Selection and Drift
To understand evolution by natural selection, it is important to determine the rates
of evolutionary change possible under selection
Eg. calculate numbers of generations required for selectively favourable mutation
It is useful to know if natural selection is capable of producing change over time
scales observed in fossil records or living species
Directional: situation in which variant frequencies or trait means subject to pressures
of selection that cause them to change in a consistent direction for many generations
- Deterministic evolution occurs if population is infinite (fully describe the
process to changing the frequency of an allele at a particular locus
- Stochastic is opposite of deterministic: random, but we can predict the mean
frequency of alleles
Deterministic Dynamics
Dependent on fitness: favourable alleles go to fixation, deleterious alleles are
eliminated – neither is certain in finite populations
Alleles represent by large numbers of individuals: infinite populations, common
alleles in large finite populations (never true for new mutations)
New Beneficial Mutations
Same as selection, the Poisson distribution can be used to
model the appearance of a new mutation
Probability of observing k mutant offspring if the
expected number is λ
k=0, no offspring
λ: expected number of offspring= 1+s
Review: Poisson Distribution
- Discrete distribution of the number of time a rare events occurs (can test
assumptions; do rare events occur at random)
- Observations are count data
- 2 categories – one much rarer than the other (typically p < 0.1 and n p < 5)
- Variance approximately = mean
Assumptions
- Sampling is random
- Outcomes independent of each other
- Events distributed at random – genuine Poisson distributions hard to find in
nature, however it is the only model suitable for objects that are distributed
at random
, Unless there is a strong selection coefficient (s)
the probability of immediate extinction is very
high
Bearing in mind the logarithmic scale
The larger the selection coefficient (s), the lower
the probability of immediate extinction
In real life s is very small (0-5%): it is rare that a
mutation will double your fitness or increase
number of offspring by 10%
A large proportion of strongly beneficial mutations are immediately lost
Fixation of new mutations
Probability of fixation of new mutations – using a poisson
distribution of population size
Haploids: p[fixation] = ~2s (fitness of mutant
heterozygote is 1+s)
Diploids: p[fixation] = ~2(1-h)s
(Long derivation!)
Chance plays a role in evolution!
Important implication – new mutation that confers a
1% selective advantage in a heterozygote has a 1/50
chance of fixation
Selective advantage in homozygotes is
irrelevant, as first few critical generations new
gene is too rare to occur in homozygous state
Initially, it appears that a favourable recessive
mutation cannot be fixated – but some degree
of inbreeding will confer a chance of recessive
mutation occurring in homozygotes (hence a
chance of fixation)
Favourable mutation only has a small chance of
becoming established in a population even if
, there is a sizeable selective advantage in heterozygotes OR population is extremely
large
- Reflects fact that mutations initially present at low copy numbers
- No. of carrier individuals fluctuate from generation to generation leading to
high chance of random loss
- Many independent mutations must occur before one has a good chance of
fixation
Directional selection has a strong random element – isolated populations will tend to
diverge genetically even if they are exposed to same selection pressure
- Stochastic invasion of beneficial mutations and adaptive trajectory differences
between populations
Richard Lenski et al. – experiment began in Feb 1988
- Using 12 cultures of clonal E.coli – at regular intervals, take a sample and store
(frozen), then used to compare old populations to new populations (comparing to
the ancestral condition)
- 12 cultures all adapt at different rates- via comparison to relative growth rate
compared to ancestor
- Specialisation to experimental media
but decline in growth on other media:
ability to exploit other media
declines
- Various decay in metabolic pathways
differ between populations (even
though all populations are replicates) – some have not lost their ability to
metabolise using certain pathways simply because they have not yet developed a
mutation in those pathways
- Speed and pathway of adaptation differs suggests that chance plays a role in
evolution
New Deleterious Alleles
There is a chance that for a random fixation of
deleterious alleles (from combination of drift and weak
selection?)
