1 A review of fitness Fitness has two components: 1. Viability; - - PDF document

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Functional divergence 1: FFTNS and Shifting balance theory

There is no conflict between neutralists and selectionists

• n the role of natural selection:

Natural selection is the only explanation for adaptation

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A review of fitness Fitness has two components: 1. Viability; an individual’s ability to survive to reproduce 2. Fecundity; an individual’s reproductive output. Evolutionary fitness is symbolized with W

Waa WAa WAA Phenotype 0.76 1 1 aa Aa AA Genotype Symbolism

A review of fitness

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WAA > WAa > Waa

0.2 0.4 0.6 0.8 1 Fitness AA Aa aa Genotypes

Directional selection occurs when selection favors the phenotype at an extreme of the range of phenotypes.

• exerts pressure for FIXATION (frequency goes to 1)
• imposes a direction on evolution

A review of fitness: Directional selection

0.2 0.4 0.6 0.8 1 Fitness AA Aa aa Genotypes

WAA < WAa > Waa

Overdominant selection occurs when the heterozygote has a greater fitness than either homozygote.

• also called balancing selection or heterozygote advantage
• maintains a stable polymorphism; acts against fixation

A review of fitness: overdominat selection

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Symbolism for generation 0 Genotype AA Aa aa Frequency p0

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2p0q0 q0

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Phenotype WAA WAa Waa

WAA : WAa : Waa Survival ratio:

p2WAA : 2pqWAa : q2Waa

Genotype ratio: Problem: the genotype ratios do not sum to 1.

A review of fitness:

W = p2WAA + 2pqWAa + q2Waa

Normalize by dividing by the grand total after selection:

W = AVERAGE FITNESS

W − 1

Genetic load:

A review of fitness:

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Fisher’s fundamental theorem of natural selection: FFTNS

In words: The rate of increase in the average fitness of a population is equal to the genetic component of the variation in fitness

Fisher’s fundamental theorem of natural selection: FFTNS

FFTNS is based on the well known formula for the response of a population to phenotypic selection (R).

R = h2 × S

h2: The proportion of total phenotypic variance that is predictably transmitted to next generation (i.e., additive genetic component of variance) S: SELECTION DIFFERENTIAL; the difference between the mean phenotype of those under selection and the mean phenotype of the population.

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FFTNS

( )

W W V W R

a

= ∆ =

The change in population fitness depends on just two parameters. : The average fitness of the population Va(W): Additive component of the total variation in fitness

W Biological implications of FFTNS

1. Populations can’t adapt without genetic variance in fitness

• Va(W) : zero or positive only
• Va(W) = 0, then change in average fitness = 0

2. Rate of population evolution depends on mean fitness 3. Fitness always increases

• Not as trivial as it seems.
• populations only go to local maximum
• populations cannot explore entire set of outcomes
• selection can prevent further adaptation

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Adaptive topography

Adaptive topography; a surface of mean fitness for a population where peaks represent the highest values of mean fitness, and valleys the lowest values of mean fitness. Also called: Adaptive landscape Fitness topography Fitness landscape

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.4 0.6 0.8 1 frequncey of allele "a" Ave fitness of popualtion WAA = 0.1 WAa = 0.75 Waa = 1 Directional selection

Adaptive topography

W = p2WAA + 2pqWAa + q2Waa The most simple case: 1 locus, 2 alleles, directional selection

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Adaptive topography

Another simple case: 1 locus, 2 alleles, overdominant selection W = p2WAA + 2pqWAa + q2Waa

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.4 0.6 0.8 1 freqeuncy of allele "a" Ave fitness of poplation WAA = 0.5 WAa = 1 Waa = 0.1

Adaptive topography

More complex case: 1 locus, 3 alleles, overdominant & directional selection …. we need a De Finetti diagram

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Introduction to the De Finetti diagram:

Alleles 2 and 3 have freq =0 at this vertex Alleles 1 and 2have freq =0 at this vertex Alleles 1 and 3 have freq =0 at this vertex Indicates: Allele 1: freq = 0.35 Allele 2: freq = 0.15 Allele 3: freq = 0.50 Allele 1 Allele 2 Allele 3 0.5 0.35 0.15 Lowest mean fitness Global peak in mean fitness Local peak in mean fitness Valley on the fitness landscape Allele 1 Allele 2 Allele 3

Adaptive topography

More complex case: 1 locus, 3 alleles, overdominant & directional selection

Lines: fitness contours where the frequencies of the three alleles yield the same population fitness

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Adaptive topography

More complex case: 1 locus, 3 alleles, overdominant & directional selection

end here start here start here end here

Difficult assumptions of FFTNS 1. Constant fitness through time 2. Complete linkage equilibrium 3. Fitness must be the phenotype 4. No genetic drift

• not useful as a general model over long periods of time
• very useful for examining specific aspects of the evolutionary process

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A new term: the marginal fitness of an allele Marginal fitness: the average fitness of all individuals in a population that bear a certain allele. Also called: average affect of an allele Notation for “a” allele: Wa marginal fitness

Allele A (freq = p) Allele a (freq = q)

Wa = q(Waa) + p(WAa)

Allele A (freq = p) Allele a (freq = q) Allele c (freq = r)

Wa = q(Waa) + p(WAa) + r(Wac)

Wa - W = 0; no change in frequency of a Wa - W > 0; the a allele increases in frequency Wa - W < 0; the a allele decreases in frequency

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Adaptation in hum an populations: sickle cell haem oglobin Sickle morphology of RBCs leads to a “crisis”

Sickle morphology is triggered by extreme deoxygenating event (0.1 to 1 second). Crisis leads to anemia

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Sickle cell ”crisis” and anemia have profound clinical consequences

S-RBC lifespan: 2 0 days ( verses 1 2 0 )

The genetics you probably already know

A allele: normal hemoglobin S allele: single amino acid substitution at position 6 (GLU → Val)

Sickle cell anaemia 40% sickling of RBCs Normal Blood Phenotype SS AS AA Genotypes

AS phenotyoe: 1 . Selective sickling of plasm odium infected cells: direct destruction [ ?] 2 . High oxygen radical production by sickle-cells kills parasites [ ?] 3 . Prom otes im m une system attack

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S allele is maintained in human populations by natural selection A and S allele polymorphism is classic example of overdominant selection

1: Fitness and mortality are estimated as an average over 72 west African populations of

• humans. Data from Cavalli-Sforza and Bodmer (1971).

0.2 1 0.89* Fitness1 very high Low moderate Mortality1 Sickle cell anaemia 40% sickling of RBCs Normal Blood Phenotype SS AS AA Genotypes

* Cerebral anem ia is not fun

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A and S allele polymorphism is classic example of overdominant selection

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.4 0.6 0.8 1 freqeuncy of allele "S" Ave fitness of poplation

Peak in average fitness of population

As before, the fitness of the population can only go “uphill”. Marginal fitness calculations verify this result. I nitial freq of S = 0 .0 1 : WS = 0.99 and = 0.89 WS - = 0.11; the S allele will increase I nitial freq of S = 0 .2 5 : WS = 0.8 and = 0.89 WS - = -0.088; the S allele will decrease W W W W

Natural selection arrives at a solution that protects about 20% of the population

There is another allele called C

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A and C allele polymorphism is classic example of directional selection

Data from Cavalli-Sforza and Bodmer (1971). 1 0.89* 0.89* Fitness Resistant Normal Normal Blood Phenotype CC AC AA Genotypes

* Cerebral anem ia is not fun

A and C allele polymorphism is classic example of directional selection

As before, the fitness of the population can only go “uphill”. Marginal fitness calculations verify this result. I nitial freq of C = 0 .0 1 : WC = 0.891 and = 0.890 WC - = + 0.001; the C allele will slowly increase I nitial freq of C = 0 .2 5 : WC = 0.917 and = 0.90 WC - = + 0.02; the C allele will increase W W W W

