Chapter 7 Genetics of populations

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Chapter 7 Genetics of populations

• Read Chapter 7 of text

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Chapter 7 Genetics of populations

• We saw in chapter 6 that a cross between two
  individuals heterozygous for a dominant allele
  produces a 31 ratio of individuals expressing
  the dominant phenotype to those expressing the
  recessive phenotype.
• For example brachydachtyly (shortening of the
  digits) displays this pattern of inheritance.

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Population genetics

• In the early 1900s when Mendels work was
  rediscovered there was confusion about how these
  simple patterns of inheritance affected
  populations.
• Why, for example, was not 3 of every 4 people a
  person with brachdactyly?
• Why did not dominant alleles replace recessive
  alleles?

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Population genetics

• The confusion stemmed from confusing what was
  happening at the level of the individual with
  what occurs at the population level.
• Individual-level thinking enables us to figure
  out the result of particular crosses.

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Population genetics

• Population level thinking however is needed to
  figure out how the genetic characteristics of
  populations change over time.
• It enables us to figure out quantitatively what
  is happening in a population as a result of
  evolution. Remember, evolution occurs when
  genotype frequencies change over time.

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Hardy-Weinberg Model a null model for population
genetics.

• Null models provide us with a baseline. They
  tell us what we expect to be the case if certain
  forces are not operating.
• The Hardy-Weinberg equilibrium tells us what we
  expect to happen to genotype frequencies when
  forces such as natural selection are not
  operating on a population.

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Hardy-Weinberg Model a null model for population
genetics.

• The Hardy-Weinberg model enables us to determine
  what allele and genotype frequencies we would
  expect to in a population if all that is
  happening is alleles are being randomly assigned
  to gametes and those gametes meet up at random.

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Hardy-Weinberg Model

• The Hardy-Weinberg model examines a situation in
  which there is one gene with two alleles A1 and
  A2.
• There are three possible genotypes A1A1,
• A2 A2,and A1 A2

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Hardy-Weinberg Model

• Hardy and Weinberg used their model to predict
  what would happen to allele frequencies and
  genotype frequencies in the absence of any
  evolutionary forces.
• Their model produced three important conclusions

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Hardy-Weinberg Model

• The three conclusions of the H-W model. In the
  absence of evolutionary processes acting on them
• 1. The frequencies of the alleles A1 and A2 do
  not change over time.
• 2. If we know the allele frequencies in a
  population we can predict the equilibrium
  genotype frequencies (frequencies of A1A1, A2
  A2,and A1 A2).

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Hardy-Weinberg Model

• 3. A gene not initially at H-W equilibrium will
  reach H-W equilibrium in one generation.

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Assumptions of Hardy-Weinberg

• 1. No selection.
• If individuals with certain genotypes survived
  better than others, allele frequencies would
  change from one generation to the next.

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Assumptions of Hardy-Weinberg

• 2. No mutation
• If new alleles were produced by mutation or
  alleles mutated at different rates, allele
  frequencies would change from one generation to
  the next.

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Assumptions of Hardy-Weinberg

• 3. No migration
• Movement of individuals in or out of a population
  would alter allele and genotype frequencies.

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Assumptions of Hardy-Weinberg

• 4. Large population size.
• Population is large enough that chance plays no
  role. Eggs and sperm collide at same frequencies
  as the actual frequencies of p and q.
• If assumption was violated and by chance some
  individuals contributed more alleles than others
  to next generation allele frequencies might
  change. This mechanism of allele frequency
  change is called Genetic Drift.

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Assumptions of Hardy-Weinberg

• 5. Individuals select mates at random.
• Individuals do not prefer to mate with
  individuals of a certain genotype. If this
  assumption is violated allele frequencies will
  not change, but genotype frequencies might.

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Deriving the H-W model
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Hardy-Weinberg Equilibrium

• Assume two alleles A1 and A2 with known
  frequencies (e.g. A1 0.6, A2 0.4.)
• Only two alleles in population so their allele
  frequencies add up to 1.

