Mutation Rates
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Ultimately, the source of genetic variation observed among individuals in
populations is gene mutation. Mutation generates new alleles, and these are the
substance of all evolutionary change.
The mutation rate is defined as the probability that a copy of an allele changes to
some other allelic form in one generation.
Mutation rates at the gene level depends on mutation rates at other levels:
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Mutation rates for different kinds of mutations can be expressed as mutations per
locus, per gene, per nucleotide, and per gamete. All of these indicate a specific type
of mutation occurring per generation (higher eucaryotes) or per DNA replication
(microorganisms), reflecting mutations arising anew in the unit time.
In addition, mutations rates may be expressed is relation to visible phenotypes or
in relation to of DNA sequence changes
Therefore, it is useful distinguishing between mutation rates:
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per base pair per generation (or replication)
per gene per generation (or replication)
per genome or gamete per generation (or replication)
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Nucleotide mutation rate
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Rates of spontaneous mutation seem to be determined by evolutionary balances
between the deleterious consequences of too many mutations and the additional
energy and time required to further reduce mutation rates.
In microorganisms, the rate of mutation for any nucleotide (point mutations) is
generally included between 10-9 and 10-10 per DNA replication.
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Although this rate of mutation may seem exceedingly small, the total amount of new
genetic variation introduced by spontaneous mutation at each DNA replication is
significant. Consider the genome of E. coli, of the size of about 5 x 106 bp. With a
mutation rate intermediate between those listed above (say 5 x 10-10), 25 x 10-4, or one
every 400 cells carries a new point mutation.
This means that in a single large bacterial culture (1 litre), in which concentrations of 2 x
109 cells/ml are easily obtained (=2 x 1012 total cells), some 5 x 109 new mutations are
present, corresponding to 1,000 mutations for each base pair.
In practice, all possible nucleotide substitutions and all possible single
insertion/deletions, as well as many large rearrangements are represented in a moderately
large bacterial population
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Evolution in a glass
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Experimental work with bacteria, eukaryotic micro-organisms and
very small animals can tell us much about the occurrence and
properties of mutations, including beneficial mutations. Over the last
fifty years or so beneficial mutations have been observed to occur in a
number of studies
Most of these experiments were done in a continuous culture system
called a chemostat.
A chemostat consists of a bottle in which the organisms grow. Growth
medium (i.e. food) is continuously pumped into the bottle and waste
products, residual medium and organisms flow out. The contents of
the bottle are well mixed so that each critter in the chemostat has an
equal chance of getting at each bit of food. Factors that affect the
growth of the organisms such as temperature are controlled,
sometimes quite rigourously. Several variations of chemostats have
been developed.
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The chemostat
Continuous culture, in a device called a chemostat, can be used to maintain a bacterial population
at a constant density, a situation that is, in many ways, more similar to bacterial growth in natural
environments. In a chemostat, the growth chamber is connected to a reservoir of sterile medium.
Once growth is initiated, fresh medium is continuously supplied from the reservoir. The volume
of fluid in the growth chamber is maintained at a constant level by some sort of overflow drain.
Fresh medium is allowed to enter into the growth chamber at a rate that limits the growth of the
bacteria. The bacteria grow (cells are formed) at the same rate that bacterial cells (and spent
medium) are removed by the overflow. The rate of addition of the fresh medium determines the
rate of growth because the fresh medium always contains a limiting amount of an essential
nutrient.
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Schematic diagram of a chemostat, a device for the
continuous culture of bacteria. The chemostat relieves the
environmental conditions that restrict growth by
continuously supplying nutrients to cells and removing
waste substances and spent cells from the culture medium
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Fluctuations of mutant strains
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In an early study, resistance to a phage was used as a marker to follow the
appearance of some mutations in a chemostat culture.
Novick and Szilard grew E. coli in a chemostat at a steady-state density of about 3 ×
108 cells per ml. Periodically they assayed cells sampled from the chemostat for
resistance to infection by bacteriophage T5 and calculated the density of T5 resistant
cells in the culture.
At no time was phage T5 present in the chemostat nor had the cells in the chemostat
been exposed to phage T5. They found that there was always a fraction of cells in
the culture that was resistant to T5.
The density of resistant cells fluctuated betweeen 102 and 103 per ml.
The increases and decreases reflect the occurrence of mutations within strains in the
chemostat. The initial increase in the frequency of resistant cells occurs because a
mutation occurs within a T5 resistant strain that makes it (and its descendents) the
fastest growing cells in the culture. As long as this strain remains the fastest growing
one its representation in the population will increase. Eventually different favorable
mutation occurs in a cell that is sensitive to T5 that makes it (and its descendents)
the fastest growing cells in the culture. This causes the frequency of T5 resistance to
decline. Later a different mutation occurs in a T5 resistant strain that makes it the
fastest growing strain. Its frequency increases, and so on.
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Neutral mutations
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It is important to note that in this environment sensitivity and resistance to infection
by T5 is a neutral trait here. Because there is no T5 in the environment, resistance
does not provide an advantage.