Natural selection arrives at a solution that protects about 100% of the population

Peak in average fitness of population

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.4 0.6 0.8 1 frequncey of allele "a" Ave fitness of popualtion “c”

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Most human populations have adapted by going to a balanced A/S polymorphism Let’s consider a population with A, S and C alleles

Genotypes AA AS SS AC SC CC Frequency p2 2pq q2 2pr 2qr r 2 Fitness 0.89 1 .2 .89 .71 1.31 Mortality1 moderate low Very high moderate moderate low Anaemia none some severe none some none 1: Fitness and mortality are estimated as an average over 72 west African populations of humans. Data from Cavalli-Sforza and Bodmer (1971).

Frequency of A = p Frequency of S = q Frequency of C = r

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WS = q(WSS) + p(WAS) + r(WSC) WS = 0.12(0.2) + 0.879(1) + 0.001(0.71) WS = 0.903 WC = r(WCC) + p(WAC) + q(WSC) WC = 0.001(1.31) + 0.879(0.89) + 0.12(0.71) WC = 0.869 Frequency of A = 0.879 = p Frequency of S = 0.120 = q Frequency of C = 0.001 = r

= 0.903

W

Population close to balanced A/S polymorphism:

Let’s consider a population with A, S and C alleles

1 . I m portance of historical effects 2 . Natural selection can prevent adaptation

Let’s consider a population with A, S and C alleles

Frequency of A = 0.879 = p Frequency of S = 0.05 = q Frequency of C = 0.01 = r WS = 0.957 WC = 0.885 = 0.898 WS - = 0.06; The S allele invades! WC - = -0.01; the C allele cannot invade! W

Assum e both S and C are rare:

W W

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S allele A allele C allele The C allele has to start with a high frequency in order for it to invade In this region the C allele only needs to be a littler more than 10%

Adaptive topography for three allele case [same as before]

Frequency of A = 0.64 = p Frequency of S = 0.25 = q Frequency of C = 0 .1 1 = r WS = 0.768 WC = 0.891 = 0.877 WS - = -0.10; The S allele is a gonner! WC - = + 0.01; the C allele invades! W

Assum e both S and C are rare:

W W

Let’s consider a population with A, S and C alleles

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Adaptive topography for three allele case Natural selection cannot move population across the valley! Two other population genetic forces can: 1. Strong genetic drift: increase C > 10% 2. Inbreeding: does not change allele frequencies

• reduce frequency of AS heterozygote
• Increase frequency of CC homozygote

Sewall Wright: shifting balance theory (SBT) of evolution “The problem as I see it is that of a mechanism by which species may continually find its way from lower to higher peaks… ”

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SBT: assumptions

Assumption 1: Large amount of polymorphism in equilibrium.

• Variation must be relevant to fitness
• Fitness variation is relevant to “minor factors”

Assumption 2: Each gene has many phenotypic effects [pleiotropy] Assumption 3: Complex adaptive topography Assumption 4: Multiple, partially isolated populations

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SBT: Three phases 1. Phase of genetic Drift [exploration] 2. Phase of Mass selection 3. Phase of inter-population selection

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Difficulties with SBT

• 1. Species never get stuck on peaks;

there is always a way off.

• 2. Ne of natural populations too large

for drift to move them around to the degree required by SBT

SBT has been controversial since the beginning

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Modern difficulties with SBT

1. Requires: low migration rates for exploration and transition [ phases 1 and 2] ; and higher migration rates for phase 3. 2. Population structures typical of natural populations seem to be too small for phase 1 3. Group selection is a weak force for evolution, and hence unlikely to result in a shift in equilibrium: an extremely high amount of migration is required among sub-populations for phase 3 to work. 4. Alternatives seem more likely.

Wright suggested some alternatives

• 1. Change in environment..
• 2. Mutation..
• 3. Change in strength of selection..

It seems that SBT and the alternatives require some “waiting”

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SBT and FFTNS are important theories Their status and role are quite different from that of the neutral theory