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

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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