What was done
The authors employed "fine-grained temperature reconstructions and historical population data sets" to "statistically test a hypothesized relationship between temperature change and population growth (i.e., cooling associated with below average population growth) in China over the past millennium."

What was learned
As revealed by historical statistics, Lee et al. report that "war peaks, population collapses, and dynastic changes matched closely with cooling (Zhang et al., 2005, 2006)." Noting that their work "further verified the synchronistic relationship between population and climate cycles," they state that this relationship appears to have been "fundamental, not incidental, in causing human misery and the resultant historical downturns in Chinese history," citing two additional corroborative studies of the subject (Hinsch, 1988; Li 1999), although they add that the "temperature-population relationship was mediated by geographic factors, the aridity threshold, and social factors."

What it means
Putting it rather bluntly, the three Hong Kong researchers state that "given that human populations are food limited, and the fact that in many places populations have reached dangerously high levels and which also lack a safety margin, the onset of bad times associated with cooling would bring a fast response expressed as population shrinkage."

References
Hinsch, B. 1988. Climatic change and history in China. Journal of Asian History 22: 131-159.

Li, B. 1999. Qihou bianhua yu zhongguo lishishang renkou de jici daqi daluo. Population Research 23: 15-19.

Zhang, D., Jim, C.Y., Lin, C.S., He, Y.Q. and Lee, H.F. 2005. Climate change, social unrest and dynastic transition in ancient China. Chinese Science Bulletin 50: 137-144.

Zhang, D.D., Jim, C.Y., Lin, G.C.S., He, Y.Q., Wang, J.J. and Lee, H.F. 2006. Climatic change, wars and dynastic cycles in China over the last millennium. Climatic Change 76: 459-477.