Genetic Drift and Neutral Theory
Lecture 4
Lecture Outline
1.
Genetic Drift
2.
Effective population size
• Founder Effect
3.
The Neutral Theory of Molecular Evolution
Evolution results from chance (unpredictable) and deterministic (predictable)
factors
Evolution
Natural Selection
Deterministic nonrandom process
Mutation
Genetic Drift
…
Random processes
Natural selection and genetic drift are the two most important causes of allele
substitution in populations
Natural Selection
Genetic Drift
Population
Infinite and finite populations
Finite populations (natural populations)
Adaptation
Results in adaptation
Does not result in adaptation
Differences
Accounts for some differences in Accounts for most of the differences in
DNA sequences among species
DNA sequences among species
Active
In some loci in some populations In all loci in all populations
Some evolutionary geneticists hold the opinion that genetic drift should be the
“null hypothesis” used to explain an evolutionary observation unless there is
positive evidence of natural selection or some other factor
Sewall Wright
Motoo Kimura
The Theory of Genetic Drift
Genetic Drift as Sampling Error
The frequency of an allele can change because one or more of its copies happen
not to be included in those gametes that unite into zygotes, or may happen not
to be carried by the offspring that survive to reproductive age
The genes included in any generation, whether in newly formed zygotes or in
offspring that survive to reproduce, are a sample of the genes carried by the
previous generation. Any sample is subject to random variation or sampling error
50%
46%
50%
54%
The Theory of Genetic Drift
Coalescence
Looking backwards in time all gene copies in the population ultimately are
descended from a single ancestral copy, because given long enough, all other
original gene lineages become extinct
The genealogy of the genes in the present
population is said to coalesce back to a single
common ancestor
By chance:
• A population will eventually become
monomorphic for one allele or the other
• The probability that one allele will be
fixed, rather than other alleles, equal the
initial frequency of that allele
The frequency of heterozygotes declines as one
of the allele frequencies shift closer to 1
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
Metapopulation
Deme 2N
p q
Neutral alleles
time?
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
Metapopulation
Deme 2N
p q
pt
p'
…
Neutral alleles
time
When the frequency changes from p= ½ to p' in the following generation it will
change to some other value p'' either higher or lower with equal probability
Since no stabilizing force returns the allele frequency towards ½, p will
eventually drift either to 0 or 1: the allele is either lost or fixed
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
What happens to genetic variation at a locus in a deme?
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
The allele frequency describes a random walk, analogous to a New Year’s Eve
reveler staggering along a very long train platform with a railroad track on either
side: if he is so drunk that he does not compensate steps towards one side with
steps towards the other, he will eventually fall off the edge of the platform onto
one of the two tracks
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
How does population size affect this process?
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
If an allele has just arisen by mutation what would be its likelihood of reaching
fixation?
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
What happens to the allele frequency in the metapopulation?
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
What happens to the frequency of heterozygotes in each deme? and in the
metapopulation?
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
Some demes reach p=0 pr p=1 and can no
longer change. Among those in which fixation
of one or the other allele has not yet occurred,
the allele frequencies continue to spread out,
with all frequencies between 0 and 1
eventually becoming equally likely
pt
p q
…
time
Demes that initially are genetically identical
evolve by chance to have different genetic
constitutions
The Theory of Genetic Drift
Random Fluctuation in Allele Frequencies
Small Populations
• Larger oscillations
• Alleles are more rapidly
fixed (7) or lost (5)
Large Populations
• Smaller oscillations
• Alleles less rapidly fixed (0) or
lost (0)
The variance in allele frequency among the demes continues to increase from
generation to generation
Evolution by Genetic Drift
• Allele frequencies fluctuate at random within a population and eventually
one or another becomes fixed
• Genetic variation at a locus declines and is eventually lost
• An allele’s probability of fixation equals its frequency at that time and is not
affected by its previous history
• Populations with the same initial allele frequency (p) diverge and a
proportion p of the population is expected to become fixed for that allele
• If an allele has just arisen by mutation its likelihood of reaching fixation is
1/2N: it is more likely to be fixed in a small population than in a large
population
• In a diploid population, the average time to fixation of a newly arisen neutral
allele that does become fix is 4N generations: evolution by genetic drift
proceeds faster in small than in large populations
•Among a number of initially identical demes in a metapopulation, the
average allele frequency does not change but the frequency of heterozygotes
declines to 0 in each deme and in the metapopulation as a whole
Evolution by Genetic Drift
Effective Population Size
The EFFECTIVE SIZE (Ne) of an actual POPULATION is the number of individuals in a
population in which every adult contribute the same number of genes to the
next generation in which the rate of genetic drift would be the same as in the
actual population
Evolution by Genetic Drift
Effective Population Size
The effective population size Ne can be smaller than the census size N for
several reasons:
• Variation in the number of progeny produced by each of the sexes
• Unequal sex-ratio
• Natural selection changes variation in progeny number
• Inbreeding
• Fluctuations in population size
Evolution by Genetic Drift
Founder Effect
BOTTLENECK
Restrictions in size through which populations may pass
FOUNDER EFFECT
Random genetic drift that ensues the establishment of a new
population by a small number of colonists
What would one expect from the
formation of new populations by
just a few individuals?
Evolution by Genetic Drift
Founder Effect
BOTTLENECK
Restrictions in size through which populations may pass
FOUNDER EFFECT
Random genetic drift that ensues the establishment of a new
population by a small number of colonists
Polydactylia
Ellis-van Creveld
Amish of Pennsylvania
Evolution by Genetic Drift
Founder Effect
1. If the colony rapidly grows: allele
frequencies will not be greatly altered
from those in the source population
although some rare alleles will not
have been carried by the founders
2. If the colony remains small: genetic
drift will alter allele frequencies and
erode genetic variation
3. If the colony persists and grows: new
mutations eventually restore
heterozygosity to higher levels
The Neutral Theory of Molecular Evolution
Random genetic drift:
• Has played an important role in the evolution of phenotypic features of
organisms?
