Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini Mutation Rates Ultimately, the source...

Genetica per Scienze Naturalia.a. 03-04 prof S. Presciuttini

Mutation Rates Ultimately, the source of Ultimately, the source of genetic genetic variation variation observed among individuals in observed among individuals in

populations ispopulations is gene gene mutationmutation.. Mutation generates new alleles, and these are the Mutation generates new alleles, and these are the substance of all evolutionary change.substance of all evolutionary change.

The The mutation ratemutation rate is defined as the probability that a copy of an allele changes to is defined as the probability that a copy of an allele changes to some other allelic form in one generation.some other allelic form in one generation.

Mutation rates at the gene level depends on mutation rates at other levels:Mutation rates at the gene level depends on mutation rates at other levels: Mutation rates for different kinds of mutations can be expressed as Mutation rates for different kinds of mutations can be expressed as mutations per mutations per

locus, per gene, per nucleotide, locus, per gene, per nucleotide, andand per gamete per gamete. All of these indicate a specific type . All of these indicate a specific type of mutation occurring of mutation occurring per generationper generation (higher eucaryotes)(higher eucaryotes) oror per DNA replication per DNA replication (microorganisms)(microorganisms), , reflecting mutations arising anew reflecting mutations arising anew in the unit timein the unit time..

In addition, mutations rates may be expressed is relation to In addition, mutations rates may be expressed is relation to visible phenotypesvisible phenotypes or or in relation to of in relation to of DNA sequence changesDNA sequence changes

Therefore, it is useful distinguishing between mutation rates: Therefore, it is useful distinguishing between mutation rates: per base pair per generation (or replication)per base pair per generation (or replication) per gene per generation (or replication)per gene per generation (or replication) per genome or gamete per generation (or replication)per genome or gamete per generation (or replication)


Nucleotide mutation rate Rates of spontaneous mutation seem to be determined by evolutionary balances Rates of spontaneous mutation seem to be determined by evolutionary balances

between the deleterious consequences of between the deleterious consequences of too too many mutations and the additional many mutations and the additional energy and time required to further reduce mutation rates.energy and time required to further reduce mutation rates.

In microorganisms, tIn microorganisms, the rate of mutation for any nucleotide he rate of mutation for any nucleotide (point mutations) (point mutations) is is generally included between generally included between 1010-9-9 and and 1010-10-10 per DNA replication per DNA replication..

Although this rate of mutation may seem exceedingly small, the total amount of new 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 genetic variation introduced by spontaneous mutation at each DNA replication is significant. Consider the genome ofsignificant. Consider the genome of E. coli E. coli, of the size of about 5 x 10, of the size of about 5 x 106 6 bp. With a bp. With a mutation rate intermediate between those listed above (say 5 x 10mutation rate intermediate between those listed above (say 5 x 10 -10-10), 25 x 10), 25 x 10-4-4, or one , or one every 400 cells carries a new point mutation.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 This means that in a single large bacterial culture (1 litre), in which concentrations of 2 x 10109 9 cells/ml are easily obtained (=2 x 10cells/ml are easily obtained (=2 x 101212 total cells), some 5 x 10 total cells), some 5 x 1099 new mutations are new mutations are present, corresponding to 1,000 mutations for each base pair.present, corresponding to 1,000 mutations for each base pair.

In practice, all possible nucleotide substitutions and all possible single In practice, all possible nucleotide substitutions and all possible single insertion/deletions, as well as many large rearrangements are represented in a moderately insertion/deletions, as well as many large rearrangements are represented in a moderately large bacterial populationlarge bacterial population


Evolution in a glass Experimental work with bacteria, eukaryotic micro-organisms and Experimental work with bacteria, eukaryotic micro-organisms and

very small animals can tell us much about the occurrence and very small animals can tell us much about the occurrence and properties of mutations, including beneficial mutations. Over the last properties of mutations, including beneficial mutations. Over the last fifty years or so beneficial mutations have been observed to occur in a fifty years or so beneficial mutations have been observed to occur in a number of studiesnumber of studies

Most of these experiments were done in a continuous culture system Most of these experiments were done in a continuous culture system called a called a chemostatchemostat. .

A chemostat consists of a bottle in which the organisms grow. Growth A chemostat consists of a bottle in which the organisms grow. Growth medium (i.e. food) is continuously pumped into the bottle and waste medium (i.e. food) is continuously pumped into the bottle and waste products, residual medium and organisms flow out. The contents of products, residual medium and organisms flow out. The contents of the bottle are well mixed so that each critter in the chemostat has an 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 equal chance of getting at each bit of food. Factors that affect the growth of the organisms such as temperature are controlled, growth of the organisms such as temperature are controlled, sometimes quite rigourously. Several variations of chemostats have sometimes quite rigourously. Several variations of chemostats have been developed.been developed.