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Hardy-Weinberg Equilibrium

• Can predict frequencies of genotypes in next
  generation using allele frequencies.
• Possible genotypes are A1A1 , A1A2 and A2A2

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Hardy-Weinberg Equilibrium

• Assume alleles A1 and A2 enter eggs and sperm in
  proportion to their frequency in population (i.e.
  0.6 and 0.4)
• Assume sperm and eggs meet at random (one big
  gene pool).

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Hardy-Weinberg Equilibrium

• Then we can calculate expected genotype
  frequencies.
• A1A1 To produce an A1A1 individual, egg and
  sperm must each contain an A1 allele.
• This probability is 0.6 x 0.6 or 0.36
  (probability sperm contains A1 times probability
  egg contains A1).

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Hardy-Weinberg Equilibrium

• Similarly, we can calculate frequency of A2A2.
• 0.4 x 04 0.16.

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Hardy-Weinberg Equilibrium

• Probability of A1A2 is given by probability sperm
  contains A1 (0.6) times probability egg contains
  A2 (0.4). 0.6 x 04 0.24.

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Hardy-Weinberg Equilibrium

• But, theres a second way to produce an A1A2
  individual (egg contains A1 and sperm contains
  A2). Same probability as before 0.6 x 0.4
  0.24.
• Overall probability of A1A2 0.24 0.24 0.48.

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Hardy-Weinberg Equilibrium

• Genotypes in next generation
• A1A1 0.36
• A1A2 0.48
• A2 A2 0.16
• Adds up to one.

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Hardy-Weinberg Equilibrium

• General formula for Hardy-Weinberg.
• Let p frequency of allele A1 and q frequency
  of allele A2.
• p2 2pq q2 1.

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Hardy Weinberg Equilibrium with more than 2
alleles

• If there are three alleles with frequencies P1,
  P2 and P3 such that P1 P2 P3 1
• Then genotype frequencies given by
• P12 P22 P32 2P1P2 2P1 P3
• 2P2P3

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Conclusions from Hardy-Weinberg Equilibrium

• Allele frequencies in a population will not
  change from one generation to the next just as a
  result of assortment of alleles and zygote
  formation.
• If the allele frequencies in a gene pool with two
  alleles are given by p and q, the genotype
  frequencies will be given by p2, 2pq, and q2.

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Conclusions from Hardy-Weinberg Equilibrium

• The frequencies of the different genotypes are a
  function of the frequencies of the underlying
  alleles.
• The closer the allele frequencies are to 0.5 the
  greater the frequency of heterozygotes.

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Working with the H-W equation

• You need to be able to work with the
  Hardy-Weinberg equation.
• For example, if 9 of 100 individuals in a
  population suffer from a homozygous recessive
  disorder can you calculate the frequency of the
  disease causing allele? Can you calculate how
  many heterozygotes you would expect in the
  population?

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Working with the H-W equation

• p2 2pq q2 1. The terms in the equation
  represent the frequencies of individual
  genotypes.
• P and q are allele frequencies. It is vital that
  you understand this difference.

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Working with the H-W equation

• 9 of 100 (frequency 0.09) of individuals are
  homozygotes. What term in the H-W equation is
  that equal to?

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Working with the H-W equation

• Its q2.
• If q2 0.09, whats q? Get square root of q2,
  which is 0.3.
• If q0.3 then p0.7. Now plug p and q into
  equation to calculate frequencies of other
  genotypes.

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Working with the H-W equation

• p2 (0.7)(0.7) 0.49
• 2pq 2 (0.3)(0.7) 0.42
• Number of heterozygotes 0.42 times population
  size (0.42)(100) 42.

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Working with the H-W equation 3 alleles

• There are three alleles in a population A1, A2
  and A3 whose frequencies respectively are 0.2,
  0.2 and 0.6 and there are 100 individuals in the
  population.
• How many A1A2 heterozygotes will there be in the
  population?

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Working with the H-W equation 3 alleles

• Just use the formulae P1 P2 P3 1 and P12
  P22 P32 2P1P2 2P1 P3 2P2P3 1
• Then substitute in the appropriate values for the
  appropriate term
• 2P1P2 2(0.2)(0.2) 0.08 or 8 people out of
  100.

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Hardy-Weinberg Equilibrium

• Hardy Weinberg equilibrium principle identifies
  the forces that can cause evolution.
• If a population is not in H-W equilibrium then
  one or more of the five assumptions is being
  violated.

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Hardy-Weinberg Equilibrium

• If we relax the H-W assumption of no selection
  how does that affect allele frequencies?

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Strength of selection

• To quantify the strength of selection against a
  recessive allele we can use a parameter (s)
  called the selection coefficient to describe the
  reduction in fitness of one phenotype vs the
  other.

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Strength of selection

• For example pocket mice coat color is affected by
  a gene with two alleles D and d. D allele is
  dominant.
• DD dark phenotype
• Dd dark phenotype
• Dd light phenotype
• On dark backgrounds light phenotype will be
  selected against.

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Strength of selection

• The higher the value of s the more strongly
  natural selection will act.

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Frequency independent selection

• The mouse coat color example is an example of
  frequency-independent selection. The fitness of
  a trait is not associated with how common the
  trait is.

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Directional selection

• The commonest form of frequency- independent
  selection is directional selection.
• Under directional selection one allele is
  consistently favored over the other allele so
  selection drives allele frequencies in only one
  direction towards a higher frequency of the
  favored allele.
• Eventually favored allele may replace other
  alleles and become fixed.

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Empirical examples of allele frequency change
under selection

• Clavener and Cleggs work on Drosophila.
• Two alleles for ADH (alcohol dehydrogenase breaks
  down ethanol) ADHF and ADHS

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Empirical examples of allele frequency change
under selection

• Two Drosophila populations maintained one fed
  food spiked with ethanol, control fed unspiked
  food.
• Populations maintained for multiple generations.

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Empirical examples of allele frequency change
under selection

• Experimental population showed consistent
  long-term increase in frequency of ADHF
• Flies with ADHF allele have higher fitness when
  ethanol present.
• ADHF enzyme breaks down ethanol twice as fast as
  ADHS enzyme.

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Fig 5.13
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Empirical examples of allele frequency change
under selection Jaeken syndrome

• Jaeken syndrome patients severely disabled with
  skeletal deformities and inadequate liver
  function.

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Jaeken syndrome

• Autosomal recessive condition caused by
  loss-of-function mutation of gene PMM2 codes for
  enzyme phosphomannomutase.
• Patients unable to join carbohydrates and
  proteins to make glycoproteins at a high enough
  rate.
• Glycoproteins involved in movement of substances
  across cell membranes.

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Jaeken syndrome

• Many different loss-of-function mutations can
  cause Jaeken Syndrome.
• Team of researchers led by Jaak Jaeken
  investigated whether different mutations differed
  in their severity. Used Hardy-Weinberg
  equilibrium to do so.

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Jaeken syndrome

• People with Jaeken syndrome are homozygous for
  the disease, but may be either homozygous or
  heterozygous for a given disease allele.
• Different disease alleles should be in
  Hardy-Weinberg equilibrium.

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Jaeken syndrome

• Researchers studied 54 patients and identified
  most common mutation as R141H.
• Dividing population into R141H and other
  alleles. Allele frequencies are
• Other 0.6 and R141H 0.4.

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Jaeken syndrome

• If disease alleles are in H-W equilibrium then we
  would predict genotype frequencies of
• Other/other 0.36
• Other/R141H 0.48
• R141H/R141H 0.16

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Jaeken syndrome

• Observed frequencies are
• Other/Other 0.2
• Other/R141H 0.8
• R141H/R141H 0
• Clearly population not in H-W equilibrium.

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Jaeken syndrome

• Researchers concluded that R141H is an especially
  severe mutation and homozygotes die before or
  just after birth.
• Thus, there is selection so H-W assumption is
  violated.

