title: Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.
abstract: Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems. Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal. By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs. In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the P variance initially shows a decaying trend. Here we resolve this puzzle using observability measures from control theory. By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics. We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition. Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation. We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition.
authors.affiliation: School of Engineering, The University of Waikato, Hamilton, Waikato, New Zealand.
authors.forename: Ehsan
authors.initials: E
authors.lastname: Negahbani
authors.affiliation: School of Engineering, The University of Waikato, Hamilton, Waikato, New Zealand.
authors.forename: D Alistair
authors.initials: DA
authors.lastname: Steyn-Ross
authors.affiliation: School of Engineering, The University of Waikato, Hamilton, Waikato, New Zealand.
authors.forename: Moira L
authors.initials: ML
authors.lastname: Steyn-Ross
authors.affiliation: Departamento de Engenharia Eletrônica, Universidade Federeal de Minas Gerais, Belo Horizonte, MG, Brazil.
authors.forename: Luis A
authors.initials: LA
authors.lastname: Aguirre
mesh_terms: D000818:Animals; D004463:Ecology; D005399:Fishes; D008962:Models, Theoretical