The chemostat

Schematic diagram of a chemostat, a device for the Schematic diagram of a chemostat, a device for the continuous culture of bacteria. The chemostat relieves the continuous culture of bacteria. The chemostat relieves the environmental conditions that restrict growth by environmental conditions that restrict growth by continuously supplying nutrients to cells and continuously supplying nutrients to cells and rremoving emoving waste substances and spent cells from the culture mediumwaste substances and spent cells from the culture medium

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.


Fluctuations of mutant strains In In an earlyan early study study,, resistance to a resistance to a phagephage was used as a marker to follow the was used as a marker to follow the

appearance of some mutations in a chemostat culture.appearance of some mutations in a chemostat culture. Novick and Szilard grew Novick and Szilard grew E. coliE. coli in a chemostat at a steady-state density of about 3 × in a chemostat at a steady-state density of about 3 ×

101088 cells per ml. Periodically they assayed cells sampled from the chemostat for cells per ml. Periodically they assayed cells sampled from the chemostat for resistance to infection by bacteriophage T5 and calculated the density of T5 resistance to infection by bacteriophage T5 and calculated the density of T5 resistant cells in the culture.resistant cells in the culture.

At no time was phage T5 present in the chemostat nor had the cells in the chemostat 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 been exposed to phage T5. They found that there was always a fraction of cells in the culture that was resistant to T5.the culture that was resistant to T5.

The density of resistant cells fluctuated betweeen 10The density of resistant cells fluctuated betweeen 1022 and 10 and 1033 per ml. per ml. The increases and decreases reflect the occurrence of mutations within strains in the 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 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 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 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 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 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 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 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.that makes it the fastest growing strain. Its frequency increases, and so on.


Neutral mutations It is important to note that in this environment sensitivity and resistance to infection 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 by T5 is a neutral trait here. Because there is no T5 in the environment, resistance does not provide an advantage.does not provide an advantage.

But it doesn't seem to provide much disadvantage either. If it provided a 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 disadvantage, the resistant cells would washout of the chemostat. In this environment, it is selectively neutral.environment, it is selectively neutral.

Mutations in other genes cause some cells to have a higher growth rate. It is just a 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 matter of whether these mutations occur first in resistant or sensitive cells that determines whether the frequency of T5 resistant cells increases or decreases.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 It's a hitchhiking effect - the T5 resistance gene just goes along for the ride with the genes causing the fluctuations.genes causing the fluctuations.

Bacteria carrying neutral mutations constitute a fluctuatingBacteria carrying neutral mutations constitute a fluctuating proportion of growing proportion of growing cultures. The fluctuations are attributedcultures. The fluctuations are attributed to periodic selection of fitter clones, with to periodic selection of fitter clones, with each successiveeach successive sweep replacing less fit members of the population, includingsweep replacing less fit members of the population, including those those with neutral mutations. The frequency of neutral mutationswith neutral mutations. The frequency of neutral mutations can also change in clonal can also change in clonal populations as a consequence of hitchhikingpopulations as a consequence of hitchhiking with favorable mutations.with favorable mutations.


An example with yeast Paquin & Adams (1983) studied haploid and diploid populations of yeast to estimate 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 the relative rate that beneficial mutations would arise in an asexual population of each type. type.

Populations were kept in a chemostat (a fairly constant environment) at a population 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 size of about 5 billion. Initially, the population was started from a single clone (one genotype). genotype).

A neutral marker, canavanine resistance then increased in frequency due to mutation A neutral marker, canavanine resistance then increased in frequency due to mutation pressure alone (amino acid mutation rate = 10pressure alone (amino acid mutation rate = 10 -7-7), although the mutations always ), although the mutations always remained low in frequency (< 10remained low in frequency (< 10-5-5) during the hundreds of generations of the ) during the hundreds of generations of the experiment. experiment.

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When a beneficial mutation When a beneficial mutation occurred, it was most likely to arise occurred, it was most likely to arise in a canavanine sensitive cell. in a canavanine sensitive cell. The beneficial mutation would then The beneficial mutation would then sweep through the population. sweep through the population. Canavanine sensitivity would "hitch-Canavanine sensitivity would "hitch-hike" along, driving back down the hike" along, driving back down the frequency of canavanine resistance.frequency of canavanine resistance.