Intensity of drift: 1/2Ne
Intensity of selection: s
Relative intensity of selection 2Nes
Large Ne: most mutations under selection
Small Ne: only mutations with large 1s1 > 1/Ne selected
2Nes > 1 = selection is stronger than drift
2Nes < 1 = drift is stronger than selection
To understand evolution by natural selection, it is important to determine the rates
of evolutionary change possible under selection
Eg. calculate numbers of generations required for selectively favourable mutation
It is useful to know if natural selection is capable of producing change over time
scales observed in fossil records or living species
Directional: situation in which variant frequencies or trait means subject to pressures
of selection that cause them to change in a consistent direction for many generations
- Deterministic evolution occurs if population is infinite (fully describe the
process to changing the frequency of an allele at a particular locus
- Stochastic is opposite of deterministic: random, but we can predict the mean
frequency of alleles
Deterministic Dynamics
Dependent on fitness: favourable alleles go to fixation, deleterious alleles are
eliminated – neither is certain in finite populations
Alleles represent by large numbers of individuals: infinite populations, common
alleles in large finite populations (never true for new mutations)
New Beneficial Mutations
Same as selection, the Poisson distribution can be used to
model the appearance of a new mutation
Probability of observing k mutant offspring if the
expected number is λ
k=0, no offspring
λ: expected number of offspring= 1+s
Review: Poisson Distribution
- Discrete distribution of the number of time a rare events occurs (can test
assumptions; do rare events occur at random)
- Observations are count data
- 2 categories – one much rarer than the other (typically p < 0.1 and n p < 5)
- Variance approximately = mean
Assumptions
- Sampling is random
- Outcomes independent of each other
- Events distributed at random – genuine Poisson distributions hard to find in
nature, however it is the only model suitable for objects that are distributed
at random
, Unless there is a strong selection coefficient (s)
the probability of immediate extinction is very
high
Bearing in mind the logarithmic scale
The larger the selection coefficient (s), the lower
the probability of immediate extinction
In real life s is very small (0-5%): it is rare that a
mutation will double your fitness or increase
number of offspring by 10%
A large proportion of strongly beneficial mutations are immediately lost
Fixation of new mutations
Probability of fixation of new mutations – using a poisson
distribution of population size
Haploids: p[fixation] = ~2s (fitness of mutant
heterozygote is 1+s)
Diploids: p[fixation] = ~2(1-h)s
(Long derivation!)
Chance plays a role in evolution!
Important implication – new mutation that confers a
1% selective advantage in a heterozygote has a 1/50
chance of fixation
Selective advantage in homozygotes is
irrelevant, as first few critical generations new
gene is too rare to occur in homozygous state
Initially, it appears that a favourable recessive
mutation cannot be fixated – but some degree
of inbreeding will confer a chance of recessive
mutation occurring in homozygotes (hence a
chance of fixation)
Favourable mutation only has a small chance of
becoming established in a population even if
, there is a sizeable selective advantage in heterozygotes OR population is extremely
large
- Reflects fact that mutations initially present at low copy numbers
- No. of carrier individuals fluctuate from generation to generation leading to
high chance of random loss
- Many independent mutations must occur before one has a good chance of
fixation
Directional selection has a strong random element – isolated populations will tend to
diverge genetically even if they are exposed to same selection pressure
- Stochastic invasion of beneficial mutations and adaptive trajectory differences
between populations
Richard Lenski et al. – experiment began in Feb 1988
- Using 12 cultures of clonal E.coli – at regular intervals, take a sample and store
(frozen), then used to compare old populations to new populations (comparing to
the ancestral condition)
- 12 cultures all adapt at different rates- via comparison to relative growth rate
compared to ancestor
- Specialisation to experimental media
but decline in growth on other media:
ability to exploit other media
declines
- Various decay in metabolic pathways
differ between populations (even
though all populations are replicates) – some have not lost their ability to
metabolise using certain pathways simply because they have not yet developed a
mutation in those pathways
- Speed and pathway of adaptation differs suggests that chance plays a role in
evolution
New Deleterious Alleles
There is a chance that for a random fixation of
deleterious alleles (from combination of drift and weak
selection?)
Intensity of drift: 1/2Ne
Intensity of selection: s
Relative intensity of selection 2Nes
Large Ne: most mutations under selection
Small Ne: only mutations with large 1s1 > 1/Ne selected
2Nes > 1 = selection is stronger than drift
2Nes < 1 = drift is stronger than selection
