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tskit-dev / msprime

Simulate genealogical trees and genomic sequence data using population genetic models
GNU General Public License v3.0
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Comments on page /demography.html #1567

Open gtsambos opened 3 years ago

gtsambos commented 3 years ago

Not an 'issue', just a log of some comments I'm making while reading this page.

In continuous-time models, when {math}M_{j,k} is close to zero, this rate is approximately equivalent to the fraction of population {math}j that is replaced each generation by migrants from population {math}k. In discrete-time models, the equivalence is exact and each row of {math}M has the constraint {math}\sum_{k \neq j} M_{j,k} \leq 1.

I'm a bit confused by this statement -- shouldn't it be approximately equivalent in both cases since the actual number is the outcome of a random process based on this parameter?

jeromekelleher commented 3 years ago

Ping @petrelharp, @nspope ?

petrelharp commented 3 years ago

Hm, well we could replace "fraction" by "expected fraction"? (Or take the point of view that these are infinite populations, in the coalescent scaling limit, and so the actual fraction is nonrandom?)

Or, maybe we should explain that the reason it's approximate for the standard coalescent is that the probability that a given genome (and, hence, lineage) is replaced over a time dt is 1 - exp(-M_{jk} dt) \approx M_{jk} dt? If we get the phrase "poisson process" in there somewhere that should help?

jeromekelleher commented 2 years ago

Is this still relevant @gtsambos?