Comments on page /demography.html

[gtsambos]

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]

Ping @petrelharp, @nspope ?

[petrelharp]

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]

Is this still relevant @gtsambos?