Testing for rapid growth of a deme with larger ancestral population

[Mario Erandi Bonillas-Monge]

Hi Fsc2 team,

I managed to run several models to calculate the divergence times and migration between 3 distinct populations. However no I want to test some scenarios where one of the populations grow faster than the other two and had larger Ne given that one of such populations have a phenotype that facilitates colonization. So In theory one of the populations should take less time since divergence to grow larger. I have been trying to think how to test this into my current model with migration and without migration, but I do not know the correct way to do it. I was thinking on just making the ancestral Ne ($ANC_S1$ or $ANC_S1$) a bounded value of e.g around 2,000,000 or more in the .est file and the growth rate in the .tpl file. However I don't know if this is the way to do it or what a sensitive value (or range) would be, or if it needs to be formulated in the complex parameters somehow. I am sharing an example of a previous model with no migration and my files  to have an idea of what I mean:

//Parameters for the coalescence simulation program : simcoal.exe
3 samples to simulate :
//Population effective sizes (number of genes)
$Npop0$
$Npop1$
$Npop2$
//Samples sizes and samples age
78
36
32
//Growth rates: negative growth implies population expansion
0
0
0
//Number of migration matrices : 0 implies no migration between demes
1
//Migration matrix 0
0 0 0
0 0 0
0 0 0
//historical event: time, source, sink, migrants, new deme size, growth rate, migr mat index
2 historical event
$TSB$ 0 1 1 $RSSB$ 0 0
$TLB$ 1 2 1 $RSLB$ 0 0
//Number of independent loci [chromosome]
1 0
//Per chromosome: Number of contiguous linkage Block: a block is a set of contiguous loci
1
//per Block:data type, number of loci, per gen recomb and mut rates
FREQ 1 0 2.8e-9 OUTEXP

// Priors and rules file
// *********************

[PARAMETERS]
//#isInt? #name   #dist.#min  #max
//all N are in number of haploid individuals
1 $ANCSIZE$   unif    100000    2e6    output
1 $Npop0$     unif    100000    2e6    output
1 $Npop1$     unif    100000    2e6    output
1 $Npop2$     unif    100000    2e6    output
1 $ANC_S1$   unif    100000    2e6    output
1 $TSB$       unif    10    2e6     output
1 $TBB$       unif    10    2e6    hide

[RULES]

[COMPLEX PARAMETERS]

1 $TLB$ = $TBB$+$TSB$ output
0 $RSSB$ = $ANC_S1$/$Npop1$ output
0 $RSLB$  = $ANCSIZE$/$Npop2$ output

Also, the command that I am using to run fsc2 is:

fsc28 -t nmig1.tpl -n400000 -m -e nmig1.est -M -L40 -q --multiSFS -C1 -c16 -B16

And the results (bestlikelihoods)  that I am having for my model are:

$ANCSIZE$       $Npop0$ $Npop1$ $Npop2$ $ANC_S1$        $TSB$   $TLB$   $RSSB$  $RSLB$  MaxEstLhood     MaxObsLhood
664555  594675  2530577 1089414 684434  524352  1447245 0.2704657
       0.6100110       -7582.823       -7196.514

What kind of changes should I do to my model and how can I know if it is a sensitive value when testing for population expansion and ancient population sizes? In my system  $Npop2$   (Pacific) is the one we assume is going to a rapid population expansion.

I will be very grateful to have your input in this issue.

All the best,

Erandi