• Has played an important role in the evolution of DNA and protein
sequences!
The Neutral Theory of Molecular Evolution holds that:
1.1 A minority of mutations are
advantageous and fixed by natural
selection
Advantageous
Neutral Fix
Neutral Lost
Disadvantagous
1.2 Many mutations are
disadvantageous and eliminated by
natural selection
1.3 The great majority of those
mutations that are fixed are
effectively neutral with respect to
fitness and are fixed by genetic drift
The Neutral Theory of Molecular Evolution
2. Most genetic variation at the molecular level is selectively neutral and lacks
adaptive significance
3. Evolutionary substitutions at the molecular level proceed at a roughly
constant rate so that the degree of sequence difference between species can
serve as a MOLECULAR CLOCK
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
uT
Constant mutation rate per gamete per generation
Assume that initially due to the great number of mutable sites, every mutation
constitutes a new DNA sequence
u0
NEUTRAL MUTATION RATE
u0=f0 uT
where f0 is the fraction of mutations that effectively neutral
EFFECTIVELY NEUTRAL
the mutant allele is so similar to other alleles in its
effect on fitness that changes in its frequency are governed by genetic
drift alone, not by natural selection
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
When will u0 be equal to uT ?
When will u0 significantly smaller than uT ?
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
u0 depends on the gene’s function:
• u0<<uT
FUNCTIONAL CONSTRAINTS
Transcribed DNA:
If many of the amino acids in the
protein it encodes cannot be altered
without seriously affecting an important
function. Second bp in codons
• u0≈uT
NO FUNCTIONAL CONSTRAINTS
Transcribed DNA:
If the protein can function well despite
any of many amino acid changes. Third
bp position in codons
Not transcribed DNA:
introns and pseudo-genes
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
What is the number of neutral mutations that arise in any generation and will
someday be fixed?
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
The number of neutral mutations that arise in any generation and will someday
be fixed is:
u0 2Ne (1/2Ne) = u0
How do you think this could be useful?
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
The number of neutral mutations that
arise in any generation and will
someday be fixed is:
u0 2Ne (1/2Ne) = u0
The rate of fixation of mutations is
theoretically constant, and equals the
neutral mutation rate. This is the
theoretical basis of the molecular clock
The time required for fixation is longer in
larger populations. More neutral mutations
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
If we know the number of differences D between the sequences of two species
how can we estimate the time of divergence?
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
The number of base pair differences between two species is D=2 u0 t (because
there are 2 lineages) therefore the number of generations since divergence is:
t = D/2u0
How is this estimate inaccurate?
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
The number of base pair differences between two species is D=2 u0 t (because
there are 2 lineages) therefore the number of generations since divergence is:
t = D/2u0
Over a sufficiently long time
some sites experience repeated
base substitutions. Thus the
observed number of differences
between species will be less than
the number of substitutions that
have transpired . As the time
since divergence becomes
greater, the number of
differences begins to plateau
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
How does the level of heterozygosity compare is small and large populations?
The Neutral Theory of Molecular Evolution
Principles of Neutral Theory
Although the identity of the several of many alleles present in the population
changes over time, the level of variation reaches an equilibrium when the rate at
which alleles arise by mutation is balanced by the rate at which they are lost by
genetic drift
The equilibrium level of variation,
represented by the frequency of
heterozygotes (H) is:
H 
4 N eu 0
4 N eu 0  1
Is higher in a large population than
in a small one
The Neutral Theory of Molecular Evolution
Evidence
Evidence shows that most, although not
all, DNA sequence evolution has been
neutral:
1.
Substitutions occur most frequently
at third-base positions in codons
2.
Rates of substitution are higher in
introns than coding regions of the
same gene and even higher in
pseudogenes than their functional
counterparts
3.
Some genes evolve much more slowly
than others. The genes that evolve
most slowly are those constrained by
their precise function
Gene Flow and Genetic Drift
A measure of the variation in allele frequency among populations is FST
The rate at which populations drift toward fixation of one allele or another is
inversely proportional to the effective population size Ne. However, the drift
toward fixation is counteracted by gene flow from other populations at rate m
These factors strike a balance at which the fixation index FST is:
F ST 
1
4 N em  1
Even if there is only one migrant per generation FST=0.2, that is, little gene flow
keeps all the demes fairly similar in allele frequency and heterozygosity remains
high
Gene Flow and Genetic Drift
Gene trees and population history
The genealogical history of genes in populations is the basis of COALESCENT THEORY
The smaller the effective size of a
population the existing gene copies
in a small population must stem
from a more recent common
ancestor than the gene copies in a
large population
Gene Flow and Genetic Drift
The Origin of Modern Homo Sapiens
The gene tree for human mitochondrial DNA supports the “out-of-Africa”
hypothesis according to which the world’s human population outside of Africa is
descended from a relatively small population that spread from Africa recently
replacing Eurasian populations of archaic Homo sapiens without interbreeding
with them
Non-African and African diverged
40,000 to 143,000 years ago.
The world’s human population is
descended from an effective
breeding population of 4,60011,200 people
This evidence supports the “outof-Africa” hypothesis
Gene Flow and Genetic Drift
The Origin of Modern Homo Sapiens
Lecture Ideas
Genetic drift
• Finite populations
• Null hypothesis
Sampling error
• Loss of heterozygosity
Population size
• Speed of fixation
• Effective population size
Founder’s effect
Mutations counteract genetic drift
• At specific loci
Migration counteracts drift
• All loci