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Testing predictions of population genetics theory

• Theory predicts that if an average individual
  carrying an allele has higher than average
  fitness that the frequency of that allele will
  increase from one generation to the next.
• Obviously, the converse should be true and a
  deleterious allele should decrease in frequency
  if its bearers have lower fitness.

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Testing predictions of population genetics theory

• If the average fitness of an allele A when paired
  at random with other alleles in the population is
  higher than the average fitness of the
  population, then it will increase in frequency.

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Tests of theory

• Dawson (1970). Flour beetles. Two alleles at
  locus and l.
• / and /l phenotypically normal.
• l/l lethal.

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Dawsons flour beetles

• Dawson founded two populations with heterozygotes
  (frequency of and l alleles thus 0.5).
• Expected allele to increase in frequency and l
  allele to decline over time.

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Dawsons flour beetles

• Predicted and observed allele frequencies matched
  very closely.
• l allele declined rapidly at first, but rate of
  decline slowed.

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Fig 5.16a
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Dawsons flour beetles

• Dawsons results show that when the recessive
  allele is common, evolution by natural selection
  is rapid, but slows as the recessive allele
  becomes rarer.
• Hardy-Weinberg explains why.

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Dawsons flour beetles

• When recessive allele (a) common e.g. 0.95
  genotype frequencies are
• AA (0.05)2 Aa (2 (0.05)(0.95) aa (0.95)2
• 0.0025AA 0.095Aa 0.9025aa
• With more than 90 of phenotypes being recessive,
  if aa is selected against expect rapid population
  change.

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Dawsons flour beetles

• When recessive allele (a) rare e.g. 0.05
  genotype frequencies are
• AA (0.95)2 Aa 2(0.95)(0.05) aa (0.05)2
• 0.9025AA 0.095Aa 0.0025aa
• Fewer than 0.25 of phenotypes are aa recessive.
  Most a alleles are hidden from selection as
  heterozygotes. Expect only slow change in
  frequency of a.

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Maintaining multiple alleles in gene pool

• Dawsons beetle work shows that deleterious rare
  alleles may be very hard to eliminate from a gene
  pool because they remain hidden from selection as
  heterozygotes.

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Maintaining multiple alleles in gene pool

• This only applies if the allele is not dominant.
  A dominant allele is expressed both as a
  heterozygote and a homozygote and so is always
  visible to selection.

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Maintaining multiple alleles in gene pool

• One way in which multiple alleles may be
  maintained in a population is through
  heterozygote advantage (also called
  overdominance).
• Classic example is sickle cell allele.

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Sickle cell anemia

• Sickle cell anemia is a condition common among
  West Africans and those of West African descent.
• Under low oxygen conditions the red blood
  corpuscles are sickle shaped.
• Untreated the condition usually causes death in
  childhood.

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Sickle cell anemia

• About 1 of West Africans have sickle cell
  anemia.
• A single mutation causes a valine amino acid to
  replace a glutamine in the alpha chain of
  hemoglobin
• The mutation causes hemoglobin molecules to stick
  together.

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Why isnt sickle cell allele eliminated by
selection?

• Only individuals homozygous for the allele get
  sickle cell anemia.
• Individuals with only one copy of the allele
  (heterozygotes) get sickle cell trait (a mild
  form of the disease)
• Individuals with the sickle cell allele (one or
  two copies) dont get malaria.

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Heterozygote advantage

• Heterozygotes have higher survival than either
  homozygote (heterozygote advantage).
• Sickle cell homozygotes die of sickle cell
  anemia, many normal homozygotes die of malaria.
• Stabilizing selection thus favors sickle cell
  allele.

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Heterozygote advantage

• A heterozygote advantage (or overdominance)
  results in a balanced polymorphism in a
  population.
• Both alleles are maintained in the population as
  the heterozygote is the best combination of
  alleles and a purely heterozygous population is
  not possible.