But it doesn't seem to provide much disadvantage either. If it provided a
disadvantage, the resistant cells would washout of the chemostat. In this
environment, it is selectively neutral.
Mutations in other genes cause some cells to have a higher growth rate. It is just a
matter of whether these mutations occur first in resistant or sensitive cells that
determines whether the frequency of T5 resistant cells increases or decreases.
It's a hitchhiking effect - the T5 resistance gene just goes along for the ride with the
genes causing the fluctuations.
Bacteria carrying neutral mutations constitute a fluctuating proportion of growing
cultures. The fluctuations are attributed to periodic selection of fitter clones, with
each successive sweep replacing less fit members of the population, including those
with neutral mutations. The frequency of neutral mutations can also change in clonal
populations as a consequence of hitchhiking with favorable mutations.
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An example with yeast
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Frequency of canavanine resistant cells
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Paquin & Adams (1983) studied haploid and diploid populations of yeast to estimate
the relative rate that beneficial mutations would arise in an asexual population of
each type.
Populations were kept in a chemostat (a fairly constant environment) at a population
size of about 5 billion. Initially, the population was started from a single clone (one
genotype).
A neutral marker, canavanine resistance then increased in frequency due to mutation
pressure alone (amino acid mutation rate = 10-7), although the mutations always
remained low in frequency (< 10-5) during the hundreds of generations of the
experiment.
8
When a beneficial mutation
occurred, it was most likely to arise
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in a canavanine sensitive cell.
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The beneficial mutation would then
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sweep through the population.
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Canavanine sensitivity would "hitch3
hike" along, driving back down the
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frequency of canavanine resistance.
1
0
0
50
100
150
Generations
200
250
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Interpreting mutant fluctuations
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This chart is an explanation of what happens in the chemostat
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Genetic drift
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Fluctuations of mutant-clone frequencies in the chemostat are
examples of the process known as genetic drift.
If a population is finite in size (as all populations are) and if a given
pair of parents of a diploid species has only a small number of
offspring, then, even in the absence of all selective forces, the
frequency of a gene will not be exactly reproduced in the next
generation, because of sampling error.
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If, in a population of 1000 individuals, the frequency of a is 0.5 in one
generation, then it may by chance be 0.493 or 0.505 in the next generation
because of the chance production of slightly more or slightly fewer progeny of
each genotype. In the second generation, there is another sampling error based
on the new gene frequency, so the frequency of a may go from 0.505 to 0.511 or
back to 0.498. This process of random fluctuation continues generation after
generation, with no force pushing the frequency back to its initial state, because
the population has no "genetic memory" of its state many generations ago. Each
generation is an independent event.
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Extinction of genetic variability by genetic drift
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The final result of this random change in allelic frequency is that the population
eventually drifts to p = 1 or p = 0. After this point, no further change is possible; the
population has become homozygous. A different population, isolated from the first,
also undergoes this random genetic drift, but it may become homozygous for allele
A, whereas the first population has become homozygous for allele a. As time goes
on, isolated populations diverge from each other, each losing heterozygosity. The
variation originally present within populations now appears as variation among
populations.
Computer simulation of genetic
drift. The frequency of an allele
(e.g., A in a system with A and a) is
shown for five replicate populations
over the course of 100 generations,
with a population size (N) of 20. The
effect of drift is inversely
proportional to population size, a
fundamental driving force in many
evolutionary divergences
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Genetic drift over evolutionary time
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The appearance, loss, and eventual incorporation of neutral mutations in the life of a
population. If random genetic drift does not cause the loss of a new mutation, then it
must eventually cause the entire population to become homozygous for the
mutation.
At that point, the mutation has been fixed.
In the figure, 10 mutations have arisen, of which 9 (light red at bottom of graph)
increased slightly in frequency and then died out. Only the fourth mutation
eventually spread into the population.
Therefore, a steady substitution
of one allele for another is
expected to occur due to genetic
drift alone
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The probability of fixation of a neutral allele
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It has been proven by matematical analysis (and it is quite intuitive)
that the probability of fixation u of any neutral allele a is equal to its
frequency in the population:
u = pa
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In a finite population, pa takes discrete values only, starting from
1/(2N) in diploid species (when one copy only of allele a is present in
the population), and incrementing at steps of 1/(2N).
In other words, the initial frequency of a mutant allele is, by
definition, pa = 1/(2N)
Thus, the probability of ultimate fixation of any new neutral mutation
is equal to the reciprocal of twice the population size.
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The concept of gene substitution
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It is important to distinguish between "Mutation" and "Substitution" with respect to
individuals and populations:
The rate of gene substitution (K) is defined as the number of mutants reaching
fixation per unit time.
If neutral mutations occur at a rate of μ per gene per generation, then the number of
mutants arising in a diploid population of size N is 2N μ mutant alleles per
generation. Since the probability of fixation for each of these mutations is 1/(2N),
we obtain the result that
K = μ.
