Transcript E-Halliburton chapter 6

BI 3010 H07
Mutations
Population genetics
Halliburton Chapter 6-7
Mutations
Mutations are the raw materials of genetic variation. Viable mutations are rare om most loci, but
this varies strongly between loci. Although the allele frequency changing affect (i.e. evolution) may be
modest on short time frames, it is the accumulated amount of allelic variants on evolutionary time
frames that has enabled genetic differentiating between individuals, populations, species, families and
higher taxa.
The cause of mutations:
Errors during DNA replication, uneven crossing-over, chromosome breaking, and meiotic non-separation
(corresponding chromosomes do not go to separate daughter cells).
Types of mutations:
Mutations can take place in sex chromosomes as well as in somatic chromosomes. Those which affect
single nucleotides are called point mutations. When a whole gene or several genes are duplicated we
speak about gene mutations. Such events are evolutionary important because they give room for natural
selection to act. For example, vertebrates usually have more than one locus (usually 2-3) coding for a
specific protein, and often these loci are more or less tissue-specific so that e.g. in heart muscle one locus
dominates the protein synthesis, while another dominates in liver tissue. Traditionally, mutations which
affect single loci are called gene mutations, while those affecting the number of or structure of chromosomes are called chromosome mutations, but this nomenclature is not very satisfactory today.
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Halliburton Chapter 6-7
Mutations
An alternative classification is:
1. Chromosome mutations (duplications, deletions, inversions, translocations)
2. Point mutations (Changes in one nucleotide)
3. "Indels": (Abbrev. for insertions/deletions. Small; one to a few hundred basepairs)
4. Gene-duplications (of one or several protein-coding genes)
Aneuploidy: One extra or missing chromosome (e.g. in Down's syndrome with an extra copy
of chromosome 21 in man).
Polyploidy: The whole set of chromosomes is duplicated, so that individuals have three or
more sets instead of two, as normally. This usually arises when cytokinesis (separation to
daughter cells) don't take place during meiosis.
More concepts:
Inversions, which can involve several genes, tend to be inherited as units. Dobzkansky called
such units "co-adapted gene complexes". There is evidence that such complexes are
maintained by some form of natural selection, in that the so-called heterokaryotypes have
higher relative fitness compared to homokaryotypes.
Translocations arise when a segment from one chromosome attaches to a non-homologous
chromosome. They can be resiprocal or not. Translocations are almost always lethal (giving
abnormal gametes and disturbance of the gene regualtion). Many types of cancer in man are
caused by such disturbances. Closely related specues often differs by only one or a few
translocations.
Fusions means that segments from two non-homologous chromosomes combine to a new
chromosome (cf Fig. 6.1 in Halliburton; chrom. # 2). Fission is the opposite phenomenon.
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Transposable elements: The insertion or deletion of long DNA sequences. Common in
both pro- and eucariotes. When a transposable element moves into or out of a proteincoding locus we have a mutation. Such elements are connected with variation in
quantitative traits (like bristle number in Drosophila), and hence interesting for breeding
geneticists.
Gene duplications: Individual genes, chromosome parts or whole chromosomes can be
duplicated. The duplicate is a new copy of one or more genes in the genome. Because the
very function of the gene is secured with only one copy, the evolutionary forces (mutation,
selection) can act without the common restraints and create viable variants with new
functions (cf "pseudogenes" which have lost their original function). Cf multiple loci for
isozymes in vertebrates, often becoming tissue-specific.
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Population genetics
Mutations
Halliburton Chapter 6-7
Mutation models
1.
Recurrent mutations: ”Wildtype” vs mutant, to and fro until an equilibrium (this is the
model in PopG.exe).
q-bar =  / ( + )
[ check formula with PopG.exe ]
where  is mutation rate and  = backmutation rate
2.
Infinite alleles model: (Single basepair mutations). Each mutation creates a unique
allele (Kimura & Crow 1964). A sentral model in population genetics.
3.
Stepwise mutation model: Based on the situation observed by protein electrophoresis.
Allows for backmutations and repeated mutations. Experience shows it is more relevant
for micro- and minisatellites.
4.
Infinite site model: Regards each nucleotide position ("site") as independent of others.
It assumes that most positions don't mutate, and that those that mutate do it only once.
This means that each "site" has only one or two alleles. Results from SNP studies
appear to fit this model, which has two versions: linkage equilibrium (Kimura 1969) and
linkage disequilibrium (Watterson 1975) between tightly linked positions.
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Population genetics
Mutations
Halliburton Chapter 6-7
Mutation rates:
Most mutation for coding DNA are harmful, and the frequency of mutants is a balance
between mutation rates and natural selection. Therefore, observed mutant frequencies are
low. The mutation frequencies can be calculated in many ways (per nucletide, locus,
chromosome or genome). It must be made clear whether mutation rates are per cell division,
generation or some unit of time. Here's an example from fruit fly (Drosophila sp.):
Ca 36 cell divisions between zygote formation and gamete production in imago. If assuming
2x10-6 mutations per locus per cell division, it counts to 72x10-6 mutations per locus per
generation (or per zygote).
Mutation rates have been shown to vary enormously; by many orders of magnitude, among
loci (see Table 6.1 in Halliburton). Mutations that cause genetic disorders typically show low
frequencies (10-5 - 10-6 per locus per generation).
Microsatellite loci can show much higher frequencies (10-3), which is the reason why they are
better gene markers for short-time genetic differentiation processes; they will react faster to
reproductive isolation/genetic drift than protein-coding loci.
Mutation rates per nucleotide per generation are lower; ca 10-8 or less. The reason for this is
that the proof-reading repair mechanism acting on DNA during replication. Mitochondrial DNA,
which has fewer repair mechanisms, thus shows higher mutation rates per nucleotide. This
means higher evolutionary rates in shorter time spans than for protein-coding loci.
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Fitness effect of mutations:
Harmful: Most frequent. Neutral: Frequencies largely unknown. Favourable: Rare
Backmutations from harmful mutations are often less frequent than the mutation itself.
Cleansing selection removes harmful mutations, or lower the frequency of them. Selection
coefficients and population sizes play roles for the efficiency of this. In very small populations
genetic drift can override selection, and more often lead to fixation of harmful mutant alleles.
”Silent”, or synonymous mutations in a codon (3rd codon position) do not change the
resultant amino acid, and should thus be ideal gene markers for studies of differentiation by
random genetic drift.
From the genetic code it can be deduced that the ration between "replacement" and "silent"
mutations should be 3:1. Studies in mammals have supported this; the portion that are neutral
is 20-30%, and sometimes higher. The probability for a neutral mutant to become fixed in the
population is 1/2Ne where Ne is the genetically effective population size [ check this using
PopG.exe ].
.
Favourable mutations are the raw material for adaptive evolusion. Natural selection can make
these increase in frequency and eventually become fixed in the population. Since their initial
frequency is very low (1/2Ne; heterozygote carrier), the probability that they are lost quickly by
genetic drift is substantial (ca 37% in the first generation). It is assumed that the frequency of
mutants with a substantial favourable effect is very low.
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The span of mutational effects:
Mutations with visible morphological effects are rare. Lethal recessive mutations are more rare then
mutations with less dramatic effects.
Mutational effects (fitness reduction) on heterozygotes:
Lethal mutations: h = 0.03
Mild mutations: h = 0.3 -0.5
(h indicated how much the fitness (w) of the heterozygote is reduced)
Simmons & Crow: ”The milder the effect of a mutant, the greater its dominance”. (Page 203)
Mutation - selection equilibrium:
When a harmful allele is rare, natural selection is less efficient in removing it (cf the eugenics
problem treated previously).
Simulation: Use PopG.exe, and set the fitness of a recessiv homozygote to 0 (i.e. S=1).
Start with a low frequency of the mutant (recessive) allele, and a population size=10.000 (to reduce
noise from genetic drift), and study the progress of the curves for frequency of the wildtype allele.
Notice the asymptotic course, with less and less effect of selection over generations (cf the eugenics
programs often advocated in the 1930ies).
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Halliburton Chapter 6-7
Mutations
When the allele frequency of a harmful mutant is affected by (recurrent) mutation rate and
natural selection, it will eventually reach an equilibrium given ny:
q = SQR(/s) [ where genotypic fitnesses are: A1A1: 1, A1A2: 1-hs, og A2A2: 1-s]
Under certain assumptions this formula can be used to calculate mutation rates at a locus. It has
been used, together with observations, to argue that lethal mutations have certain harmful affect
even in heterozygotes. [ simulate using PopG.exe ]
Mutational load (genetic load)
Single locus:
All selection works through differential mortality, and therefore increases the total mortality
in the population so that mean fitness is reduced. Mutation-selection equilibrium therefore
creates what is called "genetic load" or "segregational load"; a general reduction of the health
of the population. For a completely recessive mutation in equilibrium with selection the genetic
load (L) is:
L = , and for a not completely recessive mutation:
L = 2
In other words; in the equilibrium situation the mutational load is only depending on the mutation
rate, not on the harming effect and the severity of the mutation. The reason for this is that very
harmful mutations progress towards a lower equilibrium frequency, which is balanced by the strong
selection against them.
Summed over the entire genome (n loci):
L = 2n(-bar), where -bar is the mean mutation frequency over n loci.
An estimate from fruit fly: 0.4% reduction in viability (fitness) per generation, 1.2% per zygote.
Important concepts: Muller’s ratchet, mutational meltdown (Halliburton p. 210).
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Mutations
Population genetics
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The faith of a new mutation:
Most mutations are lost after few generations due to selection or genetic drift. What is the probability
that a neutral mutation is lost already after one generation? Or after two, or any generation in future?
If the neutral mutant is a heterozygote the probabilities for survival or loss in the first generation are:
Pr(survival) = 1 – 1/e = 0.632,
Pr(loss)
= e-1 = 0.368,
i.e. ~ 63%
i.e. ~ 37%
and
The probability for loss during 10 generations is more than 80%.
The probability that a mutant allele survives and eventually is fixed in the population depends on the
effective population size and is:
Pr(Fixation) = 1/2Ne, i.e. it's initial frequency! [ check formula with PopG.exe ]
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Genetic drift
Halliburton Chapter 6-7
Genetic Drift:
If we define evolution as any change in allele frequency in the populations, it is easy to see that genetic
drift for neutral alleles can propel evolutionary change. The change is, however, unpredictable because
it is stochastic. Genetic drift can be seen as a sampling error from one generation to the next.
The theory on this was developed by Sewall Wright in the 1930ies and 1940ies. Genetic drift is the
random variation in allele frequencies from one generation to the next. It has two causes:
1.
2.
Mendelian segregation – a diploid individual holds two copies of each gene, but produces gametes
with only one copy each.
Population size is not infinitely large - any population (or generation) is a random subset of the
gametes that were produced by the parental population (or generation).
Four main aspects of genetic drift:
1. The direction of the change in allele frequencies is unpredictable. An increase or decrease is equally
probable in any generation (except at allele frequencies very close to 0 or 1).
2. The magnitude of genetic drift depends on the effective population sizes. The smaller the population,
the larger the average gene frequency change from one population to the next.
3. The long term effect of genetic drift is to reduce genetic variability within a population (fixations).
4. Genetic drift causes populations to diverge genetically from each other by time.
Genetic drift reduces genetic variation within populations, but increases it between divergence them.
NB! Simulate various scenarios with the software PopG.exe.
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The binomial distribution:
Describes the distribution of outcomes in a set of n independents trials where each
has two possible outcome.
Let the probability for one outcome (success) be p, and for the other (failure) be (1-p).
Let X be a random variable which describes the number of successes in n trials.
X can take the values 0,1,2,....n. The binomial distribution describes the probability (Pr)
for each of the possible outcomes (i.e. number of successes in n trials). Let x denote a
specific outcome for X. Then
Pr(X=x) = [ n! / (x!(n-x)! ] [ px(1-p)n-x ]
Example: The probability for getting a 1 when throwing a dice once is 1/6.
The probability of getting exactly two "1"s (x=2) in five throws (n=5) is
Pr(X=2) = [5! / 2!3!] [ (1/6)2 (5/6)3] = 0.16
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"Genetic drift reduces genetic variability within populations"
Concepts: Identity by descent (ibd) and Identity by state (ibs)
Identity by state (IBS):
Alleles which are functionally equivalente.
Identity by descent (ibd):
Alleles which are inherited from a common ancestor in the last or previous generations.
The probability of two alleles being ibd is 1/2N and is called the inbreeding coefficient, f.
This probability increases each generation, because each generation of sampling creates a
new possibility for ibd to be added to the existing value of f. The recursion equiation is:
ft+1 = 1/(2N) + [(1 – 1/(2n) ]ft
Reduction in heterozygosity caused by genetic drift:
H, or the proportion of heterozygotes in the population, is by the Hardy-Weinberg law given
by the allele frequencies as H=2p(1-p), which has its maximum p=0.5 at a 2-allel locus.
When the allele frequencies approaches 1 or 0, the heterozygosity approaches zero.
Genetic drift makes allele frequencies approach the extremes fixation/loss sooner or later,
and the heterozygosity to be reduced by an amount 1/2N each generation.
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"Genetic drift leads to differentiation between populations":
The variance of an allele frequency p after one generation of binomial sampling is:
Var(pt+1) = pt(1-pt)/2N, and this variance increases over generations. In
generation t it s:
Vart(p) = p0(1-p0) [ 1- (1 – 1/2N)t ] (Study Fig. 7.6 – 7.9 pp 232-233 in Halliburton)
Effecive population size ( (Ne):
Definition: The size of an "ideal" population which has a genetic drift equal to the one
under study. By "ideal" is meant constant size, equal sex proportion, and equal number of
offspring in all matings.
Effect of unequal sex ratio:
Ne = 4Nm*Nf / (Nm + Nf)
which means that with e.g. 1 male, even 100 females will not constitute an effective
population size larger than approximately 4. Such a population will loose genetic variation
(measured as heterozygosity) at a high rate due to strong genetic drift.
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Halliburton Chapter 6-7
Genetic drift
Variation in effective population size over generations:
This harmonic mean is always less
than the arithmetic mean when Ne varies.
Episodes with small populations sizes
always have strong reducing effect on Ne.
Variation in family sizes within populations:
Ne = 4N / (VK +2), where
K=family size, and VK the variance in family size.
NB! Family size means the number
of offspring surviving to reproduction.
In stable populations both the mean
and the variance of k is 2.
X-linked loci:
Y-linked loci:
mtDNA loci:
Founder effects (and population
bottlenecks) give genetic drift
dependent on founder Ne, and
changes the allele frequencies
accordingly.
The heterozygosity is reduced
each generation by a quantity:
 H = - [1 / (2Ne)]
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Genetic drift
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The heterozygosity at an equilibrium between genetic drift and mutation is:
H = 4Ne / (4Ne + 1)
Genetic drift, population dynamics, and extinction (rules of thumb):
Minimum viable population size on short term: Ne = 50
Minimum viable population size on long term: Ne = 500-1000
(adjusted by Lande (1995) to 5000-10000 individuals).
How important is genetic drift in nature?
A population is "small" and genetic drift is a significant evolutionary force when, related to the other
evolutionary forces (mutation, selection, and immigration):
4N < 1
4Ns < 1
4Nm < 1
The long term effects of genetic drift and mutations are clear; all populations will loose genetic
variation and accumulate harmful mutations. Many favourable mutations will be lost, which hampers
the ability for long term adaptability. The severeness of these effects depends strongly on the
effective population size.
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Genetic drift
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Genetic drift and natural selection:
Natural selection changes allele frequencies in a predictable manner (cf the relative fitness and selection
coefficients of genotypes). Genetic drift also changes allele frequencies, but in an unpredictable way.
Which of these two forces will dominate depends on the size of the fitness advantage, and the population
size. In very small populations, genetic drift will be so strong that it hampers or even overrides the effect
of selection (cf fig. 7.16 and 7.17 in Halliburton), and even favourable mutations will appear, evolutionary
seen, as if they were neutral. This means they can more easily be lost from a small population.
NB! Simulate various scenarios with software PopG.exe.
The probability of fixation for a recessive favourable mutation (Kimura 1962) is:
Pr(fix)  1.13 s/(2N)
where s is the fitness advantage for a homozygote (i.e. double dose) for the mutation.
[ Pr(fix) for a neutral mutation = 1/(2N). Compare!]
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Halliburton Chapter 6-7
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