Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example

Area of Science:

• Ecology
• Dynamical Systems Theory
• Control Theory

Background:

• Critical fluctuations are generally considered universal early warning signals for catastrophic state transitions in dynamical systems.
• A recent study questioned the universality of these signals using an ecological fisheries model, reporting silent early warning signals from predator (P) and adult prey (A) populations.

Purpose of the Study:

• To re-evaluate the universality of early warning signals in an ecological fisheries model.
• To investigate why some populations may not exhibit expected early warning signals prior to bifurcation.
• To apply observability measures from control theory to identify reliable early warning indicators.

Main Methods:

• Performed a full eigenvalue analysis of the three-population (juvenile prey J, adult prey A, predator P) fisheries model.
• Utilized observability analysis by computing the observability coefficient for each population variable.
• Quantified the ability of each population variable to describe changing internal dynamics.

Main Results:

• Eigenvalue analysis confirmed saddle-node (SN) bifurcation for juvenile prey (J) and predator (P) populations, but not for adult prey (A).
• Observability analysis demonstrated that precursor fluctuations are best observed using the juvenile prey (J) variable.
• The predator (P) variable showed increased fluctuations only near the bifurcation point, with observability analysis explaining its initially poor forecasting capability despite undergoing bifurcation.

Conclusions:

• Observability analysis provides complementary information to eigenvalue analysis for identifying variables that carry early warning signs.
• The study resolves the puzzle of decaying variance trends in poorly observable variables, clarifying their forecasting limitations.
• Early warning signals are best identified by considering the observability of system variables, not solely the presence of bifurcation.