Interpreting mutant fluctuations This chart is an explanation of what happens in the chemostatThis chart is an explanation of what happens in the chemostat


Genetic drift Fluctuations of mutant-clone frequencies in the chemostat are Fluctuations of mutant-clone frequencies in the chemostat are

examples of the process known as examples of the process known as genetic driftgenetic drift.. If a population is finite in size (as all populations are) and if a given If a population is finite in size (as all populations are) and if a given

pair of parents pair of parents of a diploid species of a diploid species has only a small number of has only a small number of offspring, then, even in the absence of all selective forces, the offspring, then, even in the absence of all selective forces, the frequency of a gene will not be exactly reproduced in the next frequency of a gene will not be exactly reproduced in the next generation, because of sampling error.generation, because of sampling error. If, in a population of 1000 individuals, the frequency of If, in a population of 1000 individuals, the frequency of aa is 0.5 in one is 0.5 in one

generation, then it may by chance be 0.493 or 0.505 in the next generation 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 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 each genotype. In the second generation, there is another sampling error based on the new gene frequency, so the frequency of on the new gene frequency, so the frequency of aa may go from 0.505 to 0.511 may go from 0.505 to 0.511 or back to 0.498. This process of random fluctuation continues generation after 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 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 the population has no "genetic memory" of its state many generations ago. Each generation is an independent event.generation is an independent event.


Extinction of genetic variability by genetic drift The final result of this random change in allelic frequency is that the population The final result of this random change in allelic frequency is that the population

eventually drifts to eventually drifts to pp = 1 or = 1 or pp = 0. After this point, no further change is possible; the = 0. After this point, no further change is possible; the population has become homozygous. A different population, isolated from the first, population has become homozygous. A different population, isolated from the first, also undergoes thisalso undergoes this random genetic drift, random genetic drift, but it may become homozygous for allele but it may become homozygous for allele AA, whereas the first population has become homozygous for allele , whereas the first population has become homozygous for allele aa. As time goes . As time goes on, isolated populations diverge from each other, each losing heterozygosity. The on, isolated populations diverge from each other, each losing heterozygosity. The variation originally present variation originally present withinwithin populations now appears as variation populations now appears as variation amongamong populations.populations.

Computer simulation of genetic Computer simulation of genetic drift. The frequency of an allele drift. The frequency of an allele (e.g., A in a system with A and a) is (e.g., A in a system with A and a) is shown for five replicate populations shown for five replicate populations over the course of 100 generations, over the course of 100 generations, with a population size (N) of 20. The with a population size (N) of 20. The effect of drift is inversely effect of drift is inversely proportional to population size, a proportional to population size, a fundamental driving force in many fundamental driving force in many evolutionary divergencesevolutionary divergences


Genetic drift over evolutionary time The appearance, loss, and eventual incorporation of The appearance, loss, and eventual incorporation of neutralneutral mutations in the life of a mutations in the life of a

population. If random genetic drift does not cause the loss of a new mutation, then it 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 must eventually cause the entire population to become homozygous for the mutation.mutation.

At that point, the mutation has been fixed.At that point, the mutation has been fixed. In the figure, 10 mutations have arisen, of which 9 (light red at bottom of graph) 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 increased slightly in frequency and then died out. Only the fourth mutation eventually spread into the population.eventually spread into the population.

Therefore, a steady substitution Therefore, a steady substitution of one allele for another is of one allele for another is expected to occur due to genetic expected to occur due to genetic drift alonedrift alone


The probability of fixation of a neutral allele It has been proven by matematical analysis (and it is quite intuitive) It has been proven by matematical analysis (and it is quite intuitive)

that the probability of fixation that the probability of fixation u u of any neutral allele of any neutral allele aa is equal to its is equal to its frequency in the population:frequency in the population:

u = pu = paa

In a finite population, pIn a finite population, paa takes discrete values only, starting from takes discrete values only, starting from

1/(2N) in diploid species (when one copy only of allele a is present in 1/(2N) in diploid species (when one copy only of allele a is present in the population), and incrementing at steps of 1/(2N).the population), and incrementing at steps of 1/(2N).

In other words, the initial frequency of a mutant allele is, by In other words, the initial frequency of a mutant allele is, by definition, pdefinition, paa = 1/(2N) = 1/(2N)

Thus, the probability of ultimate fixation of any new neutral mutation Thus, the probability of ultimate fixation of any new neutral mutation is equal to the reciprocal of twice the population size.is equal to the reciprocal of twice the population size.


