Open AccessExpanded view of ecosystem stability: A grazed grassland case study
Author(s) -
Gidon Eshel,
Yohay Carmel
Publication year - 2017
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0178235
Subject(s) - eigenvalues and eigenvectors , stability (learning theory) , forcing (mathematics) , fixed point , nonlinear system , ecology , ecological stability , steady state (chemistry) , ecosystem , mathematics , theoretical ecology , computer science , physics , mathematical analysis , biology , population , chemistry , demography , quantum mechanics , machine learning , sociology
Analysis of stability under linearized dynamics is central to ecology. We highlight two key limitations of the widely used traditional analysis. First, we note that while stability at fixed points is often the focus, ecological systems may spend less time near fixed points, and more time responding to stochastic environmental forcing by exhibiting wide zero-mean fluctuations about those states. If non-steady, uniquely precarious states along the nonlinear flow are analyzed instead of fixed points, transient growth is possible and indeed common for ecosystems with stable attractive fixed points. Second, we show that in either steady or non-steady states, eigenvalue based analysis can misleadingly suggest stability while eigenvector geometry arising from the non-self-adjointness of the linearized operator can yield large finite-time instabilities. We offer a simple alternative to eigenvalue based stability analysis that naturally and straightforwardly overcome these limitations.