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Underdominance (heterozygote disadvantage)

• Underdominance is when the heterozygote has lower
  fitness than either homozygote.
• This situation is In this case one or other
  allele will go to fixation, but which depends on
  the starting allele frequencies

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Frequency-dependent selection

• In some cases the costs and benefits of a trait
  depend on how common it is in a population.

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Positive frequency-dependent selection

• In this case the commoner a phenotype is the more
  successful it is.
• If two phenotypes are determined by single
  alleles one allele will go to fixation and the
  other be lost, but which one depends on the
  starting frequencies.

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Positive frequency-dependent selection

• In flat snails individuals mate face to face
  and physical constraints mean only individuals
  whose shells coil in the same direction can mate
  successfully.
• Higher frequencies of one coil direction leads to
  more mating for that phenotype and eventually it
  replaces the other types.

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Negative frequency-dependent selection

• Under negative frequency-dependent selection a
  trait is increasingly favored the rarer it
  becomes.

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Negative frequency-dependent selection

• Color polymorphism in Elderflower Orchid
• Two flower colors yellow and purple. Offer no
  food reward to bees. Bees alternate visits to
  colors.
• How are two colors maintained in the population?

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Negative frequency-dependent selection

• Gigord et al. hypothesis Bees tend to visit
  equal numbers of each flower color so rarer color
  will have advantage (will get more visits from
  pollinators).

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Negative frequency-dependent selection

• Experiment provided five arrays of potted
  orchids with different frequencies of yellow
  orchids in each.
• Monitored orchids for fruit set and removal of
  pollinaria (pollen bearing structures)

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Negative frequency-dependent selection

• As predicted, reproductive success of yellow
  varied with frequency.

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5.21 a
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Negative frequency-dependent selection

• Another example of negative frequency-dependent
  selection involves a scale-eating cichlid fish in
  Lake Tanganyika.
• The fish come in left- and right-mouthed morphs.
  They attack their victims from behind.

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Negative frequency-dependent selection

• Because each morph always attacks the same side
  of its victims when the frequency of a morph
  increases the victims become good at guarding
  against attacks from that side.
• The common morph then suffers reduced feeding
  success and declines in abundance.

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Negative frequency-dependent selection

• As a result the morphs fluctuate in frequency
  over time.

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Mutation as an evolutionary force

• It is obvious that selection is a very powerful
  evolutionary force but how strong is mutation
  alone as an evolutionary force?
• To check Two alleles A and a.
• Frequency of A 0.9, a 0.1.

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Mutation as an evolutionary force

• Assume A mutates to a at rate of 1 copy per
  10,000 per generation (high rate, but within
  observed range) and all mutations occur in
  gametes.
• How much does this change gene pool in next
  generation?

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Mutation as an evolutionary force

• Hardy Weinberg genotypes in current generation
• 0.81 AA, 0.18 Aa, 0.01 aa
• With no mutation allele frequency in gene pool
  0.9 A, 0.1 a

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Mutation as an evolutionary force

• But mutation reduces frequency of A and increases
  frequency of a
• A a
• 0.9 - (0.0001)(0.9) 0.1 (0.0001)(0.9)
• 0.89991A 0.10009a

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Mutation as an evolutionary force

• Not a big change.
• After 1000 generations frequency of A 0.81.

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Mutation as an evolutionary force

• Mutation alone clearly not a powerful
  evolutionary force.
• But mutation AND selection make a very powerful
  evolutionary force.

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Lenskis E. coli work

• Lenski et al. studied mutation and selection
  together in an E. coli strain that did not
  exchange DNA (hence mutation only source of new
  variation).
• Bacteria grown in challenging environment (low
  salts and low glucose medium) so selection would
  be strong.

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Lenskis E. coli work

• 12 replicate populations tracked over about
  10,000 generations.
• Fitness and cell size of populations increased
  over time.
• Pattern of change interesting steplike.
• Why is it steplike?