The concept of gene substitution It is iIt is important to distinguish betweenmportant to distinguish between "Mutation" and "Substitution" "Mutation" and "Substitution" wwith respect to ith respect to

individuals and populationsindividuals and populations:: The The rate of gene substitutionrate of gene substitution (K) is defined as (K) is defined as the number of mutants reaching fixation the number of mutants reaching fixation

per unit time.per unit time. If neutral mutations occur at a rate of μ per gene per generation,If neutral mutations occur at a rate of μ per gene per generation, then the number of then the number of

mutants arising in a diploid population of size Nmutants arising in a diploid population of size N is 2N μ mutant alleles per generation.is 2N μ mutant alleles per generation. Since the probability ofSince the probability of fixation for each of these mutations is 1/(2N), we obtain the fixation for each of these mutations is 1/(2N), we obtain the resultresult thatthat

K = μ.K = μ. ThusThus theoretically, if the mutation rate μ is constant over time,theoretically, if the mutation rate μ is constant over time, neutral alleles neutral alleles

accumulate at a fixed rate independently ofaccumulate at a fixed rate independently of population size, and their rate of population size, and their rate of accumulation can be used as anaccumulation can be used as an evolutionary clock to measure divergence times. This evolutionary clock to measure divergence times. This is one ofis one of the fundamental tenants of molecular evolution.the fundamental tenants of molecular evolution.

This result can be intuitively understood by noting that, in a large population, theThis 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 ofnumber of mutations arising every generation is high but the fixation probability of each mutation is low.each mutation is low. In comparison, in a small population, the number of mutations In comparison, in a small population, the number of mutations arising every generation is low, but the fixation probability of each mutation is high.arising every generation is low, but the fixation probability of each mutation is high. As a consequence, the rate of substitution for neutral As a consequence, the rate of substitution for neutral mmutations is independent of utations is independent of population size.population size.


Esimating nucleotide mutation rate in human TThe result that the mutation rate forhe result that the mutation rate for neutral mutations neutral mutations

is equal to the rateis equal to the rate of of evolutionary substitution has evolutionary substitution has been the basis of an approach been the basis of an approach to measuring the human to measuring the human mutationmutation raterate at the nucleotide level. at the nucleotide level.

A direct comparison ofA direct comparison of stretches of DNA without stretches of DNA without function can function can pprovide an estimaterovide an estimate of the mutation rate of the mutation rate per generation between speciesper generation between species whose divergence time whose divergence time and generation length areand generation length are known. known.


Bacteria, Archae, and Eukaryotic microbes produce about one mutation per 300 Bacteria, Archae, and Eukaryotic microbes produce about one mutation per 300 chromosome replications. For E. coli this works out to be between 10chromosome replications. For E. coli this works out to be between 10 -6-6 and 10 and 10-7-7 mutations per gene per generation, however it is important to note that there are 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 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 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 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 predicted from a normal distribution.) Higher eukaryotes have the same rate of spontaneous mutation, so that rates per sexual generation are about one spontaneous mutation, so that rates per sexual generation are about one mutation per gamete (close to the maximum compatible with life). RNA viruses mutation per gamete (close to the maximum compatible with life). RNA viruses have much higher mutation rates -- about one mutation per genome per have much higher mutation rates -- about one mutation per genome per chromosome replication -- and even small increases in their mutation rates are chromosome replication -- and even small increases in their mutation rates are lethal.lethal.

Because a complex individual has a trillion or so nucleotides, each individual is Because a complex individual has a trillion or so nucleotides, each individual is likely to sustain one or more mutations.likely to sustain one or more mutations.

Rates of expressed gene mutations average about 1 per 100,000 to 1 per million:Rates of expressed gene mutations average about 1 per 100,000 to 1 per million: rates of expression of phenotypic effects are often higher because they are controlled by rates of expression of phenotypic effects are often higher because they are controlled by

many genesmany genes


The The mutation ratemutation rate is a measure of the frequency of a given mutation per generation 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. (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 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 means that each gamete has ca. 1 chance in 100,000 of carrying a new mutation for achondroplasia. achondroplasia.

A. Mutation rates are based almost exclusively on rare autosomal dominant or X-A. Mutation rates are based almost exclusively on rare autosomal dominant or X-linked recessive traits. It is virtually impossible to measure autosomal recessive linked 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 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 Duchenne muscular dystrophy and neurofibromatosis type-1 (the largest genes known) to several genes in the range of 1 in 10,000,000. known) to several genes in the range of 1 in 10,000,000.

