A good summary can be found here http://www.yale.edu/ynhti/curriculum/units/1998/7/98.07.02.x.html

I would assume that hygiene/medicine played a greater role than food production, since actual starvation was rarely a major cause of death (compared to epidemics), and population increase is the difference between birth rate and death rate.

Thanks for the summary. I' am still looking for a more recent research report that tells about the timing and proportional influence of changes in fertility, child mortality, adult life expectancy, and their underlying factors.

There are too many data. I think one can find many data with a lot of work at http://unstats.un.org/unsd/demographic/

By the way, I agree with Felix.

There is also US Census homepage on world population which provides some historical estimates: http://www.census.gov/population/international/data/worldpop/table_population.php

But I was rather looking for a (recent) study that discusses the timing of certain factors. An example: Due to rising food supply the fertility increased significantly in the 19th century and only afterwards the effects of lower child mortality due to hygienic measures became visible (in the population figures). Growing adult life expectancy due to the successes of medicine played only a role (for global population growth) during the second half of the 20th century. Or is there a better model?

The world bank has a great database since 1960. Earlier is more sketchy.