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5.25
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Lenskis E. coli work

• Step-like pattern results when a new mutation
  occurs and sweeps through the population as
  mutant bacteria out-reproduce competitors.
• Remember, without mutation evolution would
  eventually cease. Mutation is ultimate source of
  genetic variation.

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Mutation-selection balance

• Most mutations are deleterious and natural
  selection acts to remove them from population.
• Deleterious alleles persist, however, because
  mutation continually produces them.

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Mutation-selection balance

• When rate at which deleterious alleles being
  eliminated is equal to their rate of production
  by mutation we have mutation-selection balance.

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Mutation-selection balance

• Equilibrium frequency of deleterious allele q
  square root of µ/s where µ is mutation rate and s
  is the selection coefficient (measure of strength
  of selection against allele ranges from 0 to 1).
  
• See Box 7.8 for derivation of equation.

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Mutation-selection balance

• Equation makes intuitive sense.
• If s is small (mutation only mildly deleterious)
  and µ (mutation rate) is high than q (allele
  frequency) will also be relatively high.
• If s is large and µ is low, than q will be low
  too.

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Mutation-selection balance

• Spinal muscular atrophy is a generally lethal
  condition caused by a mutation on chromosome 5.
• Selection coefficient estimated at 0.9.
  Deleterious allele frequency about 0.01 in
  Caucasians.
• Inserting above numbers into equation and solving
  for µ get estimated mutation rate of 0.9 X 10-4

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Mutation-selection balance

• Observed mutation rate is about 1.1 X10-4, very
  close agreement in estimates.
• High frequency of allele accounted for by
  observed mutation rate.

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Is frequency of Cystic fibrosis maintained by
mutation selection balance?

• Cystic fibrosis is caused by a loss of function
  mutation at locus on chromosome 7 that codes for
  CFTR protein (cell surface protein in lungs and
  intestines).
• Major function of protein is to destroy
  Pseudomonas aeruginosa bacteria. Bacterium causes
  severe lung infections in CF patients.

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Cystic fibrosis

• Very strong selection against CF alleles, but CF
  frequency about 0.02 in Europeans.
• Can mutation rate account for high frequency?

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Cystic fibrosis

• Assume selection coefficient (s) of 1 and q
  0.02.
• Estimate mutation rate µ is 4.0 X 10-4
• But actual mutation rate is only 6.7 X 10-7

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Cystic fibrosis

• Is there an alternative explanation?

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Cystic fibrosis

• May be heterozygote advantage.
• Pier et al. (1998) hypothesized CF heterozygotes
  may be resistant to typhoid fever.
• Typhoid fever caused by Salmonella typhi
  bacteria. Bacteria infiltrate gut by crossing
  epithelial cells.

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Cystic fibrosis

• Hypothesized that S. typhi bacteria may use CFTR
  protein to enter cells.
• If so, CF-heterozygotes should be less vulnerable
  to S. typhi because their gut epithilial cells
  have fewer CFTR proteins on cell surface.

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Cystic fibrosis

• Experimental test.
• Produced mouse cells with three different CFTR
  genotypes
• CFTR homozygote (wild type)
• CFTR/?F508 heterozygote (?F508 most common CF
  mutant allele)
• ?F508/?F508 homozygote

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Cystic fibrosis

• Exposed cells to S. typhi bacteria.
• Measured number of bacteria that entered cells.
• Clear results

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Fig 5.27a
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Cystic fibrosis

• ?F508/?F508 homozygote almost totally resistant
  to S. typhi.
• Wild type homozygote highly vulnerable
• Heterozygote contained 86 fewer bacteria than
  wild type.

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Cystic fibrosis

• Further support for idea ?F508 provides
  resistance to typhoid provided by positive
  relationship between ?F508 allele frequency in
  generation after typhoid outbreak and severity of
  the outbreak.

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Fig 5.27b
Data from 11 European countries
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Non-Random mating

• Another assumption of Hardy-Weinberg is that
  random mating takes place.
• The most common form of non-random mating is
  inbreeding which occurs when close relatives mate
  with each other.

