Download Evolutionary Genetics: Part 8 Natural Selection

Evolutionary Genetics: Part 8
Natural Selection
S. chilense
S. peruvianum
Winter Semester 2012-2013
Prof Aurélien Tellier
FG Populationsgenetik
Color code
Color code:
Red = Important result or definition
Purple: exercise to do
Green: some bits of maths
Population genetics: 4 evolutionary forces
random genomic processes
(mutation, duplication, recombination, gene conversion)
molecular diversity
natural
selection
random spatial
process (migration)
random demographic
process (drift)
Natural selection
Natural selection - Intro
so far we looked at neutral models = neutral theory (Kimura)
It assumes that every individual in a population has the same chance to
produce offsprings
This contradicts the Darwinian view = fitter individuals will produce
more or more viable offsprings and eventually form the basis of future
generations
Natural selection - Intro
To unify these approaches, is to attribute selection coefficients to some
genotypes
selection coefficient (s) = how much offsprings has an individual
compared to reference (reference offspring =1)
s = 0.05 means that that allele has 1.05 offspring
Kimura = most s are close to zero, i.e. alleles do not affect fitness
Natural selection
Fitness is a trait of a phenotype
high fitness = individual produce much viable offsprings that contribute to
future generations
A phenotype has a genotypic basis, so we can attribute fitness to genotypes
HOWEVER, The relationship between genotype and phenotype is complex
Research is called: the genotype-phenotype map
Stadler and Stephens, 2002
In the models, we hide the mechanisms explaining where the fitness difference
come from
Types of natural selection
Types of selection
Positive selection = one allele give an advantage to its carrier
Negative selection = one allele gives a disadvantage to its carrier
Balancing selection = several alleles are maintained in the population
Examples:
mutation change a protein:
Can be positive: resistance to an insecticide
Can be negative: protein has decreased affinity for substrate, or create stop
codon and the protein is truncated
A mutation can change the expression of the gene or protein concentration
Can be positive or negative for fitness
Types of natural selection
Viability selection
Individuals with high fitness not only produce much osffsprings, but also viable
offsprings reaching maturity
The survival of the offspring to adulthood is hard: from zygote to adult
Types of natural selection
Sexual selection
evolutionary success means having large number of offsprings
in sexual species, it is possible only if you find a mate, some phenotypes a better
at finding mates
assortative mating = mating of alike individuals (in humans mating according to
social status)
dissassortative mating = mating of disalike individuals (in plants self
incompatibility prevent selfing)
sexual selection also for male competition or female choosiness (peacock males)
Types of natural selection
Gametic selection
Gametes can be more or less successful, ex: the protein of sperm/egg cells
In meiosis, some genotypes are more likely to produce gametes than others (=
meiotic drive)
Fecundity selection
Fitness depends on how many gametes on individual produces
ex: in plants, fitness depends on the pollen produced, more pollen = potentially
more seeds
Types of natural selection
Density dependent selection
The fitness of an individual depends on the density of the population (how
many individuals there are)
some phenotypes do well at low density, others better when there is competition
Frequency-dependence selection
The fitness depends on the frequency of the phenotype in the population
This is typical for host-parasite coevolution
Woolhouse et al. 2002
Types of natural selection
Pleiotropy
The alleles at one locus affect several phenotypic traits of an individual
Epistasis
Many quantitative traits are influenced by several
genes (height, weight,…)
The alleles at these genes can have different effect
depending on other alleles
A model of natural selection
Fitness table
Genotypes
A 1A 1
A 1A 2
A2A2
Frequency in offspring
p2
2pq
q2
Relative fitness
w11
w12
w22
Frequency after selection
p 2 w11 / w
2 pqw12 / w
q 2 w22 / w
Where w = p 2 w11 + 2 pqw12 + q 2 w22
Is the mean fitness of the population
A selective advantage is always relative to the other individuals
A model of natural selection
Fitness table : simplified
Genotypes
A 1A 1
A 1A 2
A2A2
Frequency in offspring
p2
2pq
q2
Relative fitness
1
1-hs
1-s
Frequency after selection
p2 / w
2 pq(1 − hs) / w
q 2 (1 − s ) / w
Where w = p 2 + 2 pq(1 − hs) + q 2 (1 − s ) Is the mean fitness of the population
With 1 being the fitness of the homzygote A1A1 genotype
h is the dominance coefficient (heterozygous effect)
s is the selection coefficient
A model of natural selection
Fitness table : simplified
Genotypes
A 1A 1
A 1A 2
A2A2
Frequency in offspring
p2
2pq
q2
Relative fitness
1
1-hs
1-s
Frequency after selection
p2 / w
2 pq(1 − hs) / w
q 2 (1 − s ) / w
Meaning of h values:
h=0 => A1 is dominant and A2 is recessive
h=1 => A2 is dominant and A1 is recessive
0 < h < 1 => incomplete (partial) dominance
h < 0 => overdominance
h > 1 => underdominance
A model of natural selection
Fitness table : simplified
Genotypes
A 1A 1
A 1A 2
A2A2
Frequency in offspring
p2
2pq
q2
Relative fitness
1
1-hs
1-s
Frequency after selection
p2 / w
2 pq(1 − hs) / w
q 2 (1 − s ) / w
Where w = p 2 + 2 pq(1 − hs) + q 2 (1 − s ) Is the mean fitness of the population
This formula is based on Fisher‘s theorem of Natural selection
The fitness of the population is maximized!
And the fitness of the population can only increase
A model of natural selection
Fitness table : simplified
Genotypes
A 1A 1
A 1A 2
A2A2
Frequency in offspring
p2
2pq
q2
Relative fitness
1
1-hs
1-s
Frequency after selection
p2 / w
2 pq(1 − hs) / w
q 2 (1 − s ) / w
When one genotype is favoured (h > 0)
We can calculate the change in allele frequency from one generation to the next by
selection
∆s p =
pqs [ ( ph + q(1 − h) ]
w
WF model with natural selection
A Wright-Fisher model with selection
The Wright-Fisher model gives allele frequencies, and not genotypes
What is the probability of choosing randomly an A1 allele?
It is the proba of choosing A1A1 or (1/2) of choosing A1A2 genotypes
The probability of an allele from the next generation picks an A1 ancestor:
p 2 + (1 − sh) pq p(1 − sh) + shp 2
pɶ =
=
w
w
w = p 2 + 2(1 − sh) pq + (1 − s )q 2
WF model with natural selection
A Wright-Fisher model with selection
If there are i alleles A1 in the previous generation t, what is the probability that
there are j alleles A1 at generation t+1:
 2N  j
2N − j
P [ X t +1 = j | X t = i ] = 
= Binom(2 N , pɶ i ; j )
 pɶ i (1 − pɶ i )
 j 
With
pɶ i =
ɶ
pi
2N
Little graph to explain
 2N   i 
In the classic neutral Wright-Fisher P [ X t +1 = j | X t = i ] = 


