1 selection dan graur 2 conditions for maintaining hardy-weinberg equilibrium: 1. random mating 2....

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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


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Genetic?Fitness related?

Wealth


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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.

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.

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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FitnessFitness ww1111 ww1212 ww2222


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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FitnessFitness ww1111 ww11 11 ww2222


AA1 1 dominancedominance

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Genotype A1A1A1A2A2A2

Fitness 1 1 1 + s


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Δq=pq2s

1+q2s

A2

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FitnessFitness ww1111 ww22 22 ww2222



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Fitness 1 1 + s 1 + s

codominanceAA2 2 dominancedominance

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Δq=p2qs

1−s−p2sA2

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FitnessFitness ww1111 ((ww11 11 + + ww2222)/2 )/2 ww2222


Codominance (genic selection)Codominance (genic selection)

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Fitness 1 1 + s 1 + 2s

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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.


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)


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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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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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FitnessFitness ww1111 ww12 12 > > ww1111,,ww2222 ww2222


OverdominanceOverdominance

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FitnessFitness ww1111 ww12 12 < < ww1111,,ww2222 ww2222


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.

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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

71Glutamic acid Valine

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mvhltpmvhltpeeeksavtalwgkvneksavtalwgkvnvdevggealgrllvvypwtqvdevggealgrllvvypwtqrffesfgdlstpdavmgnpkrffesfgdlstpdavmgnpkvkahgkkvlgafsdglahldvkahgkkvlgafsdglahldnlkgtfatlselhcdklhvdnlkgtfatlselhcdklhvdpenfrllgnvlvcvlahhfgpenfrllgnvlvcvlahhfgkeftppvqaayqkvvagvankeftppvqaayqkvvagvanalahkyh alahkyh 147aa147aa

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mvhltpmvhltpvveksavtalwgkvneksavtalwgkvnvdevggealgrllvvypwtqvdevggealgrllvvypwtqrffesfgdlstpdavmgnpkrffesfgdlstpdavmgnpkvkahgkkvlgafsdglahldvkahgkkvlgafsdglahldnlkgtfatlselhcdklhvdnlkgtfatlselhcdklhvdpenfrllgnvlvcvlahhfgpenfrllgnvlvcvlahhfgkeftppvqaayqkvvagvankeftppvqaayqkvvagvanalahkyh alahkyh 147aa147aa

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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

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…

1 selection dan graur 2 conditions for maintaining hardy-weinberg equilibrium: 1. random mating 2....

Documents

genetic changes

fitness w

relative fitness

absolute fitness

genetic structur

constant value of fitness

deterministic ones

deterministic rules