C. Mutation rate studies C. Mutation rate studies nevernever measure all the possible mutations at a locus. Many measure all the possible mutations at a locus. Many of the mutations cause no obvious phenotypic effect and could only be recognized of the mutations cause no obvious phenotypic effect and could only be recognized by direct analysis of DNA sequences. by direct analysis of DNA sequences.

D. The rate of nucleotide substitutions is on the order of 1 per 100,000,000 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 nucleotides. Since there are 3 billion nucleotides per genome, that means that every gamete has about 30 new mutations involving nucleotide substitutions. gamete has about 30 new mutations involving nucleotide substitutions.


Mutation rates per generationMutation rates per generation Per base pair ~10Per base pair ~10-8 -8 - 10- 10-9-9

Per gene ~10Per gene ~10-6 -6 - 10- 10-5-5

Per genome ~0.02 - 1Per genome ~0.02 - 1 BUT -- These are highly variable from gene to gene, individual to BUT -- These are highly variable from gene to gene, individual to

individual, species to speciesindividual, species to species


Mutation rates

Mutation rate estimates:Mutation rate estimates: From divergence among humans and chimpanzees: From divergence among humans and chimpanzees:

μ = 10 μ = 10-9-9 per site (bp) per year or 2*10 per site (bp) per year or 2*10-8-8 per site per generation per site per generation Phenotypic effect: μ = 10Phenotypic effect: μ = 10-6-6 to 10 to 10-5 -5 per locus, gamete and generationper locus, gamete and generation Viability: 0.5 per gamete per generationViability: 0.5 per gamete per generation

At the molecular level, each human gamete genome may carry 200 At the molecular level, each human gamete genome may carry 200 new nucleotide substitutionsnew nucleotide substitutions

At the population level: A lot of new variation every generation!At the population level: A lot of new variation every generation!


The Rise and Fall of New Mutations Even when a mutation confers a selective advantage the Even when a mutation confers a selective advantage the

first few generations are dominated more by the whims of first few generations are dominated more by the whims of fate than by natural selectionfate than by natural selection The single individual carrying the mutation might die prematurely The single individual carrying the mutation might die prematurely

or its offspring might not find a mateor its offspring might not find a mate

Seventy two years ago J.B.S. Haldane used an approach Seventy two years ago J.B.S. Haldane used an approach known as branching to calculate the probability that a new known as branching to calculate the probability that a new advantageous mutation will become fixed in a populationadvantageous mutation will become fixed in a population He found this to be approximately 2sHe found this to be approximately 2s, , where s is the relative where s is the relative

fitness advantage that those possessing the new mutation have fitness advantage that those possessing the new mutation have relative to those who lack the mutationrelative to those who lack the mutation. . Since selection is thought Since selection is thought to be fairly weak on most amino acid variants, s~ 10-3-10-5, this to be fairly weak on most amino acid variants, s~ 10-3-10-5, this probability could be quite lowprobability could be quite low


Haldane’s Approach

Imagine that the new mutation sits at the root of a tree of Imagine that the new mutation sits at the root of a tree of descendantsdescendants

Once the tree branches a few times, random pruning is Once the tree branches a few times, random pruning is unlikely to kill off all of the branches at onceunlikely to kill off all of the branches at once

The crucial phase is therefore the first few generations of The crucial phase is therefore the first few generations of existence when the number of branches is smallexistence when the number of branches is small


Central question is the probability that the mutation will persist through the initial

branching process

Solving this problem yields the 2s resultSolving this problem yields the 2s result


Population size constant

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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.

Generalized this approach to include cases in Generalized this approach to include cases in which population size rises and falls through which population size rises and falls through timetime


Probability of Fixation

2(s + r), where r is the rate of population increase or 2(s + r), where r is the rate of population increase or decreasedecrease

Thus, a mutant that finds itself in a rapidly growing Thus, a mutant that finds itself in a rapidly growing population is much more likely to be fixed than one in a population is much more likely to be fixed than one in a shrinking populationshrinking population


Rate of gene substitutionRate of gene substitution 1. Overall rate (K) of substitution of a gene by various 1. Overall rate (K) of substitution of a gene by various

successivesuccessive neutral mutations is the number of mutant alleles reaching neutral mutations is the number of mutant alleles reaching

fixationfixation per generation.per generation.

Genetica per Scienze Naturali a.a. 03-04 prof S. Presciuttini Mutation Rates Ultimately, the source...

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