Evolution: change in allele frequencies within a ...dgray/Evol322/Chapter6.pdfAdults produce gametes...
Transcript of Evolution: change in allele frequencies within a ...dgray/Evol322/Chapter6.pdfAdults produce gametes...
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Mendelian Population Genetics
• Evolution: change in allele frequencies withina population over time
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A mouse is a vehicle for mousegene replication
Mice with Aagenotypes
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IF no mutation…Gametes
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IF random mating
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Zygotes
Sum = 1
Then zygotes grow up to be adults
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IF no survival selection, and IF nobiased migration, and IF no biased
random death
THEN you get these adult genotypes, whichproduce gametes……
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Adults produce gametes IF nomutation….
Those are the same allele frequencieswe started with!! A = 0.6 a = 0.4
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There was no evolutionarychange….IF
• No mutation
• Random mating
• No biased migration
• No biased selected mortality (selection)
• No biased random mortality (drift)
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The general case
Developed by Hardy 1908
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Mind your p’s and q’s
• If p = frequency of A1 allele
• And q = frequency of A2 allele
• And if there are only two alleles in thepopulation at this locus
• Then p + q = 1– Alternatively q = 1- p
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Randomly combining gametes inthe general case
• Sperm are A1 withprobability p
• Eggs are A1 withprobability p
• So A1A1 zygotesare produced withprobability of p X p= p2
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And so on….• A1A1 genotype has frequency of p2
• A1A2 genotype has frequency of pq
• A2A1 genotype has frequency of pq
• A2A2 genotype has frequency of q2
• But A1A2 is the same as A2A1 = 2 pq
• Frequencies must add to 1p2 + 2pq + q2 = 1
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Hardy-Weinberg Equilibrium
• If a simple set of assumptions holds, thenthe allele frequencies in a population willnot change
• If we symbolize allele frequencies as p andq, then genotype frequencies are p2, 2pq,and q2
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What are those simple assumptions?
• No selection: genotypes survive at equalrates (i.e. no survival selection) andcontribute gametes to the next generationequally (i.e. no sexual selection)
• No mutation: the alleles we are accountingfor stayed the same, none disappeared orwere created anew by mutation
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What are those simple assumptions?
• No biased migration: genotypes do not enter orexit the population non-randomly
• No biased random events: genotypes do not getzapped by lightning (or whatever) non-randomly;if so, called genetic drift
• Mating is random by genotype. Violating thisassumption affects genotype frequency, not allelefrequency. This is NOT the same thing as sexualselection (unequal gametic contribution ofgenotypes).
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What a bunch of malarcky!
• Obviously those five conditions are almostnever met!
• So when those conditions are not met, allelefrequencies WILL change, i.e. evolutionwill occur
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Still, what good is that?
• Hardy-Weinberg equilibrium model is anull model
• It is a random expectation given a specificset of assumptions
• Specification of those assumptions allowsus to see when and how evolutionarychange does occur
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And what about the only twoalleles nonsense?
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Non-equilibrium: violations ofHardy-Weinberg
• Mutation
• Selection
• Migration
• Drift
• Non-random mating
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Pop Quiz
• A has frequency of 0.9, what is thefrequency of a (if only two alleles)?
• p2 + 2pq + q2……=
• What are the HW genotypic frequencies?
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Hardy-Weinberg recap
• If a set of five assumptions is met:– Then, allele frequencies won’t change
– And,
– Genotypic frequencies follow from• p2 + 2pq + q2 = 1
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Mutation as an evolutionary Force
• Mutation critical for genetic variation
• But can mutation, by itself, have muchevolutionary impact on allele frequencies?
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A = functional allele; a = mutantknockout
• Mutation from A to a– Mutation rate of 1 per 10,000
– plausible but high
• Mutation from a to A negligible
• Suppose, initially A allele has a frequencyof 0.9
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What is the effect of mutation?
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Effect over time?
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Mutation - selection balance
• Mutations are random• In finely tuned organisms, most mutations
are bound to be bad• Bad mutations selected against• Also created anew• Rate of creation by mutation = rate of
removal by selection• Called mutation-selection balance
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Deleterious mutations selectedagainst
• How common should any particulardeleterious mutation be?
