Detecting chaos in a citrus orchard: Reconstruction of nonlinear dynamics from very short ecological time series

Abstract

The reconstruction of nonlinear dynamics from short ecological time series has been an attractive subject in ecology for the last two decade since May’s classical work. Nonlinear time series analysis (NTSA) is used to investigate deterministic chaos. However, most ecological time series are too short to perform NTSA, which usually requires a time series whose size is in the thousands. Here we propose a way to reconstruct local dynamics from a very short ecological time series whose data point is smaller than ten. For most tree crops such as citrus, nuts and acorns, the yield alternates between high- and low-bearing years. Isagi et al. [Isagi Y, Sugimura K, Sumida A, Ito H. How does masting happen and synchronize? J Theor Biol 1997;187:231–9] proposed a mechanistic model that describes masting as chaos and can be applied to alternate bearing. Here we have used an ensemble data set consisting of the yields of 48 individual trees over seven years to test our proposed method and have successfully validated this method by a one-year forward prediction three times in 2002, 2003 and 2004. We also show the applicability of NTSA tools such as Lyapunov exponents, correlation dimension and deterministic nonlinear prediction on the reconstructed local dynamics.