A novel approach to detecting a regime shift in a lake ecosystem

Summary 1. Certain classes of change in the characteristics of an ecosystem, labelled regime shifts, have been observed in marine and freshwater ecosystems world-wide. Few tools, however, have been offered to detect and identify regime shifts in time-series data. 2. We use a novel approach based on tools taken from the world of statistics, and econometrics to examine the occurrence of a regime shift in the predatory zooplankton population of Lake Kinneret, Israel. The tools are a free-knot spline mean function estimation method and a Markov-switching vector autoregression model. 3. Our approach detected, with high probability, the occurrence of a regime shift in the zooplankton population in the early to mid-1990s. This was in-line with expectations based on similar events observed in the lake. 4. The suggested approach is a step forward from existing approaches in that it does not require any pre-determent of threshold values but rather relies on a hidden underlying stochastic process that yields probabilities of regime shifts. Thus, it can therefore be applied without introducing any prior biases into the analysis. The approach is, therefore, an objective method in detecting the likely occurrence of a regime shift.

[1]  Stephen R. Carpenter,et al.  Dystrophy and eutrophy in lake ecosystems : implications of fluctuating inputs , 1997 .

[2]  V. Smetácek,et al.  Organism life cycles, predation, and the structure of marine pelagic ecosystems , 1996 .

[3]  D. Haydon,et al.  Alternative stable states in ecology , 2003 .

[4]  L. Schumaker Spline Functions: Basic Theory , 1981 .

[5]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[6]  Brian R. Herwig,et al.  Thresholds and Stability of Alternative Regimes in Shallow Prairie–Parkland Lakes of Central North America , 2009, Ecosystems.

[7]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[8]  S. Carpenter,et al.  Catastrophic shifts in ecosystems , 2001, Nature.

[9]  M. Scheffer,et al.  Hydrology-Driven Regime Shifts in a Shallow Tropical Lake , 2009, Ecosystems.

[10]  Tamar Zohary,et al.  Changes to the phytoplankton assemblage of Lake Kinneret after decades of a predictable, repetitive pattern , 2004 .

[11]  S. Carpenter,et al.  ESTIMATING COMMUNITY STABILITY AND ECOLOGICAL INTERACTIONS FROM TIME‐SERIES DATA , 2003 .

[12]  Yosef Z. Yacobi,et al.  Primary production and phytoplankton in Lake Kinneret: A long‐term record (1972‐1993) , 1995 .

[13]  L. McCook Macroalgae, nutrients and phase shifts on coral reefs: scientific issues and management consequences for the Great Barrier Reef , 1999, Coral Reefs.

[14]  G. Daskalov,et al.  Trophic cascades triggered by overfishing reveal possible mechanisms of ecosystem regime shifts , 2007, Proceedings of the National Academy of Sciences.

[15]  Growth and production of the dominant pelagic fish, Acanthobrama terraesanctae, in subtropical Lake Kinneret, Israel , 1999 .

[16]  H. Krolzig Markov-Switching Vector Autoregressions , 1997 .

[17]  P. C. Reid,et al.  Phytoplankton change in the North Atlantic , 1998, Nature.

[18]  Moshe Gophen,et al.  Nitrogen deficiency, phosphorus sufficiency, and the invasion of Lake Kinneret, Israel, by the N2-fixing cyanobacterium Aphanizomenon ovalisporum , 1999, Aquatic Sciences.

[19]  Stephen R. Carpenter,et al.  Regime shifts in lake ecosystems : pattern and variation , 2003 .

[20]  Stephen R. Carpenter,et al.  Management of eutrophication for lakes subject to potentially irreversible change , 1999 .

[21]  Steven R. Hare,et al.  Empirical evidence for North Pacific regime shifts in 1977 and 1989 , 2000 .

[22]  Philip Hans Franses,et al.  Nonlinear Time Series Models in Empirical Finance: Frontmatter , 2000 .

[23]  Tamar Zohary,et al.  Alternative states in the phytoplankton of Lake Kinneret, Israel (Sea of Galilee) , 2007 .

[24]  H. Krolzig Markov-Switching Vector Autoregressions: Modelling, Statistical Inference, and Application to Business Cycle Analysis , 1997 .

[25]  M. Genkai-Kato Regime shifts: catastrophic responses of ecosystems to human impacts , 2007, Ecological Research.

[26]  Daniel Gervini,et al.  Free‐knot spline smoothing for functional data , 2006 .

[27]  Stephen R. Carpenter,et al.  Probabilistic Estimate of a Threshold for Eutrophication , 2008, Ecosystems.

[28]  C. S. Holling,et al.  Regime Shifts, Resilience, and Biodiversity in Ecosystem Management , 2004 .

[29]  S. Carpenter,et al.  Catastrophic regime shifts in ecosystems: linking theory to observation , 2003 .

[30]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .