Gene Substitution

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Gene Substitution

• Dan Graur

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Gene substitution is the process whereby a mutant
allele completely replaces the predominant or
wild type allele in a population. Gene
substitution occurs when a mutant allele arises
in a population as a single copy in a single
individual, increases its frequency to 1 (i.e.,
becomes fixed) after a certain number of
generations.
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Frequency of 1
Very low frequency
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Not all mutants, however, reach fixation. In
fact, the majority of them are lost after a few
generations.
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Very low frequency
Frequency of 0
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Fixation probability The probability that a
particular allele will become fixed in a
population depends on (1) its frequency (2)
its selective advantage or disadvantage (3) the
effective population size
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The case of genic selection 1. three genotypes
A1A1, A1A2, A2A2 2. fitness values 1,
1 s, 1 2s, The probability of fixation of
A2 is where q is the frequency of allele A2.
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As s approaches 0 (neutral mutation), the
equation reduces to P ??q
The fixation probability for a neutral allele
equals its frequency in the population.
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A new mutant arising in a diploid population of
size N has an initial frequency of 1/(2N). If the
mutation is neutral the probability of fixation
is P 1/(2N).
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For a neutral mutation, i.e., s 0 For
positive values of s and large values of
N
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Thus, if an advantageous mutation arises in a
large population and its selective advantage over
the rest of the alleles is small (up to 5),
then the fixation probability is approximately
twice its selective advantage. For example, the
probability of fixation of a new codominant
mutation with s 0.01 is 2.
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Probabilities of Fixation
Population size Neutral mutation Advantageous mutation (s 0.01) Deleterious mutation (s 0.001)
1,000 0.05 2 0.004
10,000 0.005 2 1020
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Mutation accumulation assay
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Fixation Time The time required for the fixation
(or the loss) of an allele depends on (1) its
frequency (2) its selective advantage or
disadvantage (3) the effective population size
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Conditional Fixation Time The time of fixation
of mutants which do not undergo fixation is 8.
Thus, we only deal with the mean fixation time
of those mutants that will eventually become
fixed in the population. This variable is called
the conditional fixation time.
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Conditional Fixation Time In the case of a new
neutral mutation whose initial frequency in a
diploid population is by definition q 1/(2N),
the mean conditional fixation time is
approximated by For a mutation with a
selective advantage of s, the mean conditional
fixation time is approximated by
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Conditional Fixation Times
Population size Generation time Neutral mutation Advantageous mutation (s 0.01) Deleterious mutation (s 0.01)
1,000,000 2 years 8 million years 5,800 years ?

1. Less than 5,800 years
2. More than 8 million years
3. More than 5,800 but less than 8 million years
4. 8 million years
5. 5,800 years

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Conditional Fixation Times
Population size Generation time Neutral mutation Advantageous mutation (s 0.01) Deleterious mutation (s 0.01)
1,000,000 2 years 8 million years 5,800 years 5,800 years

1. Less than 5,800 years
2. More than 8 million years
3. More than 5,800 but less than 8 million years
4. 8 million years
5. 5,800 years ?

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Rate of Gene (or Allele) Substitution number
of mutants reaching fixation per unit time
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Rate of Gene Substitution Neutral mutations
If neutral mutations occur at a rate of u per
gene per generation, then the number of mutants
arising at a locus in a diploid population of
size N is 2Nu per generation. The probability
of fixation for each neutral mutation is 1/(2N).
The rate of substitution of neutral alleles is
obtained by multiplying the total number of
mutations by the probability of their fixation.
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A property of populations
A property of individuals
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Intuitive explanation In a large population the
number of mutations arising in every generation
is high, but the fixation probability of each
mutation is low. In a small population the
number of mutations arising in every generation
is low, but the fixation probability of each
mutation is high. The rate of substitution for
neutral mutations is independent of population
size.
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Rate of Gene Substitution Advantageous
mutations If advantageous mutations occur at a
rate of u per gene per generation, then the
number of mutants arising at a locus in a diploid
population of size N is 2Nu per generation. The
probability of fixation for each mutation is
2s. The rate of substitution of advantageous
alleles is 4Nsu.
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Deleterious mutations
Neutral mutations
Overdominant mutations
Advantageous mutations
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• Mutational Meltdown The double jeopardy of small
  populations
• It is possible for deleterious mutations to
  become fixed via genetic drift.
• Deleterious mutations occur more frequently than
  advantageous mutations.
• In small populations, random genetic drift is
  more important than selection.
• Small populations may be driven to extinction due
  to (1) accumulation of deleterious alleles, and
  (2) the fact that selection is too week to allow
  for advantageous mutations to accumulate.

Michael Lynch
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Multilocus models Previously, we assumed that
the genetic transmission of an allele at one
locus was independent of the transmission of
another allele at a different locus. Under this
assumption, we could treat each locus separately.
In practice, however, the transmission of an
allele at a locus may be dependent on the
transmission of alleles at other loci. The most
common cause for this lack of independence is
linkage, i.e., the close physical proximity of
two loci on the same chromosome and the finite
rate of meiotic recombination in the sequence
separating the two loci from each other.
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• Linkage equilibrium and disequilibrium
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• A diploid organism.
• Two autosomal loci, A and B.
• Each locus with two alleles, A1 and A2 at locus
  A, and B1 and B2 at locus B.
• Linkage equilibrium occurs if the association
  between the alleles at the two loci is random.
• Linkage disequilibrium occurs if some
  combinations of alleles occur significantly more
  or significantly less frequently in a population
  than would be expected from a random association
  between the alleles at the two loci.

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• Hitchhiking and genetic draft
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• A population withtwo neutral haplotypes, A2B1
  and A2B2, coexist with frequencies of p2 and q2,
  respectively.
• An advantageous mutation, A1, arises on the
  haplotype carrying the B1 allele. (Completely
  arbitrary, it could have arisen on on the
  haplotype carrying the B2 allele.)
• Without the advantageous allele arising at locus
  A, the probability of fixation for alleles B1 and
  B2 would have been p2 and q2, respectively.
• The linkage to the advantageous allele A1,
  however, alters these expectations. On its way to
  fixation, the advantageous mutation A1 will carry
  along the linked B1 allele, and will ultimately
  render the population monomorphic at locus B.

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• Hitchhiking and genetic draft
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• Advantageous mutations reduce or eliminate
  genetic variation at genetically linked sites
  (selective sweep).
• A neutral or even deleterious allele that is
  sufficiently tightly linked to a positively
  selected allele increases its frequency and may
  be swept to fixation (genetic hitchhiking).
• In genetic hitchhiking, only the initial
  conditions are stochastic, the rest of the
  process is deterministic (genetic draft).

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• Selective sweeps leave several characteristic
  molecular signatures in the population
• Eliminate nucleotide variation in the region of
  the genome close to the bene?cial allele.
• Cause an excess of high-frequency derived (new)
  alleles.
• Create long-range associations with neighboring
  locithe long-range haplotype, That is, a
  selective sweep will lead to creation of linkage
  disequilibrium over large swaths of DNA around
  the positively selected variant.
• The positive selection in one population causes
  large frequency differences between
  populationslarger than for neutrally evolving
  alleles.

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A selective sweep takes approximately
generations.
In addition, the signature of positive
selection may be identifiable for an additional
amount of time, depending on the rates of
mutation and recombination in the relevant
region.
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For how long after the fact can an evolutionary
detective identify a selective sweep in the human
population?
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The estimated human effective population size is
10,000. The mean generation time is 25
years. If a lucky mutation has a selective
advantage of 5, the sweep will be complete in
10,000 years. If a lucky mutation has a
selective advantage of 1, the sweep will be
complete in 50,000 years. SELECTIVE SWEEPS CAN
ONLY BE DETECTED FOR VERY SHORT PERIODS OF TIME
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Detecting recent selective sweeps due to selection
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Why are we (adult UH students) able to drink milk?
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The digestion of the disaccharide lactose, the
primary sugar present in milk, into its
monosaccharide constituents, glucose and
galactose, is catalyzed by a small-intestine
enzyme called lactase-phlorizin hydrolase (LPH or
lactase).
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Lactase persistence

• In mammals, levels of lactase decline rapidly
  after weaning, and adults are not able to digest
  lactose. In humans, most individuals are unable
  to digest lactose as adults (lactose intolerant),
  i.e., they carry the trait lactase
  nonpersistence. Digestion of fresh milk in
  individuals who are lactose intolerant can result
  in diarrhea, which for most of human history was
  lethal.

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In populations in which the only source of milk
is the mother, lactase nonpersistence is a
selectively advantageous trait, since
breastfeeding is a potent, albeit imperfect,
contraceptive, which inhibits menstruation and
delays resumption of ovulation. However, in
some populations, a derived genetic trait has
appeared, in which the ability to digest lactase
is maintained in adults. Such individuals are
lactose tolerant due to lactase persistence. This
trait is particularly common in populations that
have traditionally practiced dairying, i.e., in
populations which can obtain milk
extramaternally.
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Lactase persistence
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Lactase persistence arose at least twice in human
populations
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The lactase-persistence haplotypes
West Africa
North Europe
Bersaglieri et al. 2004
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Background selection   In the case of strong
negative selection on a locus, genetically linked
(neutral advantageous) variants will also be
removed, producing a decrease in the level of
variation surrounding the locus under purifying
selection. This process of purging
non-deleterious alleles from the population due
to spatial proximity to deleterious alleles is
called background selection. Background
selection is the opposite of Selective sweep.
Because the deleterious mutations driving
background selection are removed from the
population, they are extremely difficult to
detect.
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Epistasis Previously, we assumed that each locus
contributes independently to the fitness of the
individual (i.e., different loci do not interact
with one another in any manner that affects the
fitness). Thus, each locus can be dealt with
separately. This is not, however, always the
case! Epistasis refers to interactions among
alleles at different loci resulting in
non-independent effects. In other words,
epistasis occurs when the effects of an allele at
one locus are modified by one or several alleles
at other loci.
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Epistasis Epistasis may be defined at the
fitness level or at the level of the phenotype.
We distinguish between functional epistasis, in
which alleles at different loci produce
non-independent phenotypic effects, and fitness
epistasis, in which alleles at different loci
non-independently determine the fitness of their
carrier, whether or not epistasis is detectable
at the level of the phenotype.
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Epistasis The genetic-background effect,
according to which a mutation may have different
effects on fitness depending on the genome in
which it occurs, may be regarded as a generalized
kind of fitness epistasis.
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Epistasis Positive epistasis means that the
phenotype (or the fitness) is higher than
expected. Negative epistasis means that the
phenotype (or the fitness) is lower than
expected.
In the literature, one may find different terms,
such as, synergistic, diminishing, antagonistic,
aggravating, ameliorating, buffering,
compensatory, and reinforcing Confusing!
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Epistasis Positive epistasis means that the
phenotype (or the fitness) is higher than
expected. Negative epistasis means that the
phenotype (or the fitness) is lower than
expected.

• Mutation a at locus 1 increases IQ by 1 point.
• Mutation b at locus 2 increase IQ by 2 points.
• The two mutations together (say, following
  recombination) increase IQ by 12 points.

• Is the epistasis positive or negative?
• Is the epistasis functional or fitness epistasis?