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Printable Handouts
Navigable Slide Index
- Introduction
- Talk outline
- 1st summary: the site frequency spectrum
- The presumed ancestral state
- Site frequency spectrum
- Part 1: the site frequency spectrum (SFS)
- 2nd summary: distance between heterozygote sites
- Histogram of distance between heterozygote sites
- Part 2: distance between heterozygote sites (1)
- 1a. Wright-Fisher with no mutations
- 1a. Allele count dynamics
- 1a. Allele frequency behaviour
- 1b. The coalescent process (1)
- 1b. The coalescent process (2)
- 1b. Time between coalescent events: 2 individuals
- 1b. Time between coalescent events: 3 individuals
- 1b. Time between coalescent events: general
- 1c. Adding mutations
- 1d. Combinatorics
- 1d. The expected SFS: basic result
- 1d. Proof of basic result (1)
- 1d. Proof of basic result (2)
- 1e. Example (exome sequencing of chimps)
- 1e. Discussion
- Part 2: distance between heterozygote sites (2)
- 2a. Wright-Fisher with recombination
- 2b. The ancestral process
- 2b. The ancestral recombination graph (ARG)
- 2b. Tree heights inferred from the ARG
- 2b. Time between coalescent/recombination events
- 2b. Two loci and two sequences (example 1)
- 2b. Two loci and two sequences (example 2)
- 2b. Two loci and two sequences (example 3)
- 2b. Two loci and two sequences: complete ARG
- 2c. Continuous time Markov chains (CTMCs)
- 2c. Probability of no change
- 2c. Transition density conditional on change
- 2d. Distance between segregating sites
- 2e. Distance between segregating sites: example
- 2e. Simulation study: detecting a bottleneck
- Conclusion and outlook
Topics Covered
- The site frequency spectrum (SFS)
- Wright-Fisher with no mutations
- The coalescent process (backwards Wright-Fisher)
- Adding mutations
- The expected SFS
- Distance between heterozygote sites
- Wright-Fisher with recombination
- The ancestral recombination graph (ARG)
- Probability tree heights along the sequence
- Expected histogram for distance between heterozygote sites
- Simulation study: detecting a bottleneck
Talk Citation
Hobolth, A. (2016, March 31). Statistical models in population genetics [Video file]. In The Biomedical & Life Sciences Collection, Henry Stewart Talks. Retrieved October 8, 2024, from https://doi.org/10.69645/BDJP8119.Export Citation (RIS)
Publication History
Financial Disclosures
- Dr. Asger Hobolth has not informed HSTalks of any commercial/financial relationship that it is appropriate to disclose.
Other Talks in the Series: Statistical Genetics
Transcript
Please wait while the transcript is being prepared...
0:00
ASGER HOBOLTH: Hello everybody,
my name is Asger Hobolth,
and I will give you an introduction
to statistical models
in population genetics.
0:09
So the main purpose of statistical
models in population genetics
is to formulate
models that allows us
to understand and
describe genetic variation
observed in DNA sequences.
I've decided to divide my talk
into two parts, responding
to do different summaries of genetic
variation from DNA sequence data.
So in the first part of my talk,
I will talk about the site frequency
spectrum, which is
an often-used statistic
for summarizing genetic variation.
And in the second
part of my talk, I will
talk about how you
can model distances
between heterozygote sites.
This is a more involved problem,
and the theory's a bit more difficult.
But this is also
an often-used statistic
for summarizing genetic variation.
The theory that we will need is
the so-called Wright-Fisher model,
which is a forward
model of evolution.
And then it is the corresponding
backwards process,
which is called
the coalescent process.
And this coalescent
process basically
gives us what is called
a tree, and we will
have to add mutations on this tree.
And this will give us
a model for DNA sequences.
And basically, using coalescent
process with mutations,
we can derive the side
frequency spectrum.
So we can derive the summary of
what we expect the first summary
statistics to look like.
And in the second
part of the talk,
we will have to add the so-called
recombination process
through the basic coalescent
process, and we will have to,
instead of work with
the trees, we will
have to work with the so-called
ancestral recombination graph.
But I will come back to all this.