From the time of the introduction of smokeless powder in Nitro Express double rifles through World War II, what was the ratio of dangerous game double rifles to bolt actions used in Africa ?

To what extent was the selection determined less on functionality and optimization for use on dangerous game and more on ease of availablity of rifle and ammo and their costs ?

Just a SWAG, I would guess 1-1000. Doubles then, like now, were too expensive for the average hunter, rancher, settler et al. I would guess that one way to get a good representative number would be if you could get the records from one of the bigger English makers and compare the ratio, although not all doubles or bolts were DGR's. Compound the problem with the fact that lots of settlers were using bolt calibers that we normally don't consider as DGR class, like 8x57, .318 W.R. 9.3x62 etc. Hell, My guess is probably conservative!

Hammer
For some answers to your question read
"The RIFLE Its Development For Big-Game Hunting"
by S.R. Truesdale.

Published by Safari Press.

I believe the ratio of double use was significantly higher in India than in Africa after introduction of the Mauser.