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Thus theoretically, if the mutation rate μ is constant over time, neutral alleles
accumulate at a fixed rate independently of population size, and their rate of
accumulation can be used as an evolutionary clock to measure divergence times.
This is one of the fundamental tenants of molecular evolution.
This result can be intuitively understood by noting that, in a large population, the
number of mutations arising every generation is high but the fixation probability of
each mutation is low. In comparison, in a small population, the number of mutations
arising every generation is low, but the fixation probability of each mutation is high.
As a consequence, the rate of substitution for neutral mutations is independent of
population size.
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Esimating nucleotide mutation rate in human
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The result that the mutation rate for neutral mutations is equal
to the rate of evolutionary substitution has been the basis of an
approach to measuring the human mutation rate at the
nucleotide level.
A direct comparison of stretches of DNA without function can
provide an estimate of the mutation rate per generation
between species whose divergence time and generation length
are known.
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Bacteria, Archae, and Eukaryotic microbes produce about one mutation per 300
chromosome replications. For E. coli this works out to be between 10-6 and 10-7
mutations per gene per generation, however it is important to note that there are
certain "hot spots" or "cold spots" for spontaneous mutations. (A "hot spot" is a
site that has a higher rate of mutations than predicted from a normal distribution,
and a "cold spot" is a site with a lower rate of mutations than predicted from a
normal distribution.) Higher eukaryotes have the same rate of spontaneous
mutation, so that rates per sexual generation are about one mutation per gamete
(close to the maximum compatible with life). RNA viruses have much higher
mutation rates -- about one mutation per genome per chromosome replication -and even small increases in their mutation rates are lethal.
Because a complex individual has a trillion or so nucleotides, each individual is
likely to sustain one or more mutations.
Rates of expressed gene mutations average about 1 per 100,000 to 1 per million:
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rates of expression of phenotypic effects are often higher because they are controlled by
many genes
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The mutation rate is a measure of the frequency of a given mutation per generation
(or per gamete, which is equivalent). Ordinarily, rates are given for specific loci.
Thus the mutation rate for achondroplasia is 6-13 mutants per million gametes. This
means that each gamete has ca. 1 chance in 100,000 of carrying a new mutation for
achondroplasia.
A. Mutation rates are based almost exclusively on rare autosomal dominant or Xlinked recessive traits. It is virtually impossible to measure autosomal recessive
traits accurately. B. The range of known mutation rates varies from 1 in 10,000 for
Duchenne muscular dystrophy and neurofibromatosis type-1 (the largest genes
known) to several genes in the range of 1 in 10,000,000.
C. Mutation rate studies never measure all the possible mutations at a locus. Many
of the mutations cause no obvious phenotypic effect and could only be recognized
by direct analysis of DNA sequences.
D. The rate of nucleotide substitutions is on the order of 1 per 100,000,000
nucleotides. Since there are 3 billion nucleotides per genome, that means that every
gamete has about 30 new mutations involving nucleotide substitutions.
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Mutation rates per generation
Per base pair ~10-8 - 10-9
Per gene ~10-6 - 10-5
Per genome ~0.02 - 1
BUT -- These are highly variable from gene to gene, individual to
individual, species to species
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Mutation rates
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Mutation rate estimates:
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From divergence among humans and chimpanzees:
μ = 10-9 per site (bp) per year or 2*10-8 per site per generation
Phenotypic effect: μ = 10-6 to 10-5 per locus, gamete and generation
Viability: 0.5 per gamete per generation
At the molecular level, each human gamete genome may carry 200
new nucleotide substitutions
At the population level: A lot of new variation every generation!
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The Rise and Fall of New Mutations
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Even when a mutation confers a selective advantage the
first few generations are dominated more by the whims of
fate than by natural selection
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The single individual carrying the mutation might die prematurely
or its offspring might not find a mate
Seventy two years ago J.B.S. Haldane used an approach
known as branching to calculate the probability that a new
advantageous mutation will become fixed in a population
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He found this to be approximately 2s, where s is the relative fitness
advantage that those possessing the new mutation have relative to
those who lack the mutation. Since selection is thought to be fairly
weak on most amino acid variants, s~ 10-3-10-5, this probability
could be quite low
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Haldane’s Approach
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Imagine that the new mutation sits at the root of a tree of
descendants
Once the tree branches a few times, random pruning is
unlikely to kill off all of the branches at once
The crucial phase is therefore the first few generations of
existence when the number of branches is small
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Central question is the probability that the
mutation will persist through the initial
branching process
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Solving this problem yields the 2s result
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Population size constant
time
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Otto, S.P. and M.C. Whitlock. 1997. The probability
of fixation in populations of changing size. Genetics
146:723-733.
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Generalized this approach to include cases in
which population size rises and falls through
time
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Probability of Fixation
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2(s + r), where r is the rate of population increase or
decrease
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Thus, a mutant that finds itself in a rapidly growing
population is much more likely to be fixed than one in a
shrinking population
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Rate of gene substitution
1. Overall rate (K) of substitution of a gene by various
successive
neutral mutations is the number of mutant alleles reaching
fixation
per generation.
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