• Depends on how bad (strength of selection)
• Depends on how often re-created (mutationrate)
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Is that useful information?• Two examples
• Spinal muscular atrophy, study by Wirth et al.– Caused by mutation in telSMN
– Telomeric survival motor neuron
• Cystic fibrosis, study by Pier et al.– Most common lethal autosomal recessive disease
in Caucasians
– Proximate cause bacteria Pseudomonas aeruginosalung damage
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Spinal muscular atrophy
• telSMN knock out mutants frequency of 0.01• Selection coefficient ~ 0.9• Can use equation to estimate what mutation rate
would be needed to counter s = 0.9, and give q^of 0.01
• And the calculated answer is 0.9 X 10-4
mutations per allele per generation• Wirth et al. directly measured rate of 1.1 X 10-4
• Mutation-selection balance
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Cystic fibrosis
• Chromosome 7 mutations for protein calledCystic fibrosis transmembrane conductanceregulator (CFTR)
• Expressed in lining of lungs and intestines• In lungs, enables cells to destroy
Pseudomonas aeruginosa• Until recently most cistic fibrosis sufferers
died before reproducing (i.e. selection veryvery strong, approaching s = 1)
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Cystic fibrosis mutation-selectionbalance?
• Could mutation selection balance maintainmutants at frequency of 0.02 with s = 1?
• Yes, but mutation rate would have to beabout 4 X 10-4
• Observed mutation rate much lower, ca. 6.7X 10-7
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Does something else maintaincystic fibrosis causing mutations
at that level?
• This is an important question to ask in thiscase; note that it was not necessary to askthis in the case of Spinal Muscular Atrophy
• The answer could have important medicalimplications
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A possible answer
• What if mutation(s) favored in another context?
• Recall CFTR expressed in intestine as well aslung
• Pier et al hypothesized a function for mostcommon disease causing allele– Prevents intestinal infection by Salmonella typhi
• Agent causes Typhoid fever
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DeltaF508 allele, cystic fibrosis,and Typhoid fever
• deltaF508 most common cystic fibrosiscausing allele
• In humans, homozygotes would get cysticfibrosis
• Could heterozygotes be protected fromTyphoid fever?
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Mouse study
• Heterozygotes moreresistant toSalmonella typhi
• Homozygotes almostcompletely protected
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Pleiotropy and genetic correlation
• deltaF508 single allele with multiple(pleiotropic) effects
• Genetic correlation– Lung lining phenotype will show some
similarity to intestine lining phenotype– Not completely separate traits for selection to
act upon independently
• And that’ s what is next: selection
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Selection as an evolutionary force
• Hardy-Weinberg null model assumptions• Individuals of all genotypes survive at equal
rates, and contribute gametes equally to thegene pool
• Bottom line is differential reproductivesuccess: some genotypes out reproduceothers
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example
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Result
• 7.5% increase in frequency of B1 allele7.5% decrease in frequency of B2 allele
• Population has evolved
• Also true for much weaker selection
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Selection across generations
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Empirical Example: Adh
• Alcohol dehydrogenase– Enzyme breaks down ethanol
• Cavener & Clegg Drosophila melanogasterexperiment– Two replicate populations on ethanol spiked
food– Two replicate populations on ethanol free food
• Tracked allele frequency across time
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Adh semi-natural selection experiment
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Selection and genotypic frequency
• If a set of five assumptions is met:– Then, allele frequencies won’t change
– And,
– Genotypic frequencies follow from• p2 + 2pq + q2 = 1
• Does selection alter genotype frequency?– Sometimes, for one generation
• Heterozygote advantage
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Selection and genotype frequencyAllele freq. 0.5, 0.5
Heterozygotes fitter
After selection
Allele freq. 0.5, 0.5
Predicts genotype
Frequency of
0.25, 0.5, 0.25
Observe 0.167, 0.667,0.167
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Generalizing Selection
• Recall development of Hardy-Weinbergargument
• We took special case of A = 0.6 and a = 0.4
• Then generalized using p as frequency of theA allele and q as frequency of the alternativeallele a
• Can we develop a general model of selection?
