In olden times and in poor countries today, there exists "maternal mortality"-- mothers dying in childbirth.
This surely created a gender imbalance. The solution to this gender imbalance was simple. WAR. Send boys off to die and/or capture womens.
War, of course, has "evolved", but even today, you can see examples of humans making war with humans that are little different than animals fighting over mates on the discovery channel.
War is quite good at reducing the excess number of men to woman in a tribe. Of course, on the flip side, sometimes there is an excess number of women. The natural solution is "polygamy", with one alpha male mating with all the females he can keep. This is a common occurence amongst animals.
I'm not sure how an "evolved" society will address a gender imbalance. Rumor has it we are about to find out thanks to china.
China has 1.11 males per female at birth. Other countries like this are armenia(1.16) Bahrain(1.372 adults thanks to migrant workers) Oman(1.419 migrants again), India(1.12 at birth), and more.
Precious few nations have "excess" adult females, but there's two reasons: tourism, and war. Island nations untouched by war and frequented by tourists often have higher female populations, I'm sure this is influenced by the fact women do better in hospitality jobs.
In the end, I think our porous borders will allow us to see quality-based osmosis.
Women will migrate to countries with higher qualities of life and shortages of women. Men will migrate to countries short on men with higher qualities of life. Collapse shall be rare, slow, and self-correcting. Russia, is in such a slow collapse currently, with a negative population growth of 0.484. Eventually this can only reverse-- land is productive, and savvy businessmen will find a way to exploit the land under any legal arrangement eventually.
In particular, I think the US census population pyramid for Russia is wrong: it predicts 128 million for 2025 and 109 million for 2050. This assumes the current trends of population will continue. They probably won't. I imagine the Russians will target and hit 1.5 million births per year, and will up the incentives every time they miss.