Download Genetic Load

Neutral theory 1:
Genetic load and introduction
Neutral theory
1. Mutation
2. Polymorphism
Neutral theory: connected these is a new (radical) way
3. Substitution
1
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
•
6.
7.
some such changes can have large discrete effects
diversification occurs by speciation
•
usually a gradual process
•
usually by geographic isolation
microevolution ⇒ macroevolution
Neo-Darwinism
Balance school
Classical school
• Most new mutations are deleterious
• Most new mutations are deleterious
• Natural selection is of central importance
• Natural selection is of central importance
•Polymorphism is a function of selection
•Polymorphism is a function of selection
• Polymorphism is common
• Polymorphism is very rare
•Balancing selection is comparable to
purifying selection in micro-evolution
• Positive Darwinian selection and
balancing selection are rare with respect to
purifying selection in micro-evolution
• Genetic variation connected to
morphological variation.
• Prediction: most populations will be
heterozygous at most loci
• Too much “genetic load” for genetic
variation to connect with morph. variation
•Prediction: most populations will be
homozygous at most loci
2
“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)
3
Protein electrophoresis: big changes in the 1960’s
(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: the results are in …
Lewontin and Hubby (1966):
Harris (1966):
• 5 natural populations of Drosophila
• Humans
• 18 loci
• 71 loci
• 30% of loci (27 over the 5 popn.s)
were polymorphic
• 28% (20) were polymorphic
• Human heterozygosity: 7% (2-53%)
• Fruitfly heterozygosity: 11%
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
4
Genetic load
Genetic load: the extent to which the fitness of an individual is below the
optimum for the population as a whole due to the deleterious alleles that
the individual carries in its genome.
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.
W
= average fitness
Genetic load (L) = 1 - W
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]
5
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.
no selective death: large excess
no selective death: small excess
120
120
100
100
Background
mortality when all
individuals have the
same fitness
80
60
40
80
60
Background
mortality when all
individuals have the
same fitness
40
20
20
0
0
1
2
1
2
Population declines:
Genetic death > reproductive excess
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.
Change in recessive allele frequency over time under different intensities of negative
selection
1
s=0
s = 0.01
Frequency of a allele
0.9
0.8
0.7
0.6
s = 0.1
s = 0.5
s = 0.9
0.5
0.4
0.3
0.2
0.1
0
1
26
51
76
101
126
151
176
201
226
251
Generations
There is a cost to selection, in genetic death, during this time period
6
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
Haldane’s “Cost of selection”
(1957)
propotion that die due to selection
C=∑
=
proportion that survive
14444444
4244444444
3
Assume directional
selection of a new
mutation:
∑
L
W
× Ne
C × Ne gives the total
selective death; this
must be sum over
generations it take to
fix the allele
over all generations it takes to fix the allele
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/ W = 0.1/0.9 = 0.111
C1 x Ne = 50 extra individuals per 1st generation
Total generation to fix allele = 100
Population 1:
Population 2:
Population 2:
Reproductive excess = 0
Reproductive excess = 0.1
Cost = C - R
Generation = 53
Generation = 100
- Extinction: C53 = 499.1
Cost = 0.111 – 0.1 = 0.011
… “soft selection”
- fixed beneficial allele
- C100 = 334.6
- survival: N =165.4
7
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 -W
And remember that the average fitness under these assumptions was:
W = 1 – sq2
We can make substitutions:
L=1- W
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).
8
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
Fitness
of phenotypes.
1
0.8
0.6
0.4
0.2
0
wAA > wAa > waa
AA
Aa
aa
Genotypes
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.
9
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
Deleterious recessive
Genotype
AA
Aa
aa
Frequency
p02
2p0q0
q02
wmodel
1
1
1-s
w
1
1
0.66
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
10
Genetic load: segregational
The model
Genotype
AA
Aa
aa
Frequency
p02
2p0q0
q02
w
1 – s1
1
1 – s2
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.
11
Neutral theory of molecular evolution
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
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.
12