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ASGER HOBOLTH: Hello everybody,
my name is Asger Hobolth,
and I will give you an introduction
to statistical models
in population genetics.
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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.
