The statistical evidence does not support this view. With only one possible exception.
We have passed peak child. The number of (human) children being born (on Earth) in any year has remained the same for 5-8 years. The total (human) population of is starting to plateau. Estimates are that we could easily support everyone at a lifestyle similar to what we have but with a lot less waste. Th comment used was something like everyone on the planet could live on a quarter acre block per family with a three bedroom house, electricity, et al and inside the area of Texas (the second biggest state in the USA). I think Texas is a bit bigger than Tasmania the smallest state in Australia.
The population of Africa, and to a lesser extend the Middle East and Southern Asia (the poorest parts of the world, with the exception of some oil-rich countries) continue to boom hard while the population of the top developed countries (notably Europe and North East Asia) will decline. Every year the USA becomes less ethnically white and more black/hispanic. In 1950, 90.5% of the USA was white. Nowadays, in the group 1-4 year olds, white Americans are already less than half. And blacks and hispanics on average do worse at school than whites and North East Asians.
In a way that is a balance yes but not a balance that stays the same.
Look at the countries with the highest and lowest birth rate:
https://en.wikipedia.org/wiki/List_...Country_ranking_and_comparison:_1970_and_2013
Note that ALL european countries have a birth rate below the replacement rate of 2.1 in 2013. And many European countries are far below that. And don't get fooled by relatively high birth rates in some North Western European countries like France. The birth rate of native Europeans in North Western European countries is 1.5 - 1.6 . The difference is made up by much higher fertility rates of third world immigrants.
In 1900, 1/3rd of the world population was of European descent. In 1950 this has dropped to 25%. In 2000, this has dropped to 14%. Meanwhile European countries are the oldest countries in the world, with roughly half the population past reproductive age (40 years old). In many 3rd world countries, 90% of the population is still young enough for reproduction. So even with similar reproductive rates the relative share of ethnic Europeans in the world's population will decline considerably (half). But the reproductive rates of Europeans are well below the rest of the world and even below replacement levels. Soon the population of European countries will not only decline in relative numbers but also in absolute numbers.
lecture "dangerous demographics":
https://www.youtube.com/watch?v=-w3meSupCME
Why is this relevant? Almost all the technological and scientific progress since the Middle Ages has been done in Europe or its colony North America. North East Asia has caught up with the Europeans lately and may possibly take over its leadership eventually, but North East Asia has its own declining birthrates.
With current demographic trends, within a century, Europeans will be reduced to 1-2% of the world's population. That means that Europeans will be very weak militarily and if another world war breaks out, run a real risk of losing and going extinct. Or they may simple become numerically overwhelmed by mass migration from the third world.
The western Roman Empire collapsed due to a combination of low birth rates and mass migration from outside the Roman Empire. The same could happen to Western civilizations at the end of the 21st century.
Once the native population of Europe and North East Asia have effectively vanished, the world will have changed considerably, and that may possibly be the start of a new technological and scientific Dark Age.
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, maybe even replacing it with a -X% 
Feedback on the various modmod effects and balance would be particularly appreciated.
