Restriction enzyme analysis

Restriction enzyme analysis

The new(ish) population genetics

Old view New view

Allele frequency changelooking forward in time; alleles

either 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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1

2N

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 ) ≈4N

k(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 1−1

k

⎛

⎝ ⎜

⎞

⎠ ⎟

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 €

4N

k(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

1

jj=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

200 150 0100 50

051015

MonthsYears

Time before present

Effective

population

size

Inferred Mycoplasma expansion 17 years ago

104

103

102

10

2.57.512.5

Shape (node depths) of higher level trees depend on extrinsic factors

Interordinal molecular phylogeny of mammals

“Lucky Mother” conceptfor mtDNA