restriction enzyme analysis the new(ish) population genetics old view new view allele frequency...
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Restriction enzyme analysis
The new(ish) population genetics
Old view New view
Allele frequency changelooking forward in time; alleleseither the same or different
Shape of gene tree lookingbackward in time; alleles are
related phylogenetically
The first ‘gene tree’, 1979
Diploid individuals
Dissolved individuals
Wright, Kingman and the coalescentSewell Wright
J. F. C. Kingman
Probability of common ancestry of two Randomly chosen alleles in previous generation
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12N
Probability that 10 sequences have j ancestors in previous
generation
Probability that all k copies from a sample came from differentcopies in the preceding generation
So, the time it takes for two copies from a sample to come from thesame copy in the preceding generation is:
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E(uk ) ≈ 4Nk(k −1)€
1−Gkk ≈ k(k −1)4N
And, the total time it takes for all copies from a sample to come from acommon ancestral copy is:
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4N 1− 1k
⎛ ⎝ ⎜
⎞ ⎠ ⎟With large k
(units in generations)
4N generations
Expected fixation time of neutral allele in population of size N
(Kimura)
Shape of gene trees from a random mating
population
How to draw a coalescent tree
1. Sample k copies from a population of 2N chromosomes2. Go back in time, drawing from an exponential distribution,
with the average being
3. Combine two lineages4. Decrease k by 15. If k-1, stop; otherwise, go back to step 1, using k-1 as a starting
point €
4Nk(k −1)
Root of a gene tree captured in very few samples
Stochastic nature of the coalescent process
Estimating genetic diversity within
populations
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θ =Sn
1jj=1
n−1
∑=
θ= 4N = average number ofdifferences between two randomly sampledsequences from a population
“Watterson’s theta”
or θ = observed number of differences between all pairsof sequences from a population. Also called “”
past present
Genetic diversity (θ) or
population size
Signatures of stable and expanding populations Long internal branchesShort external branches
Short internal branchesLong external branches
Stable population Expanding population
• Mycoplasma is transmitted horizontally, often at bird feeders
• Expanded throughout the eastern US in just five years
• Has now crossed the Rockies and is spreading south through California.
Rapid spread of Mycoplasma in House Finch
populations
Courtesy Cornell Lab of Ornithology
Serially-sampled phylogeny of 12
Mycoplasma strains
Years before present 30 20 10 0
Estimated coalescence of chickenand finch strains, (611 yrs.)(95 % c.i. 484-753 yrs.)
Numerous fixed SNP and indeldifferences, including CRISPR deletion
Estimated mutation rate:~9.3 x 10-10 per site per year;24 homoplasious sites suggestrecombination
Phylogeny obtained using BEAST, strict clock, 10 million cycles, sampling every 1000 cycles743,011 aligned sites
Shape (node depths) of higher level trees depend on extrinsic
factorsInterordinal molecular phylogeny of mammals
“Lucky Mother” conceptfor mtDNA
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