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Inbreeding

• Most extreme form of inbreeding is self
  fertilization.
• In a population of self fertilizing organisms all
  homozygotes will produce only homozygous
  offspring. Heterozygotes will produce offspring
  50 of which will be homozygous and 50
  heterozygous.
• How will this affect the frequency of
  heterozygotes each generation?

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Inbreeding

• In each generation the proportion of heterozygous
  individuals in the population will decline.

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Inbreeding in California Sea Otters

• Because inbreeding produces an excess of
  homozygotes in a population deviations from
  Hardy-Weinberg expectations can be used to detect
  such inbreeding in wild populations.

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Inbreeding in California Sea Otters

• Sea otters once abundant along the west coast of
  the U.S were almost wiped out by fur hunters in
  the 18th and 19th centuries.
• California population reached a low of 50
  individuals (now over 1,500). As a result of
  this bottleneck the population has less genetic
  diversity than it once had.

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Inbreeding in California Sea Otters

• Population still at a low density and Lidicker
  and McCollum (1997) investigated whether this
  resulted in inbreeding.
• Determined genotypes of 33 otters for PAP locus,
  which has two alleles S (slow) and F (fast)

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Inbreeding in California Sea Otters

• The genotypes of the 33 otters were
• SS 16
• SF 7
• FF 10
• This gives approximate allele frequencies of S
  0.6 and F 0.4

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Inbreeding in California Sea Otters

• If otter population in H-W equilibrium, genotype
  frequencies should be
• SS 0.6 0.6 0.36
• SF 20.60.4 0.48
• FF 0.40.4 0.16
• However actual frequencies were
• SS 0.485, SF 0.212, FF 0.303

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Inbreeding in California Sea Otters

• There are more homozygotes and fewer
  heterozygotes than expected for a random mating
  population.
• Having considered alternative explanations for
  deficit of heterozygotes Lidicker and McCollum
  (1997) concluded that sea otter populations show
  evidence of inbreedng.

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General analysis of inbreeding

• Self-fertilization and sibling mating most
  extreme forms of inbreeding, but matings between
  more distant relatives (e.g. cousins) has same
  effect on frequency of homozygotes, but rate is
  slower.

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General analysis of inbreeding

• F Coefficient of inbreeding probability that
  two alleles in an individual are identical by
  descent (both alleles are copies of a particular
  ancestors allele in some previous generation).
• F increases as relatedness increases.

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General analysis of inbreeding

• If we compare heterozygosity of inbred population
  Hf with that of a random mating population Ho
  relationship is
• Hf Ho (1-F)
• Anytime Fgt0 frequency of heterozygotes is reduced
  and frequency of homozygotes naturally increases.

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General analysis of inbreeding

• Calculating F. Need to use pedigree diagrams.
• Example Female is daughter of two half-siblings.
• Two ways female could receive alleles that are
  identical by descent.

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Half-sibling mating
Male
Female
Male
Male
Female
Fig 6.27a
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Fig 6.27b
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General analysis of inbreeding

• Total probability of scenario is 1/16 1/16
  1/8.

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Inbreeding depression

• Inbreeding increases frequency of homozygotes and
  thus the probability that deleterious alleles are
  visible to selection.
• In humans, children of first cousins have higher
  mortality rates than children of unrelated
  individuals.

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Each dot on graph represents mortality rates
for a human population. Mortality rate for
children of cousins consistently about
4 higher than rate for children of
non-relatives.
Fig 6.28
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Inbreeding effects on high blood pressure

• In a study of 2760 individuals from 25 Croatian
  islands Rudan et al. found a strong positive
  relationship between high blood pressure and the
  inbreeding coefficent.

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Inbreeding depression

• Inbreeding depression also documented in studies
  of wild animals.
• E.g. Great Tit. Two studies show that survival of
  inbred nestlings is lower than that of outbred
  individuals and that hatching success of inbred
  eggs is lower than that of outbred eggs.

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Fig. 6.30