Let's assume the ancestral species lived in lush, wet environments but that the habitat of one of its subpopulations is living in an region where the climate becomes very dry and arid. Basically these animals have 3 "options": 1. adaptation to the new conditions, or: 2. migrate to lush regions so they can resume their old lifestyle, or: 3. get extinct. Actually, all happen and are observed in an abundance on field observations and even experiments.
Now let's assume that migration is not possible (predators there, overcrowding, some geographic barrier etc.) and the species manages to adapt.
So, first the genetic variance in the species' TOTAL genome (including the ones still living in the original lush habitat AND the ones living in the area that is getting more arid) INCREASES,
WHAT? Both populations have an increase in genetic variance /diversity? And what brings this about? It would be amazing enough of one did but you are blandly saying bothdo? At the same time?
mostly by genetic innovation in the "arid" subpopulation
What is genetic innovation and why would this occur at this point?
- the ones living in the original, lush area don't need to change (other than through genetic drift) because they don't experience new environmental change.
Genetic drift does not increase genetic diversity. It’s like any subpopulation with random new gene frequencies even though this occurs within the larger population: If it acquires new traits it loses genetic diversity, which is the ONLY way new traits can be acquired.
And you haven’t said one thing to this point about how such a genetic increase is possible, what could possibly bring it about, and it looks like you have no intention of explaining that:
AFTER this increase, the genomes may split up.
But each subpopulation picks up only a part of this INCREASED genetic variance.
I HARDLY doubt ANY of the two subpopulations having a genome with less genetic variance than the original ancestral genome though. Not in the subpopulation living in the original, lush environment because there was no much need to change. But NEITHER in the "arid" subpopulation because in those animals the traits that relate to living in lush environment will be discarded (genes disabled by mutations or just by plain gene deletions) and new genes will be formed (by gene duplications or altering old ones).
A little calculation already proves this. Let's depict the original. ancestral genome in this, simplified way, where each Xi represents a single, distinct gene:
Ga = X1-X2-X3-X4-X5-X6-X7-X8-X9-X10-X11-X12-X13-X14-X15-X16
After one subpopulation experiencing arid conditions:
G1 = X1-X2-X3-X4-X5-X6-X7-X8-X9-X10-X11-X17-X13-X14-X15-X16
(the subpopulation still living in unchanged, lush conditions, hence, genome only changed a little bit due to genetic drift, represented by the gene X17, retrieved from the original gene X12)
PLUS:
G2 = X1-X2-X3-X4-X5-X17-X7-Z1-X9-Z2-X11-X12-Z3-X14-X15-X16-Z4 (the subpopulation experiencing an more arid environment, adaptation through the new genes Z1, Z2 en Z3, replacing old genes X8, X10 and X13, which are disabled, mutation of old gene X6 into X17 and the new gene Z4 - added without replacement of former genes).
So, as a matter of fact, I should redrawn the picture for G2 as follows:
G2 = X1-X2-X3-X4-X5-X17-X7-(X8)-Z1-X9-Z2-(X10)-X11-X12-Z3-(X13)-X14-X15-X16-Z4
where (X8), (X10) and (X13) represent the disables genes whose sequences still are there but "degraded" to junk DNA (to pseudogenes).
IN OTHER WORDS, in the sub-genomes there is ANY reduction in genetic variance.
I assume you meant to say there ISN’T any.
Well, I went through all of this and have no idea what you’re talking about. I expected some serious explanations at least, but all you did was say oh there was an increase in genetic diversity and both subpopulations had this increase.
You seem to be implying that the environment brought it about but offer no explanation how that could be.
As for the math, it's meaningless to me. You have to use English.
This example of a supposed increase in genetic diversity is so devoid of reason or meaning I have to ask, are you joking?