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Change in allele frequencydepends on genotypic fitness
• Why?, because selection acts on phenotypesnot alleles
• Fitness symbolized as w• Fitness of a genotype symbolized with
subscripts, so that• Fitness of A1A1 genotype has fitness w11
• Fitness of A1A2 genotype has fitness w12
• Fitness of A2A2 genotype has fitness w22
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How will allele frequency changewith unequal genotypic fitness?
• Unequal fitness needs a standard
• Fitness of a genotype is expressed relativeto a standard of the average fitness of allgenotypes
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Genotypic frequency change
• Genotypic frequency change depends on thefitness of the genotype relative to theaverage fitness
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How have allele frequencies changed?• How many A1 gametes produced?
• A1 gametes in proportion to A1A1genotype frequency multiplied by relativegenotype fitness
• Plus 1/2 of A1A2 genotype frequencymultiplied by relative genotype fitness
1/2 of 2pq = pq
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Same for A2 alleles• A2 gametes proportional to frequency of
A2A2 genotype (q2) multiplied by the relativefitness of the q2 genotype
• Plus 1/2 of the alleles contributed byheterozygotesthat is, 1/2 of the frequency of heterozygotes (2pq)
multiplied by heterozygote relative fitness
1/2 of 2pq = pq
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Allele frequency change
• Change = new allele frequency - old allelefrequency
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Ta Da!!!
• We have made a general expression thatquantitatively describes how allelefrequency will change depending on theaverage fitness of that allele
• Similarly,
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Patterns of Selection
• Selection on dominant versus recessivealleles
• Selection on heterozygotes andhomozygotes
• Frequency dependent selection
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Dominant and recessive alleles
• A dominant to a if
• AA genotype = A phenotype
• AND
• Aa genotype = A phenotype
• but
• aa genotype = a phenotype
• If so, A called dominant, a called recessive
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Suppose homozygous recessive islethal
• waa = 0
• How will frequency of a change over time?– If a is common?
– If a is rare?
• If a is common then genotype aa is prettycommon– If frequency of a = q then genotype frequency = q2
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What do we expect
• If at first a is common, it will decreaserapidly
• As it becomes more rare, it will decreasemore slowly– Because when rare, there are few aa genotypes
with fitness = 0
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Data from flour beetles
• Dawson started experiment withheterozygotes, so p = q = 0.5
• waa = 0
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Data agree with qualitativeprediction
• Rapid change when aa genotype common
• Slow change when aa genotype rare
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Selection against recessive
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Selection for recessive
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Heterozygotes
• Heterozygotes don’ t always express dominantphenotype
• Heterozygotes can have fitness– Intermediate
• Changes rate of evolution, not outcome
– Higher• Heterozygote superiority or overdominance
– Lower• Heterozygote inferiority or underdominance
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Overdominance
• Suppose genotypic fitness is as follows:wAA = 0.735wAa = 1waa = 0
• Equilibrium frequency of a allele > 0• Example seen in Drosophila melanogaster
study of Muaki and Burdick (1958)• Specific gene effects unknown
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Four populations, 2 replicates
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Overdominance generalized• Mean fitness across genotypes
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underdominance
• What if heterozygotes have lower fitness?
• Considerably more complicated
• Outcome depends on starting conditions
• One allele goes to fixation (100%)– Other allele lost
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Underdominance generalized
Adaptive landscape
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Heterozygote selection outcomes
s and t are selection terms for homozygotes
Both negative = heterozygote superiority (overdominance)
Both positive = heterozygote inferiority (underdominance)
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Frequency dependent selection
• Strength of selection depends on frequency
• For example, if the allele that is rare isfavored
• Two examples– Book scale eating fish
– Sex
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Scale eating fish Perissodus microlepisLake Tanganyika
• Mouth twisted to side, bites scales off other fish
• Left mouth bites right side of victim; Right mouthbites left; Victim fish wary
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Sex• Sex ratio (males:females) usually about 1:1• Imagine the fitness of a male if males were
really rare– That rare male would make lots of babies
• Female fitness if females rare?– Most males would not reproduce
• Imagine male female controlled by singlelocus with two alleles