1A2A2A2
Fitness 1 1 + s 1 + 2s
€
Δq=spq
1+2spq+2sq2
codominance
A2
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AA1 1 = old mutant= old mutantAA2 2 = new mutant= new mutant
codominance A2 dominance
A1 dominance
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Selection intensities
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Initial Frequencies
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IndustrialIndustrialMelanismMelanism
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A2
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Selection against recessive lethal allelesSelection against recessive lethal alleles
-hexosaminidase A is a dimeric lysosomal protein consisting of two -subunits. It is encoded by a gene on chromosome 15.
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-hexosaminidase-A catalyzes the removal of N-acetylgalactosamine from GM2 ganglioside, thereby degrading and
removing it from the nervous system.
Selection against recessive lethal allelesSelection against recessive lethal alleles
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51 Accumulation of GM2 ganglioside in neurons.
Absence of -hexosaminidase-A
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Tay-Sachs disease results from a defect in the HEXA gene encoding the subunit of -hexosaminidase A.
Warren Tay (1843-1927)Bernard Sachs (1858-1944)
Selection against recessive lethal allelesSelection against recessive lethal alleles
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Tay-Sachs is a recessive… alleleTay-Sachs is a recessive… allele
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Tay-Sachs is a recessive & lethal allelesTay-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 allelesSelection against recessive lethal alleles
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Inefficiency of selection Inefficiency of selection against recessive alleleagainst recessive allele
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It is difficult to rid a population of It is difficult to rid a population of recessive alleles, recessive alleles, because they hide because they hide behind the back of dominant alleles, behind the back of dominant alleles, and are not exposed to selection.and are not exposed to selection.
If q = 50%50%, then 50%50% of all recessive alleles are in heterozygous state.
If q = 10%10%, then 98%98% of all recessive alleles are in heterozygous state.
If q = 1%1%, then 99.98%99.98% of all recessive alleles are in heterozygous state.
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Selection against dominant lethal allelesSelection against dominant lethal alleles
Protein: huntingtinGene: 180 Kb (chromosome 4)Exons: 67Amino acids: 3,141Mode: autosomal dominant
Dr. George Sumner Huntington1850-1916
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Selection against dominant lethal allelesSelection against dominant lethal alleles
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It should be easy to rid a population It should be easy to rid a population of dominant alleles, because all of of dominant alleles, because all of them are exposed to selection at all them are exposed to selection at all frequencies.frequencies.
So why are there dominantlethal diseases?
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1.1. Recurrent Recurrent mutations.mutations.
2.2. Late age of Late age of onset.onset.
3.3. Variable Variable expressivity. expressivity.
4.4. Incomplete Incomplete penetrance.penetrance.
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GenotypeGenotype AA11AA11 AA11AA22 AA22AA22
FitnessFitness ww1111 ww12 12 > > ww1111,,ww2222 ww2222
FrequencyFrequency pp22 2 2pqpq qq22
OverdominanceOverdominance
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GenotypeGenotype AA11AA11 AA11AA22 AA22AA22
FitnessFitness ww1111 ww12 12 < < ww1111,,ww2222 ww2222
FrequencyFrequency pp22 2 2pqpq qq22
UnderdominanceUnderdominance
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€
Δq=pq(2sq- tq-s)
1+2spq+tq2
The change in the frequency of A2 from generation to generation is:
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At equilibrium, i.e., when ∆q = 0.
€
ˆ q =s
2s−t
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overdominance underdominance
s = 0.04 and t = 0.02s = - 0.02 and t = - 0.01
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Overdominant selection is inherently inefficient, even if the two homozygotes are not viable.
RIP
Powderpuff Chinese Crested
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The peculiar The peculiar case of case of sickle-cell sickle-cell anemiaanemia
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71Glutamic acid Valine
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HbHb=normal
HbHs=sickle cell trait
HsHs=sickle cell anemia
normal fitness
somewhat reduced fitness
reduced fitness
Intuitive Model
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In theory, the end In theory, the end result should have result should have been directional been directional selection — a selection — a drastic reduction drastic reduction
in in HHS S allele allele frequency in the frequency in the population.population.
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Worldwide distribution of sickle-cell anemia
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In In practice, practice, the the frequency frequency
of the of the HHSS allele may allele may reach reach enormous enormous values in values in some some populationspopulations..
>20%
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Plasmodium falciparum
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86An evolutionary “experiment”: Slave tradeAn evolutionary “experiment”: Slave trade
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Surinamendemic malaria
HS frequency = 20%
Curaçauno malaria
HS frequency = 5%
West Africa Frequency= >20%
300 years = 10-15 generations
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€
Genotype HH HH S H SH S
Fitness 1 1.27 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 Modiano D, Luoni G, Sirima BS, Simpore J, Verra F, BS, Simpore J, Verra F, Konate A, Rastrelli E, Konate A, Rastrelli E, Olivieri A, Calissano C, Olivieri A, Calissano C, Paganotti GM, D'Urbano L, Paganotti GM, D'Urbano L, Sanou I, Sawadogo A, Sanou I, Sawadogo A, Modiano G, Coluzzi M. Modiano G, Coluzzi M. 20012001. . Haemoglobin C protects Haemoglobin C protects against clinical against clinical Plasmodium Plasmodium falciparumfalciparum malaria. malaria. NatureNature 414:305-308.414:305-308.
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codonposition
6!
Glutamic acid Lysine
Hemoglobin CE to V = HS
E to K = HC
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€
Genotype HH HHC HCHC
Fitness 1 1.27 0.75€
Genotype HH HH S H SH S
Fitness 1 1.27 0.25
“…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 The peculiar case of Rh-case of Rh-blood groupsblood groups
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Underdominant selection? Why does Rh– still exist?
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Type of mutation Type of resultingselection
DeleteriousDetrimental
Purifying selection
Neutral No selectionAdvantageousAdaptiveBeneficial
Positive DarwinianSelection
Overdominant Stable balancingselection
Underdominant Unstable balancingselection
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Selection may lead to changes in allele frequencies over time.
A lack of change in allele frequencies does not necessarily indicate that selection is absent.
A summary:
A mere change in allele frequencies from generation to generation does not necessarily indicate that selection is at work.
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Selection Selection isis a a veryvery importantimportant evolutionary evolutionary
force. force. At least, in principle…At least, in principle…