It seems pretty intuitively true that they would do so, but in various theories of revolution and rebellion there are a variety of theories.
Ciccone took a look at sub-Saharan Africa and correlated the level of rainfall to civil conflicts over the last 10 years. He found that civil conflicts were very likely to correspond to years where there was a drought, and incomes in Africa's heavily agriculture-based societies, fell. He writes:
"the data show almost twice as many conflict onsets during low-rainfall-years – 23 conflicts started following low-rainfall years and 12 following high-rainfall years. Put differently, 2/3 of civil conflicts started in the 10 years with lowest rainfall and 1/3 in the 10 years with highest rainfall."And he concludes:
"My estimates indicate that a negative 5% income shock raises the likelihood of civil conflict by 15 percentage points."However,
"When I consider only civil wars – defined as civil conflicts with more than 1000 annual battle deaths – I do not find a link with droughts ...."Very interesting work well worth having a look at if you have the time.
The question of what starts revolutions has in the past described in terms of a J-Curve. James C. Davies posited that social revolutions happened after there was a large increase in expectations followed by a sharp reversal. You can think of it as an upside-down J, where you have rising prosperity and expectations of those times to continue--similar, to say, the US housing market--followed by a sharp reversal in fortune, corresponding to the inverted lip of the J.
The counter-theory, which I think was posited by Theda Skocpol in her States and Social Revolutions--but I am not sure--is that you have a J-curve, where the J is turned backwards. That is, after a steep fall in prosperity you begin to have a recovery, it is after society has begun to recover that revolutions take place.
We may see some new data in many places around the world quite soon.