Mendelian Genetics in Populations: Selection and Mutation as Mechanisms of Evolution
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Transcript of Mendelian Genetics in Populations: Selection and Mutation as Mechanisms of Evolution
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Mendelian Genetics in Populations: Selection and Mutation as Mechanisms of Evolution
I. Motivation Can natural selection change allele frequencies and if so, how quickly???
With the neo Darwinian synthesis: microevolution = change of allele frequencies
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Can persistent selection change allele frequencies: Heterozygote has intermediate fitness??????????
VERY QUICKLY!
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Developing PopulationGeneticModels
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II. Null Situation, No Evolutionary Change Hardy-Weinberg Equilibrium (parents: AA, Aa, aa)
Prob(choosing A) = pProb(choosing a) = qProbability of various combinations of A and a = (p + q)2=
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Punnett's copy of Hardy's letter to Science.
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Punnett square for a cross between two heterozygotes
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Haploid sperm and eggs fuse randomly with respect to genotype:
A = 0.6a = 0.4
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Or by copies (25 individuals)Frequency of (A) = : 9x2 + 12 = 30/50 = 0.6
Population of 25 individuals
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Sampling of haploid gametes represents binomial sampling: (2 gametes/zygote)
Prob(choosing A1) = pProb(choosing A2) = qProbability of various combinations of A1 and A2 = (p + q)2=
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The general case for random mating in the gene pool of our model mouse population(a) We can predict the genotype frequencies among the zygotes by multiplying the allele frequencies.
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p2 + p(1-p) = p
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III. 4 modes of Evolution
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IV. Natural Selection
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Fitness- the RELATIVE ability of an individual to survive and reproduce compared to other individuals in the SAME population
abbreviated as w
Selection- differences in survivorship and reproduction among individuals associated with the expression of specific values of traits or combinations of traits
natural selection- selection exerted by the natural environment, target = fitnessartificial selection- selection exerted by humans target = yield
selection coefficient is abbreviated as s
w = 1-s
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q’ – q = change in q from ONE generation to the Next
(q2)wrr + (pq)wRr -q =
change(q) = pq[ q(wrr – wRr) + p(wRr – wRR)]
What are the components of the above equation?
explore with selection against homozygote(haploid, diploid, tetraploid)
w
W
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q - q’ = -spq2
w
change(q) = pq[ q(wrr – wRr) + p(wRr – wRR)]
_________________________ W
For selection acting only against recessive homozygote:
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Haploid Selection:
qWr – q ; numerator = qWr - q(pWR + qWr)(pWR + qWr)
q(1-s) – q(p(1) + q(1-s))
q(1-s) – q(p + q – qs)
q(1-s) – q(1-qs)
q –qs – q + qqs
-qs + qqs
-qs(1-q)
-qps = -spq/ mean fitness
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How quickly can selection change allele frequencies??
theory:
for selection against a lethal recessive in the homozygote condition
say RR Rr rr and rr is lethal (dies before reproducing)
t = 1/qt - 1/qo
t is number of generations
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Predicted change in the frequency of homozygotes for a putative allele for feeblemindedness under a eugenic sterilization program that prevents homozygous recessive individuals from reproducing.
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Persistent selection can change allele frequencies: Heterozygote has intermediate fitness
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V. Examples
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Natural Selection and HIV
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Evolution in laboratory populations of flour beetles
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VI. Different types of selection
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Selection can change genotype frequencies so that they cannot be calculated by multiplying the allele frequencies
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change(q) = pq[ q(wrr – wRr) + p(wRr – wRR)] _________________________
- W
with selection against either homozygote, heterozygote is favored wrr = 1-s2, wRR = 1-s1, wRr = 1: set above to 0
substitute 1-s1 and 1-s2: -qs2 + ps1 = 0ps1 – qs2 = 0; (1-q)s1 – qs2 = 0; s1 –s1q –s2q = 0q(s1 +s2) = s1
q at equilibrium = s1/(s1 + s2)
with Rr favored, always find R, r alleles in population
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Selection favoring the Heterozygote = Overdominance
2 populations founded with allele freq = 0.5
Maintains genetic variation
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Sickle Cell Anemia
and the evolution of resistance to
malaria:
The case for
Heterozygote Advantage
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APPLICATION:
Can we calculate the selection coefficients on alleles associated with Sickle Cell??
Sickle Cell Anemia:
freq of s allele (q) = 0.17
0.17 = s1/(s1 + s2)
if s2 = 1, then s1 = 0.2
then the advantage of Ss heterozygotes is 1/0.8 = 1.25 over the SS homozygote
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Is cystic fibrosis an example of heterozygote superiority??
http://en.wikipedia.org/wiki/Typhoid_fever
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Bacteria are Typhoid Bacteria
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Selection acting against the Heterozygote= Underdominance
Analogous to speciation?
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But many examples of hybrid inviability in plants and animals consistent with underdominance but with different consequences
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Summary ofOverdominanceAnd Underdominance
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Frequency-dependent selection in Elderflower orchids
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VII. Mutation and Selection
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Bacterial evolution due to mutation
Fruit flies adapt to salt stress via mutationMutations contribute to adaptive
genetic response
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Mutation Selection Balance for a Recessive Allele
q = μ/s
SPECIAL CASE: SELECTION AGAINST LETHAL RECESSIVE:
Examine case of:
telSMN (q=0.01, μ = 1.1 x 10-4) (predicted mutation rate = 0.9 x 10-4)
cystic fibrosis (q =0.02, μ = 6.7x10-7) (predicted mutation rate 2.6 x 10-4)
Sickle cell anemia (q = 0.17)
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VIII. Conclusions
• Population genetic theory supports idea of lots of genetic variation
• Population genetic theory supports idea that natural selection can lead to evolution
• Evolution allows us to incorporate our understanding of inheritance to also understand pattern of genetic diversity