Spati-Temporal Dynamics of Bio-Production Systems by Chaos Time Series Analysis

确定性混沌的概念对生态学家很有吸引力，因为它暗示了生态系统复杂性背后的潜在秩序。非线性时间序列分析（NTSA）被用来研究确定性混沌。然而，大多数生态时间序列太短，无法执行NTSA，这需要一个大小为数千的时间序列。NTSA在生态动力学中的应用我们需要在有限的数据和观测的情况下，发展适当的方法来重建生态动力学。在这里，我们提出了“合奏重建”的动态从一个非常短的生态时间序列的大小小于10。在大多数树木作物，如柑橘，坚果和橡子，产量在高产和低产年份之间交替。Isagi等人提出了一个理论模型，将桅杆描述为可应用于交替轴承的混沌。我们使用由48棵树7年来的产量组成的集合数据集来测试我们提出的方法，并在2002年、2003年和2004年三次通过一年向前预测成功验证了该方法。我们还表明，传统的工具，如李雅普诺夫谱和关联维数可以应用于集成重建方法。这种方法提供了一个基本的工具，实现生态系统的方法对和/或适应性控制的真实的世界生态系统及其生物多样性。我们还进行了遥感估计的时空动态。

The concept of deterministic chaos is attractive for ecologists, because it implies an underlying order behind the complexity of ecological systems. 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. On the application of NTSA on ecological dynamics., we need to develop appropriate way to reconstruct ecological dynamics with limited data, and observation. 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. We also conducted remote sensing to estimate the spatio-temporal dynamics.