1 Neo-Darwinism 1. genetic variation arises at random via mutation - - PDF document

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Neutral theory 1: Genetic load and introduction Neutral theory 1. Mutation 2. Polymorphism 3. Substitution

Neutral theory: connected these is a new (radical) way

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Neo-Darwinism

1. genetic variation arises at random via mutation and recombination 2. populations evolve by changes in allele frequencies 3. allele frequencies change by mutation, migration, drift and natural selection 4. most mutations are deleterious 5. most adaptive phenotypic effects are small so changes in phenotype are slow and gradual

• some such changes can have large discrete effects

6. diversification occurs by speciation

• usually a gradual process
• usually by geographic isolation

7. microevolution ⇒ macroevolution

Neo-Darwinism

Balance school

• Most new mutations are deleterious
• Natural selection is of central importance
• Polymorphism is a function of selection
• Polymorphism is common
• Balancing selection is comparable to

purifying selection in micro-evolution

• Genetic variation connected to

morphological variation.

• Prediction: most populations will be

heterozygous at most loci

Classical school

• Most new mutations are deleterious
• Natural selection is of central importance
• Polymorphism is a function of selection
• Polymorphism is very rare
• Positive Darwinian selection and

balancing selection are rare with respect to purifying selection in micro-evolution

• Too much “genetic load” for genetic

variation to connect with morph. variation

• Prediction: most populations will be

homozygous at most loci

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“It is altogether unlikely that two genes would have identical selective values under all the conditions under which they may coexist in a population. … cases of neutral polymorphism do not exist … it appears probable that random fixation is of negligible evolutionary importance” ⎯Ernst Mayr

Neo-Darwinism 1930’s: ⎯ no way to test the predictions of different schools ⎯ arguments centered on mathematical models 1950’s and 1960’s: ⎯ protein sequencing (slow and painful) ⎯ protein gel electrophoresis (fast and cheap)

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(A) Diagram of a protein gel electrophoresis apparatus, and (B) a photograph of a “stained” protein gel, the blue “blotches” are the proteins, their position indicates how far they migrated in the electric field.

A B

Protein electrophoresis: big changes in the 1960’s Protein electrophoresis: the results are in …

Lewontin and Hubby (1966):

• 5 natural populations of Drosophila
• 18 loci
• 30% of loci (27 over the 5 popn.s)

were polymorphic

• Fruitfly heterozygosity: 11%

Harris (1966):

• Humans
• 71 loci
• 28% (20) were polymorphic
• Human heterozygosity: 7% (2-53%)

Balance school: predictions correct ! Classical school: predictions wrong (But, what about load!) Lewontin and Hubby (1966) suggested that some of the polymorphism must be neutral

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Genetic load

Genetic load: the extent to which the fitness of an individual is below the

• ptimum for the population as a whole due to the deleterious alleles that

the individual carries in its genome.

W

= average fitness

Genetic load (L) = 1 - W

Genetic load: the difference between the average fitness of the population and the fitness of the best genotype. It measures the probability of selective death of an individual in a population.

Genetic load: an example

Two alleles (A and a) with frequencies p = q = 0.5: Survival to reproduce: AA = 40% Aa = 50% aa = 30% The relative fitness values are: AA = 0.8 Aa = 1 aa = 0.6 The mean fitness of the population = 0.25(0.8) + 0.5(1) + 0.25(0.6) = 0.85 The load of this population (L) = 1 – 0.85 = 0.15

[Note that if every member of the population had the same genotype the average fitnes would equal 1 and the load on the population would be zero.]

Selective death (or genetic death): the chance that an individual will die without reproducing as a consequence of natural selection. [e.g.,15% of offspring in above]

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Genetic load: the cost of selection [ or “Haldane’s dilemma”]

Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity.

Population declines: Genetic death > reproductive excess

20 40 60 80 100 120

1 2 Background mortality when all individuals have the same fitness

no selective death: large excess Background mortality when all individuals have the same fitness no selective death: sm all excess 20 40 60 80 100 120 1 2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 26 51 76 101 126 151 176 201 226 251 Generations Frequency of a allele s = 0.1 s = 0.5 s = 0.9 s = 0 s = 0.01 Change in recessive allele frequency over time under different intensities of negative selection

Genetic load: the cost of selection [ or “Haldane’s dilemma”]

Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity.

Consider a new muation to an beneficial domiant allele: it takes time for selection to remove the “old” [deleterious recessive] allele from the population. There is a cost to selection, in genetic death, during this time period

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Genetic load: the cost of selection [ or “Haldane’s dilemma”]

Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity. Haldane’s “Cost of selection” (1957)

Population declines: Genetic death > reproductive excess

Assume directional selection of a new mutation: C × Ne gives the total selective death; this must be sum over generations it take to fix the allele

W L

∑ ∑

= = survive that proportion selection to due die that propotion C

allele fix the to it takes s generation all

• ver

4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 2 1

× Ne

Genetic load: the cost of selection [ or “Haldane’s dilemma”]

Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity.

