spatial interactions separated along "z" axis

[Bradburd]

Hi Ben!

I'm trying to run a spatially explicit model with subsequent secondary contact and I'm running into an issue.  Below, I describe the scenario in more detail, but the tl;dr question is: in an "xyz" spatiality model, is it possible to have "xy" competition within each value of "z", but with no competition between individuals in different values of "z"?

The basic idea is that we start with a parental population (P) competing and mating in "xy" space.  At some point, a daughter population (D1) is founded by a few individuals grabbed from within a small area somewhere in the parental population. We want the daughter population to be reproductively isolated from the parent population for a while, so we put it in its own value of "z" and don't allow matings across values of "z".  That daughter population expands to fill its "xy" plane (experiencing "xy" competition/mate choice).  Then, at some point, we repeat this procedure, founding a new daughter population (D2) at a new value of "z" from individuals grabbed from a location within D1.  To emphasize, we want spatial competition/mate choice/dispersal to be happening within each population (i.e., within P, D1, D2, etc.), but not between each population.

I understand that this scenario could be more easily executed using multiple subpopulations.  But, our goal is to eventually induce secondary contact by allowing individuals to stochastically disperse across values of "z" in a way that maintains their "xy" spatiality. E.g., in the "secondary contact" phase of the scenario, an individual at a particular location in "xy" space in D2 is more likely to mate with an individual that is nearby in "xy" space in "D1".  And, I think that'll be easier to implement in this framework, where we utilize the "z"-axis to create separate "subpopulations".

Any pointers you can give would be super helpful!

best,

-Gideon

[Peter Ralph]

I think that one solution would be to have the different 'z' levels
further apart than the maximum interaction distance - then, they won't
affect each other?

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[Ben Haller]

Hi Gideon,

Sorry for the slow reply.  Peter is quite right; just define the z-coordinates of the individuals such that, with the interaction kernel you are using, they don't interact when you don't want them to.  When you want them to start interacting, move them closer to each other.  You can define an "xy" InteractionType, but that means the opposite of what you want: it means that the z coordinate is not used at all when computing interaction strengths, effectively squishing the z-coordinate down to nothing so that it has no effect on interaction strength at all.

You could perhaps achieve a similar effect by defining an interaction() callback that computes interaction strengths using the formula you want; but those can be slow, so unless your model is small, just defining z-coordinates that produce the effect you want is probably best.

Cheers,
-B.

Benjamin C. Haller
Messer Lab
Cornell University

[Gideon Bradburd]

Got it - thanks Ben & Peter!

Gideon Bradburd (he/him)

Dept. Integrative Biology

Michigan State University

genescape.org

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