Detecting chaos in a citrus orchard: ensemble reconstruction of non-linear dynamics from very short ecological time series.
Sakai, Kenshi*,1, Noguchi, Yuko1, Asada, Shin-Ichi2, 1 Tokyo University of Agriculture and Technology, Fuchu, Tokyo, Japan2 Kanagawa Agricultural Reaerach Center, Odawara, Kanagawa, Japan
ABSTRACT- The concept of deterministic chaos is attractive not only for scientists but also for farmers, because it implies an underlying order behind the complexity of ecological and agricultural . Nonlinear time series analysis(NTSA) is used to investigate deterministic chaos. However, most ecological time series are too short to perform NTSA, which requires a time series whose size is in the thousands . Here we propose "ensemble reconstruction" of the dynamics from a very short ecological time series whose size is smaller than ten. In most tree crops such as citrus, nuts and acorns, the yield alternates between high and low yielding years. Isagi, et al. proposed a theoretical model that describes masting as chaos that can be applied to alternate bearing. We used an ensemble dataset consisting of the yields of 48 individual trees over 7 years to test our proposed method and successfully validated this method by one-year forward prediction three times in 2002, 2003 and 2004. We also show that conventional tools such as Lyapunov spectrum and correlation dimension can be applied with the ensemble reconstruction method. This method offers an essential tool to realize an ecosystem approach towards and/or adaptive control of real world ecosystems and their biodiversity.
Key words: deterministic chaos, ensemble reconstruction, alternate bearing
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