Ugh - Saturday morning and I'm feeling critically slowed down. Hopefully, its not an early warning of an approaching transcritical bifurcation! John Drake and Blaine Griffen have a really nice paper in the Sept 10 Issue of Nature on Early warning signals of extinction in deteriorating environments. This work follows up on the ideas of Stephen Carpenter, Will Brock and Martin Scheffer from the Resilience Alliance of trying to detect when a system is approaching a "critical threshold" before the threshold is reached. This would be useful, to say the least.
Drake and Griffen used an experimental system of Daphnia magna in microcosms to examine what would happen when populations experienced deteriorating environmental quality - in their case represented by a decrease in the amount of freeze dried algae supplied. In an environment with a constant food supply, this system behaves as a logistic population with dn/dt = rn(1-n/k), where both r and k change as the amount of food changes. The bifurcation happens as r -> 0 from either direction. The notion of "Critical Slowing Down" is a dynamical phenomenon that occurs in the vicinity of the threshold - increases in temporal autocorrelation, spatial correlation, and coefficient of variation. They found that a variety of single and composite indicators showed responses several generations before the "tipping point" was reached. Wow!
And I do mean, WOW, really. This is cool stuff. What I'm not sure is whether it will help in the real world. The difficulty arises because of the accuracy of the measurements in the experiment. They know exactly how many individuals in each population. In most cases, we will have only statistical estimates of that number, and usually, only an index to abundance. In addition, we will rarely have the luxury of data that precede the deterioration of the environment, and usually only one population instead of 30 replicates. Still, its worth thinking about more, for sure.