Choose transition values

[rosemckeon]

I want to do this based on literature for a particular system, using demography life-cycle graphs and transition matrices.

[rosemckeon]

Looking at the Mimulus study system as I know there's a lot of work on those and that whole-genome duplication (WGD) occurs. I'm honing in on M. guttatus as WGD has been documented in that species complex (Vickery 1995).

Seed bank survival might need to be enabled. Peterson 2016 used 0.534 based on a seed viability study by Elderd & Doak 2006.

Transitions in other directions need to be enabled Life-cycle graph from Peterson 2006 shows that seedlings and rosettes can both produce seeds. Seedlings can become rosettes, and rosettes can go back to become seedlings.

Transition values in that paper don't appear to be stated explicitly and I can't see them in the appendices. Demography of all the populations used to pool into matrix values are given:

As is the way that the matrix was calculated:

Where: D = seed survival G = germination F = flower production S = winter survival R = rosette production O = ovule number per flower A = proportional recruitment success of ovules relative to rosettes

So, I think I'll need to figure this out for myself

[rosemckeon]

	Seed	Seedling	Rosette
Seed	0.2409103	0.41240496	0.41240496
Seedling	0.2930897	0.50172889	0.50172889
Rosette	0.0000000	0.04977276	0.04977276

So, seeds that become rosettes = trans[3,1] = 0

[rosemckeon]

Updated values after finding the mean of all transition matrices for each population instead of using mean column values to work out a single pooled transition matrix.

	Seed	Seedling	Rosette
Seed	0.2409103	0.28853157	0.28853157
Seedling	0.2930897	0.48573766	0.48573766
Rosette	0.0000000	0.07571571	0.07571571

[rosemckeon]

@bradduthie The eigenvalues for the pooled mean matrix are all < 1.

Looking at the data table above with all the population data in. Do you think it would make more sense to use low elevation perennials from 2013? That population has an eigenvalue closest to 1 and sensitivities all at 0. But in the year before that population had much more growth. It it remiss to just pick a stable year's data, if we know that population sometimes behaves differently?

[bradduthie]

Interesting @rosemckeon -- yeah, I just had a look myself too, and now just examining the matrix itself, it does kind of seem obvious that the population is at least not increasing quickly (or at all, as you've shown). I don't think it's at all remiss to just pick a stable year, as long as you are clear in the writing that this is what you're doing. Since the question that you are interested in investigating is not really related to total population stability, I think that it's fine to just state that your model assumes a stable population, and you parameterised the model from parameter values known to be stable (but maybe an interesting Discussion point -- could fluctuating demographic values and stability affect the evolution of polyploidy?).

[rosemckeon]

@bradduthie that would be an interesting question! It does. I kicked myself for not checking the eigenvalues from the beginning!

[bradduthie]

No worries @rosemckeon -- really easy thing to miss!