j
2
N



j
i 

1
−


2
N


2N − j
WF model with natural selection
A Wright-Fisher model with selection
What is the Expectation and Variance of the Binomial with selection?
1
p(1 − sh) + shp 2
E[ X ] =
2N
w
w = p 2 + 2(1 − sh) pq + (1 − s )q 2
1
Var ( X ) ≈ p (1 − p )
2N
So only the expectation E[X] of allele frequencies changes
Selection does not affect the variance Var[X] of the frequency
In the classic neutral Wright-Fisher
1
E[ X ] = p
2N
1
Var[ X ] = p(1 − p )
2N
WF model with natural selection
A Wright-Fisher model with selection
What is the probability of fixation for an allele with advantage s ?
This was derived by Haldane and then by Kimura
(if selection is strong Ne × s >>1) (for neutral allele = 1/2N)
P[ fixation _ of _ allele] = 2hs
So an advantageous allele is lost most of the times from the population!
What is the time of fixation of an allele ? (neutral alleles = 4N)
4
Time _ to _ fixation = ln(2 N )
s
WF model with natural selection
Lets check the behaviour of selection in a model with drift
Use Populus => Drift and Selection
You can change the different coefficients of selection
WAA, Waa, Waa
What situations corresponds to positive selection?
Do selected alleles get fixed all the time?
What is the effect of population size N ?
Other types of natural selection
Darwin only considered positive selection
But mutations can be also deleterious => Purifying selection (negative
selection)
Use Populus => Drift and Selection
You can change the different coefficients of selection
WAA, Waa, Waa
What situations corresponds to negative selection?
Do selected alleles get lost all the time?
What is the effect of population size N ?
Other types of natural selection
Darwin only considered positive selection
Balancing selection => for example due to overdominance
A model of natural selection: overdominance
Fitness table : simplified
Genotypes
A 1A 1
A 1A 2
A2A2
Frequency in offspring
p2
2pq
q2
Relative fitness
1-s
1
1-t
Frequency after selection
p 2 (1 − s ) / w
2 pq / w
q 2 (1 − t ) / w
When there is overdominance (h < 0)
We can calculate the change in allele frequency from one generation to the next by
selection
pq [ qt − ps ]
∆s p =
w
A model of natural selection: overdominance
Fitness table : simplified
Genotypes
A 1A 1
A 1A 2
A2A2
Frequency in offspring
p2
2pq
q2
Relative fitness
1-s
1
1-t
Frequency after selection
p 2 (1 − s ) / w
2 pq / w
q 2 (1 − t ) / w
When there is overdominance (h < 0)
We can calculate the equilibrium frequencies for both alleles
pˆ =
t
s+t
qˆ =
s
s+t
Overdominance maintains variability as heterozygotes have an advantage
Do you know an example of overdominance?
Other types of natural selection
Darwin only considered positive selection
Balancing selection => for example due to overdominance
Use Populus => Drift and Selection
You can change the different coefficients of selection
WAA, Waa, Waa
What situations corresponds to overdominance?
Can you fix or lose alleles?
What is the effect of population size N ?
Other types of natural selection
Darwin only considered positive selection
Balancing selection => for example due to overdominance
There are other examples of Balancing selection due to negative frequencydependent selection
This is common for host-parasites coevolution (next semester)