Questions about migration parameter

[shu-ping]

Dear Joao,

First, thanks for publish this convenient tool! The friendly
user space and detailed manual are very helpful for the researchers,
especially for the students have no background on statistic and
program language. It easy understand for the beginners who want to
build ABC models.

I have some questions for asking you and group members. If any
one can give me some advices, I'll really appreciate it.

I have no doubt about the migration direction in two
populations model but a little confusing in three populations model.
In two populations model given the population 1 and population 2, m1
corresponds to the migration rate from population 2 to population 1.
In three populations model given the three topology, ((1,2):A1,3):A2,
m1/2/3/A1 correspond to the migration rates from unknown sources to
population 1/2/3/A1. Is this right? If it is, I wonder if it is
possible to set a migration matrix in popABC and then I can get the
detailed migration parameters. For example, the numbers of the row
refer the source populations and the numbers of the column refer the
sink populations.
Given the tree topology: ((1,2):4,3):5
1,2,3 = morden populations 1,2,3 4 = the ancestral population of
pop1 and pop2 ...
And set the migration matrix:
0 m2->1 m3->1 0 0
m1->2 0 m3->2 0 0
m1->3 m2->3 0 m4->3 0
0 0 m 3->4 0 0
0 0 0 0 0

Can I add this matrix in popABC and get these new migration
parameters?

[shu-ping]

Dear Joao,

Sorry for the foolish question before.I just find there is
migration weight setting in popABC.
But even I set the migration weight matrix, popABC won't output the
extra migration parameters.
Can I get more migration parameters by changing some settings in
popABC?
I mean can I get not just m1,m2,m3 and mA, but also including the
source information?

Shu-ping

[Joao Sollari Lopes]

Dear Shu-ping,

Very sorry for the late reply. Promise I'll try to be faster next
time!
You are correct, when the migration matrix is not set the migrants
entering a population are just taken randomly from the other existent
populations in the model.
This means that for the three-populations scenario half of the
migrations entering population A will come from population B and the
other half from population C.

As you mentioned, this can be changed via some kind of migration
weight matrix. In fact, this matrix will allow you to set the exact
proportions of migrants from a population X entering a population Y.

Unfortunately, the way to set this matrix is not very intuitive. I'll
try to explain it here a bit better using the following three-
population topology '(0, 1), 2)' or '1 0 2 0':

|| Neanc2 0
|| | |
t2|| ------------ |---------------|
|| | | | |
|| Neanc1 | | |
|| | | OR | |
|| | | | |
t1|| --------- | |-------| |
|| | | | | | |
|| | | | | | |
\/ Ne Ne Ne 0 1 2

Using the image above it might be easier to understand how to set the
migration weights matrix. In this case we have 3 populations to
consider with 2 periods of time:

pop0 pop1 pop2

pop0 t1 x t1 x t1 x
t2 x t2 x t2 x

pop1 t1 x t1 x t1 x
t2 x t2 x t2 x

pop2 t1 x t1 x t1 x
t2 x t2 x t2 x

First we can put 0 in the migrations between the same populations:

pop0 pop1 pop2

pop0 t1 0 t1 x t1 x
t2 0 t2 x t2 x

pop1 t1 x t1 0 t1 x
t2 x t2 0 t2 x

pop2 t1 x t1 x t1 0
t2 x t2 x t2 0

Then we can put 0 in the populations that disappear after a joining
event (from present to past):

pop0 pop1 pop2

pop0 t1 0 t1 x t1 x
t2 0 t2 0 t2 x

pop1 t1 x t1 0 t1 x
t2 0 t2 0 t2 0

pop2 t1 x t1 x t1 0
t2 x t2 0 t2 0

Now, if we want to set migration matrix as the default (i.e. randomly
migrants from the existent populations) use the following:

pop0 pop1 pop2

pop0 t1 0 t1 0.5 t1 0.5
t2 0 t2 0 t2 1.0

pop1 t1 0.5 t1 0 t1 0.5
t2 0 t2 0 t2 0

pop2 t1 0.5 t1 0.5 t1 0
t2 1.0 t2 0 t2 0

Notice that the sum of each line should be 1 (or 0 if there are no
migrants entering the population):

pop0 pop1 pop2

pop0 t1 0 t1 0.5 t1 0.5 = 1
t2 0 t2 0 t2 1 = 1

pop1 t1 0.5 t1 0 t1 0.5 = 1
t2 0 t2 0 t2 0 = 1

pop2 t1 0.5 t1 0.5 t1 0 = 1
t2 1 t2 0 t2 0 = 1

Ok, so this is how to set the migration weights matrix.

Now regarding your question, there is no way to get directly the
information regarding the source populations. However you can just
extrapolate from the proportions set in the migration weight matrix.
If these are not set it will always be half-half in a 3-pop scenario.

The reason I didn't allow more flexibility on the migration estimates
is because most of the cases there isn't enough information in the
data for more detailed estimates. Sorry about that.

Hope this long email helps.

Best,
Joao

[shu-ping]

Dear Joao,

Your suggestions were really help!
Now I understand what should I do. Thanks a lot!

Best regards,

Shu-ping