Suppose L = 0.1

Load = 10% population reduction Total size = 500 individuals Reproductive size: 450 Cost of selection (C) = L/ = 0.1/0.9 = 0.111 C1 x Ne = 50 extra individuals per 1st generation Total generation to fix allele = 100 Population 1: Reproductive excess = 0 Generation = 53

• Extinction: C53 = 499.1

W Population 2: Reproductive excess = 0.1 Generation = 100

• fixed beneficial allele
• C100 = 334.6
• survival: N =165.4

Population 2: Cost = C - R Cost = 0.111 – 0.1 = 0.011 … “soft selection”

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Genetic load: sources 1. Mutational load 2. Substitutional load [Haldane’s load] 3. Segregational load Genetic load: mutational

Let’s assume: (i) new mutations are deleterious alleles, and (ii) recessive. Remember the approximation of the equilibrium frequency of deleterious alleles [See population genetics, Topic 5 for a review]:

q = (µ/s)1/2

Remember that population load is:

L = 1 -

And remember that the average fitness under these assumptions was:

= 1 – sq2

We can make substitutions:

L = 1 - L = 1 – (1 – sq2) L = 1 – (1 – s(µ/s)) L = 1 – (1 – µ) L = µ

It is interesting that we estimate that the load is equal to the mutation rate. Because it suggests that the load is approximately independent of the reduction in fitness caused by the mutant (s).

W

W W

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Genetic load: mutational Mutational load is minor: 1. Equilibrium yields a polymorphism involving an allele that is very rare in the population 2. The load is trivial for the population, as the required excess reproductive capacity is not large. Defining directional selection

Directional selection: selection that favours the phenotype at an extreme of the range

• f phenotypes.

0.2 0.4 0.6 0.8 1 Fitness AA Aa aa Genotypes

wAA > wAa > waa

Directional selection: can be subdivided into two broad categories. These subtypes have been given different names, leading to a possible point of confusion. The next page is an attempt to clarify this issue.

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Defining two types directional selection

Type 1: Positive Darwinian selection: directional selection for fixation of a new and beneficial mutation in a population . Positive selection: Same as above. [Note that the above term is also shortened to “Darwinian selection”; this is a bad habit of which I am very guilty.] Type 2: Negative Darwinian selection: directional selection for removal of a new and deleterious mutation from a population. Negative selection: same as “negative Darwinian selection”. Purifying election: same as negative selection

Genetic load: substitutional = substitution by “type 1” directional selection

0.66 1 1

w

1 - s 1 1

wmodel

q0

2

2p0q0 p0

2

Frequency aa Aa AA Genotype Deleterious recessive

Haldane’s “cost of selection” is associated with fixation of an allele under a model such as the one above. Haldane assumed this type of load to estimate that the maximum rate of fixation of mutations in humans could not exceed 1 in 300 generations

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Genetic load: segregational

1 – s2 1 1 – s1

w

q0

2

2p0q0 p0

2

Frequency aa Aa AA Genotype The model

Segregational load is a big problem for the balance school: Well known examples exist; Haemoglobin, MHC locus, etc. Balance school would extend this to most polymorphic loci in the genome. Let’s see if this will work. Humans: 30% of loci are polymorphic (from Harris 1966) 30,000 genes (from recent genome projects), so 9000 are polymorphic Let’s assume a very small load on average: L = 0.001 Let’s assume that only half are under balancing selection (4500) [remember the balance school predicted a majority would be under balancing selection] Fitness of an individual locus = 0.999 Fitness over whole genome = 0.9994500 = 0.011 Load = 1- 0.011 = 0.989 [That is huge!!!] Cost = 0.989/0.011 = 89 [Do you know of any humans with families that big?]

Genetic load: other 1. Recombinational load 2. Incompatibility load 3. Lag load Note: all load arguments tend to be based on overly-simplistic models.

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Neutral theory of molecular evolution

Jack King and Thomas Jukes: Independently arrived at same conclusion as Kimura Published (1969) under the provocative title “Non-Darwinian evolution” I cannot over emphasize how radical this idea was at that time. Motoo Kimura:

• troubled by cost Haldane’s dilemma:
• 1 substitution every 300 generations
• troubled by Zukerkandl and Pauling’s (1965) molecular clock:
• 1 substitution every 2 years

Published a model of neutral evolution in 1968