Selection

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Selection. Dan Graur. Conditions for maintaining Hardy-Weinberg equilibrium: 1. random mating 2. no migration 3. no mutation 4. no selection 5. infinite population size. 2 mathematical approaches to studying genetic changes in populations: Deterministic models Stochastic models.

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Selection

Dan Graur

Conditions for maintaining Hardy-Weinberg equilibrium:

1. random mating

2. no migration

3. no mutation

4. no selection

5. infinite population size

Deterministic models

Stochastic models

Deterministic models assume that changes in allele frequencies from generation to generation occur in a unique manner and can be unambiguouslypredicted 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.

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.

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.

Selection

The deterministic approach

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 ofoffspring.

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.

Non-Genetic

Genetic

Variability

Arashnia levana

Non-genetic variability.

Helix aspersa

Genetic variability.

Non-Genetic

Genetic

Fitness-related

Fitness-unrelated

Variability

Genetic? No

Fitness related? Yes

Hair color

Does selection operate?

Sperm morphology

Genetic? Yes

Fitness related? Yes

Does selection operate?

Genetic?

Fitness related?

Wealth

Does selection operate?

Darwinian selection requires variation.

Lamarkian selection does not require variation.

Natural selection is predicated on the availability of genetic variation among individuals in characters related to reproductive success (variation in fitness).

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.

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.

For simplicity:

• 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.

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 ofA2

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.

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.

Genotype A1A1 A1A2A2A2

Fitness w11w12w22

Frequency p2 2pqq2

These are the variables we fiddle with

Genotype A1A1 A1A2A2A2

Fitness w11w12w22

Frequency p2 2pqq2

Dominance & Recessiveness

At the phenotypic level

At the fitness level

A1 dominance

Genotype A1A1 A1A2A2A2

Fitness w11w11 w22

Frequency p2 2pqq2

A1 dominance

Genotype A1A1 A1A2A2A2

Fitness 1 1 1 + s

A2

A2 dominance

Genotype A1A1 A1A2A2A2

Fitness w11w22 w22

Frequency p2 2pqq2

A2 dominance

codominance

Genotype A1A1 A1A2A2A2

Fitness 1 1 + s 1 + s

A2

Codominance (genic selection)

Genotype A1A1 A1A2A2A2

Fitness w11 (w11 + w22)/2 w22

Frequency p2 2pqq2

codominance

Genotype A1A1 A1A2A2A2

Fitness 1 1 + s 1 + 2s

A2

Directional Selection

codominance

A2 dominance

A1 dominance

A1 = old mutant

A2 = new mutant

Industrial

Melanism

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.

Selection against recessive lethal alleles

b-hexosaminidase-A catalyzes the removal of N-acetylgalactosamine from GM2 ganglioside, thereby degrading and removing it from the nervous system.

Absence of b-hexosaminidase-A

 Accumulation of GM2 ganglioside in neurons.

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)

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.

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.

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

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?

Recurrent mutations.

• Late age of onset.
• Variable expressivity.
• Incomplete penetrance.

Overdominance

Genotype A1A1 A1A2A2A2

Fitness w11w12 > w11,w22w22

Frequency p2 2pqq2

Underdominance

Genotype A1A1 A1A2A2A2

Fitness w11w12 < w11,w22w22

Frequency p2 2pqq2

stable

unstable

overdominance

underdominance

s = 0.04 and t = 0.02

s = - 0.02 and t = - 0.01

Overdominant selection is inherently inefficient, even if the two homozygotes are not viable.

RIP

Powderpuff

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IntuitiveModel

normal fitness

somewhat reduced fitness

reduced fitness

In theory, the end result should have been directional selection — a drastic reduction in HS allele frequency in the population.

In practice, the frequency of the HS allele may reach enormous values in some populations.

>20%

West Africa Frequency= >20%

Curaçau

no malaria

HS frequency = 5%

Surinam

endemic malaria

HS frequency = 20%

300 years = 10-15 generations

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.

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.

E to V = HS

E to K = HC

Hemoglobin C

codon

position

6!

Glutamic acid

Lysine

“…in the long term and in the absence of malaria control, HbC would replace HbS in central West Africa.”

Underdominant selection?

Why does Rh– still exist?

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.

Selection is a very

important evolutionary

force.

At least, in principle…