It is often said and repeated by many that the world has an overpopulation problem.
Let us examine the origins of this popular belief and determine if it is true or not.
This belief appears to have originated in the UK when that island appeared to be inadequate for all the new born of that era, when agriculture for was the only occupation. It appeared to the inhabitants of that limited space that it will not be able to feed everyone that inhabited that tiny island. This seems to have started a move to explore for new land and the solution of colonization of the rest of the world in the name of the king or the queen of England.
This view of the constrained has persisted over the ages and has remained with us even to this day when we know of the existence of large masses of uninhabited lands in all of the continents of our planet.
In addition to these discoveries of large tracts of land, humanity has discovered many other vocations beyond agriculture that has enabled it to remain productive and to increase the standards of living of all.
These new vistas of work and methods of enhancements to the quality of life should long ago disproved the myth of overpopulation as a societal problem, but it has not.
The rate of the population growth might be a matter of concern only when the ability to transform that growth into productive results that benefits everyone is not able to take place. If that failure happens, the solutions to address that transformation rate necessary to achieve sustainability might be addressed without the need to fret over the population growth or the rate of that growth. These two separate issues need not be linked at all.
If the transformation (of the new born into effective, productive societal member) rates were too small at any given time or in any given country or in a given society that issue of training, education, and employment needs might better be addressed as a local issue unique to that way of life perhaps, and need not be universalized as a truth for the entire humanity.
Twenty first century population transformation rates are a function of the variables that are easily measured and kept up with the changes occurring from the dynamics of the societal interactions and the capabilities, to innovate and meet the needs to find happiness and satisfaction, more so, than ever before, when the societal needs and expectations were limited to the surviveval and the obtaining of just food and the shelter.
Many of the popular beliefs, just as this myth of population growth rate to be a big hindrance to human well being were based on logic offered by groups that subscribed to the notion that there are limits to growth 
In this modern age when productivity and money are not the same as what was conceived and understood by those early economists, we find that humans have evolved into societal beings that think, produce and contribute in manners hitherto in history unparalleled while consuming very little to achieve those ends; limits to growth is as senseless as believing that, “there is growth” even when knowing there is only “transformation” from one kind of energy to another in this universe.
The best way, going forward, in my opinion, is to avoid these types of arguments by building ” a model of humanity” to simulate and use, perhaps by anyone and everyone, on the world wide web (WWW) powered by an engine that uses all the data stored in the data warehouses that have been created in the recent past.
Any-one that needs to resolve these questions of probabilities will have a realistic and accurate data to see the trends and what corrective actions if any would be feasible and do such work without any unnecessary controversy. The model could be in the lines of the human genome project that so successfully got the results that only seemed impossible before that idea was carried out.
I like building models and solving puzzles and anyone that might even remotely be interested can feel free to join-in.
 “Limits to growth” – A 1972 book published by the club of Rome : http://limitstogrowth.net/